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Physics 101 Mechanics
October 2021
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Physics 101 Mechanics
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October 12, 2021
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October 12 of 2021
A flask contains a mixture of neon (Ne), krypton (Kr), and radon (Rn) gases. Compare (a) the average kinetic energies of the three types of atoms and (b) the root-mean-square speeds. (Hint: Appendix D shows the molar mass (in g/mol) of each element under the chemical symbol for that element.)
(a) What is the total translational kinetic energy of the air in an empty room that has dimensions 8.00 m $\times$ 12.00 m $\times$ 4.00 m if the air is treated as an ideal gas at 1.00 atm? (b) What is the speed of a 2000-kg automobile if its kinetic energy equals the translational kinetic…
Consider an ideal gas at 27$^\circ$C and 1.00 atm. To get some idea how close these molecules are to each other, on the average, imagine them to be uniformly spaced, with each molecule at the center of a small cube. (a) What is the length of an edge of each cube if adjacent cubes touch but do…
If the energy of the $H_{2}$ covalent bond is -4.48 eV, what wavelength of light is needed to break that molecule apart? In what part of the electromagnetic spectrum does this light lie?
In a gas at standard conditions, what is the length of the side of a cube that contains a number of molecules equal to the population of the earth (about 7 $\times$ 10$^9$ people)?
Modern vacuum pumps make it easy to attain pressures of the order of 10${^-}{^1}{^3}$ atm in the laboratory. Consider a volume of air and treat the air as an ideal gas. (a) At a pressure of 9.00$\times$ 10${^-}{^1}{^4}$ atm and an ordinary temperature of 300.0 K, how many molecules are present…
A large organic molecule has a mass of 1.41$\times$ 10${^-}{^2}{^1}$ kg. What is the molar mass of this compound?
At an altitude of 11,000 m (a typical cruising altitude for a jet airliner), the air temperature is -56.5$^\circ$C and the air density is 0.364 kg/m$^3$. What is the pressure of the atmosphere at that altitude? (Note: The temperature at this altitude is not the same as at the surface of the…
(a) Calculate the mass of nitrogen present in a volume of 3000 cm$^3$ if the gas is at 22.0$^\circ$C and the absolute pressure of 2.00$\times$ 10${^-}{^1}{^3}$ atm is a partial vacuum easily obtained in laboratories. (b) What is the density (in kg/m$^3$) of the N$_2$ ?
Calculate the net torque about point O for the two forces applied as in $\textbf{Fig. E10.2.}$ The rod and both forces are in the plane of the page.
Calculate the torque (magnitude and direction) about point $O$ due to the force $F$ in each of the cases sketched in $\textbf{Fig. E10.1.}$ In each case, both the force $F$ and the rod lie in the plane of the page, the rod has length 4.00 m, and the force has magnitude $F =$ 10.0 N.
With the assumption that the air temperature is a uniform 0.0$^\circ$C, what is the density of the air at an altitude of 1.00 km as a percentage of the density at the surface?
With the assumptions of Example 18.4 (Section 18.1), at what elevation above sea level is air pressure 90% of the pressure at sea level?
A metal tank with volume 3.10 L will burst if the absolute pressure of the gas it contains exceeds 100 atm. (a) If 11.0 mol of an ideal gas is put into the tank at 23.0$^\circ$C, to what temperature can the gas be warmed before the tank ruptures? Ignore the thermal expansion of the tank. (b)…
A small block has constant acceleration as it slides down a frictionless incline. The block is released from rest at the top of the incline, and its speed after it has traveled 6.80 m to the bottom of the incline is 3.80 m/s. What is the speed of the block when it is 3.40 m from the top of the…
The graph in $\textbf{Fig. E2.31}$ shows the velocity of a motorcycle police officer plotted as a function of time. (a) Find the instantaneous acceleration at $t =$ 3 s, $t =$ 7 s, and $t =$ 11 s. (b) How far does the officer go in the first 5 s? The first 9 s? The first 13 s?
During an auto accident, the vehicle's air bags deploy and slow down the passengers more gently than if they had hit the windshield or steering wheel. According to safety standards, air bags produce a maximum acceleration of $60 g$ that lasts for only $36 \mathrm{~ms}$ (or less). How far (in…
A car's velocity as a function of time is given by $v_x(t) = \alpha + \beta t^2$, where $\alpha =$ 3.00 m/s and $\beta =$ 0.100 m/s$^3$. (a) Calculate the average acceleration for the time interval $t =$ 0 to $t =$ 5.00 s. (b) Calculate the instantaneous acceleration for $t =$ 0 and $t =$ 5.00…
On a compact disc (CD), music is coded in a pattern of tiny pits arranged in a track that spirals outward toward the rim of the disc. As the disc spins inside a CD player, the track is scanned at a constant $linear$ speed of $v =$ 1.25m/s. Because the radius of the track varies as it spirals…
If a certain amount of ideal gas occupies a volume $V$ at STP on earth, what would be its volume (in terms of $V$) on Venus, where the temperature is 1003$^\circ$C and the pressure is 92 atm?
A dog in an open field runs 12.0 m east and then 28.0 m in a direction 50.0$^{\circ}$ west of north. In what direction and how far must the dog then run to end up 10.0 m south of her original starting point?
A fence post is 52.0 m from where you are standing, in a direction 37.0$^{\circ}$ north of east. A second fence post is due south from you. How far are you from the second post if the distance between the two posts is 68.0 m?
An ideal gas has a density of 1.33 $\times$ 10${^-}{^6}$ g/cm$^3$ at 1.00 $\times$ 10${^-}{^3}$ atm and 20.0$^\circ$C. Identify the gas.
You decide to go to your favorite neighborhood restaurant. You leave your apartment, take the elevator 10 flights down (each flight is 3.0 m), and then walk 15 m south to the apartment exit. You then proceed 0.200 km east, turn north, and walk 0.100 km to the entrance of the restaurant. (a)…
An empty cylindrical canister 1.50 m long and 90.0 cm in diameter is to be filled with pure oxygen at 22.0$^\circ$C to store in a space station. To hold as much gas as possible, the absolute pressure of the oxygen will be 21.0 atm. The molar mass of oxygen is 32.0 g/mol. (a) How many moles of…
An explorer in Antarctica leaves his shelter during a whiteout. He takes 40 steps northeast, next 80 steps at 60$^{\circ}$ north of west, and then 50 steps due south. Assume all of his steps are equal in length. (a) Sketch, roughly to scale, the three vectors and their resultant. (b) Save the…
A large cylindrical tank contains 0.750 m$^3$ of nitrogen gas at 27$^\circ$C and 7.50 $\times$ 10${^3}$Pa (absolute pressure). The tank has a tight-fitting piston that allows the volume to be changed. What will be the pressure if the volume is decreased to 0.410 m$^3$ and the temperature is…
As a test of orienteering skills, your physics class holds a contest in a large, open field. Each contestant is told to travel 20.8 m due north from the starting point, then 38.0 m due east, and finally 18.0 m in the direction 33.0$^{\circ}$ west of south. After the specified displacements, a…
On a training flight, a student pilot flies from Lincoln, Nebraska, to Clarinda, Iowa, next to St. Joseph, Missouri, and then to Manhattan, Kansas (Fig. P1.66). The directions are shown relative to north: 0$^{\circ}$ is north, 90$^{\circ}$ is east, 180$^{\circ}$ is south, and 270$^{\circ}$ is…
A Jaguar XK8 convertible has an eight-cylinder engine. At the beginning of its compression stroke, one of the cylinders contains 499 cm$^3$ of air at atmospheric pressure (1.01 $\times$ 10${^5}$ Pa) and a temperature of 27.0$^\circ$C. At the end of the stroke, the air has been compressed to a…
You have several identical balloons. You experimentally determine that a balloon will break if its volume exceeds 0.900 L. The pressure of the gas inside the balloon equals air pressure (1.00 atm). (a) If the air inside the balloon is at a constant 22.0$^\circ$C and behaves as an ideal gas,…
(a) Calculate the density of the atmosphere at the surface of Mars (where the pressure is 650 Pa and the temperature is typically 253 $K$, with a $CO_2$ atmosphere), Venus (with an average temperature of 730 $K$ and pressure of 92 atm, with a $CO_2$ atmosphere), and Saturn's moon Titan (where…
Calculate the moment of inertia of a uniform solid cone about an axis through its center ($\textbf{Fig. P9.90}$). The cone has mass $M$ and altitude $h$. The radius of its circular base is $R$.
As noted in Exercise 1.26, a spelunker is surveying a cave. She follows a passage 180 m straight west, then 210 m in a direction 45$^{\circ}$ east of south, and then 280 m at 30$^{\circ}$ east of north. After a fourth displacement, she finds herself back where she started. Use the method of…
You are rebuilding a 1965 Chevrolet. To decide whether to replace the flywheel with a newer, lighter-weight one, you want to determine the moment of inertia of the original, 35.6-cm-diameter flywheel. It is not a uniform disk, so you can't use $I =$ \( \frac{1}{2} \) $MR^2$ to calculate the…
Two workers pull horizontally on a heavy box, but one pulls twice as hard as the other. The larger pull is directed at 21.0$^{\circ}$ west of north, and the resultant of these two pulls is 460.0 N directly northward. Use vector components to find the magnitude of each of these pulls and the…
A cylindrical tank has a tight-fitting piston that allows the volume of the tank to be changed. The tank originally contains 0.110 m$^3$ of air at a pressure of 0.355 atm. The piston is slowly pulled out until the volume of the gas is increased to 0.390 m$^3$. If the temperature remains…
BIO Biological tissues are typically made up of 98% water. Given that the density of water is 1.0 \(\times\) 10$^3$ kg/m$^3$, estimate the mass of (a) the heart of an adult human; (b) a cell with a diameter of 0.5 $\mu$m; (c) a honeybee.
To measure the specific heat in the liquid phase of a newly developed cryoprotectant, you place a sample of the new cryoprotectant in contact with a cold plate until the solution's temperature drops from room temperature to its freezing point. Then you measure the heat transferred to the cold…
As you eat your way through a bag of chocolate chip cookies, you observe that each cookie is a circular disk with a diameter of 8.50 $\pm$ 0.02 cm and a thickness of 0.050 $\pm$ 0.005 cm. (a) Find the average volume of a cookie and the uncertainty in the volume. (b) Find the ratio of the…
In another experiment, you place a layer of this cryoprotectant between one 10 cm $\times$ 10 cm cold plate maintained at -40$^\circ$C and a second cold plate of the same size maintained at liquid nitrogen's boiling temperature (77 K). Then you measure the rate of heat transfer. Another lab…
The density of air under standard laboratory conditions is 1.29 kg/m$^3$, and about 20% of that air consists of oxygen. Typically, people breathe about \(\frac{1}{2}\) L of air per breath. (a) How many grams of oxygen does a person breathe in a day? (b) If this air is stored uncompressed in a…
Careful measurements show that the specific heat of the solid phase depends on temperature (Fig. P17.117). How will the actual time needed for this cryoprotectant to come to equilibrium with the cold plate compare with the time predicted by using the values in the table? Assume that all values…
You are analyzing the motion of a large flywheel that has radius 0.800 m. In one test run, the wheel starts from rest and turns with constant angular acceleration. An accelerometer on the rim of the flywheel measures the magnitude of the resultant acceleration $a$ of a point on the rim of the…
You place 35 g of this cryoprotectant at 22$^\circ$C in contact with a cold plate that is maintained at the boiling temperature of liquid nitrogen (77 K). The cryoprotectant is thermally insulated from everything but the cold plate. Use the values in the table to determine how much heat will be…
In January 2006 astronomers reported the discovery of a planet, comparable in size to the earth, orbiting another star and having a mass about 5.5 times the earth's mass. It is believed to consist of a mixture of rock and ice, similar to Neptune. If this planet has the same density as Neptune…
An acre has a length of one furlong (\(\frac{1}{8}\) mi) and a width one-tenth of its length. (a) How many acres are in a square mile? (b) How many square feet are in an acre? See Appendix E. (c) An acre-foot is the volume of water that would cover 1 acre of flat land to a depth of 1 foot. How…
For the two vectors $\overrightarrow{A}$ and $\overrightarrow{B}$ in Fig. E1.39, find (a) the scalar product $\overrightarrow{A}$ $\cdot$ $\overrightarrow{B}$; (b) the magnitude and direction of the vector product $\overrightarrow{A}$ \(\times\) $\overrightarrow{B}$.
A technician is testing a computer-controlled, variable-speed motor. She attaches a thin disk to the motor shaft, with the shaft at the center of the disk. The disk starts from rest, and sensors attached to the motor shaft measure the angular acceleration $\alpha_z$ of the shaft as a function…
For the two vectors $\overrightarrow{A}$ and $\overrightarrow{D}$ in Fig. E1.24, find the magnitude and direction of (a) the vector product $\overrightarrow{A}$ \(\times\) $\overrightarrow{D}$; (b) the vector product $\overrightarrow{D}$ \(\times\) $\overrightarrow{A}$.
For the two vectors in Fig. E1.35, find the magnitude and direction of (a) the vector product $\overrightarrow{A}$ \(\times\) $\overrightarrow{B}$; (b) the vector product $\overrightarrow{B}$ \(\times\) $\overrightarrow{A}$.
The Crab Nebula is a cloud of glowing gas about 10 lightyears across, located about 6500 light-years from the earth ($\textbf{Fig. P9.86}$). It is the remnant of a star that underwent a $supernova$ $explosion$, seen on earth in 1054 A.D. Energy is released by the Crab Nebula at a rate of about…
During your mechanical engineering internship, you are given two uniform metal bars $A$ and $B$, which are made from different metals, to determine their thermal conductivities. Measuring the bars, you determine that both have length 40.0 cm and uniform cross-sectional area 2.50 cm$^2$. You…
For the vectors $\overrightarrow{A}$, $\overrightarrow{B}$, and $\overrightarrow{C}$ in Fig. E1.24, find the scalar products (a) $\overrightarrow{A}$ $\cdot$ $\overrightarrow{B}$; (b) $\overrightarrow{B}$ $\cdot$ $\overrightarrow{C}$; (c) $\overrightarrow{A}$ $\cdot$ $\overrightarrow{C}$.
(a) Find the scalar product of the vectors $\overrightarrow{A}$ and $\overrightarrow{B}$ given in Exercise 1.38. (b) Find the angle between these two vectors.
At a chemical plant where you are an engineer, a tank contains an unknown liquid. You must determine the liquid's specific heat capacity. You put 0.500 kg of the liquid into an insulated metal cup of mass 0.200 kg. Initially the liquid and cup are at 20.0$^\circ$C. You add 0.500 kg of water…
Given two vectors $\overrightarrow{A}$ = $-$2.00$\hat{\imath}$ $+$ 3.00$\hat{\jmath}$ $+$ 4.00$\hat{k}$ and $\overrightarrow{B}$ = 3.00$\hat{\imath}$ $+$ 1.00$\hat{\jmath}$ $-$ 3.00$\hat{k}$, (a) find the magnitude of each vector; (b) use unit vectors to write an expression for the vector…
As a physicist, you put heat into a 500.0-g solid sample at the rate of 10.0 kJ/min while recording its temperature as a function of time. You plot your data as shown in Fig. P17.111. (a) What is the latent heat of fusion for this solid? (b) What are the specific heats of the liquid and solid…
The icecaps of Greenland and Antarctica contain about 1.75% of the total water (by mass) on the earth's surface; the oceans contain about 97.5%, and the other 0.75% is mainly groundwater. Suppose the icecaps, currently at an average temperature of about -30$^\circ$C, somehow slid into the ocean…
You have probably seen people jogging in extremely hot weather. There are good reasons not to do this! When jogging strenuously, an average runner of mass 68 kg and surface area 1.85 m$^2$ produces energy at a rate of up to 1300 W, 80% of which is converted to heat. The jogger radiates heat but…
A metal sphere with radius 3.20 cm is suspended in a large metal box with interior walls that are maintained at 30.0$^\circ$C. A small electric heater is embedded in the sphere. Heat energy must be supplied to the sphere at the rate of 0.660 J/s to maintain the sphere at a constant temperature…
A physicist uses a cylindrical metal can 0.250 m high and 0.090 m in diameter to store liquid helium at 4.22 K; at that temperature the heat of vaporization of helium is $2.09 \times 10{^4} J/kg$. Completely surrounding the metal can are walls maintained at the temperature of liquid nitrogen,…
The Kinetic Energy of Running. Using Problem 9.81 as a guide, apply it to a person running at 12 km/h, with his arms and legs each swinging through $\pm$30$^\circ$ in \( \frac{1}{2} \) s. As before, assume that the arms and legs are kept straight.
(a) When the air temperature is below 0$^\circ$C, the water at the surface of a lake freezes to form an ice sheet. Why doesn't freezing occur throughout the entire volume of the lake? (b) Show that the thickness of the ice sheet formed on the surface of a lake is proportional to the square root…
If a person of mass $M$ simply moved forward with speed $V$, his kinetic energy would be \( \frac{1}{2} \)$MV^2$. However, in addition to possessing a forward motion, various parts of his body (such as the arms and legs) undergo rotation. Therefore, his total kinetic energy is the sum of the…
A brass rod 12.0 cm long, a copper rod 18.0 cm long, and an aluminum rod 24.0 cm long-each with cross-sectional area 2.30 cm$^3$-are welded together end to end to form a rod 54.0 cm long, with copper as the middle section. The free end of the brass section is maintained at 100.0$^\circ$C, and…
Rods of copper, brass, and steel-each with crosssectional area of 2.00 cm$^2$-are welded together to form a Y-shaped figure. The free end of the copper rod is maintained at 100.0$^\circ$C, and the free ends of the brass and steel rods at 0.0$^\circ$C. Assume that there is no heat loss from the…
Write each vector in Fig. E1.24 in terms of the unit vectors $\hat{\imath}$ and $\hat{\jmath}$.
One experimental method of measuring an insulating material's thermal conductivity is to construct a box of the material and measure the power input to an electric heater inside the box that maintains the interior at a measured temperature above the outside surface. Suppose that in such an…
In a container of negligible mass, 0.0400 kg of steam at 100$^\circ$C and atmospheric pressure is added to 0.200 kg of water at 50.0$^\circ$C. (a) If no heat is lost to the surroundings, what is the final temperature of the system? (b) At the final temperature, how many kilograms are there of…
Styrofoam bucket of negligible mass contains 1.75 kg of water and 0.450 kg of ice. More ice, from a refrigerator at -15.0$^\circ$C, is added to the mixture in the bucket, and when thermal equilibrium has been reached, the total mass of ice in the bucket is 0.884 kg. Assuming no heat exchange…
The pulley in $\textbf{Fig. P9.75}$ has radius $R$ and a moment of inertia $I$. The rope does not slip over the pulley, and the pulley spins on a frictionless axle. The coefficient of kinetic friction between block $A$ and the tabletop is $\mu_k$ . The system is released from rest, and block…
You have 1.50 kg of water at 28.0$^\circ$C in an insulated container of negligible mass. You add 0.600 kg of ice that is initially at -22.0$^\circ$C. Assume that no heat exchanges with the surroundings. (a) After thermal equilibrium has been reached, has all of the ice melted? (b) If all of the…
In a household hot-water heating system, water is delivered to the radiators at 70.0$^\circ$C (158.0$^\circ$F) and leaves at 28.0$^\circ$C (82.4$^\circ$F). The system is to be replaced by a steam system in which steam at atmospheric pressure condenses in the radiators and the condensed steam…
Exactly one turn of a flexible rope with mass $m$ is wrapped around a uniform cylinder with mass $M$ and radius $R$. The cylinder rotates without friction about a horizontal axle along the cylinder axis. One end of the rope is attached to the cylinder. The cylinder starts with angular speed…
A uniform disk has radius $R$$_0$ and mass $M$$_0$. Its moment of inertia for an axis perpendicular to the plane of the disk at the disk's center is \( \frac{1}{2} \)$M_0R_0^2$. You have been asked to halve the disk's moment of inertia by cutting out a circular piece at the center of the disk.…
A metal wire, with density $\rho$ and Young's modulus $Y$, is stretched between rigid supports. At temperature $T$, the speed of a transverse wave is found to be $\upsilon_1$. When the temperature is increased to $T$ + $\Delta$$T$, the speed decreases to $\upsilon_2$ < $\upsilon_1$. Determine…
(a) Equation (17.12) gives the stress required to keep the length of a rod constant as its temperature changes. Show that if the length is permitted to change by an amount $\Delta$$L$ when its temperature changes by $\Delta$$T$, the stress is equal to $${F A} = Y({\Delta L \over L_0} - a \Delta…
A disoriented physics professor drives 3.25 km north, then 2.20 km west, and then 1.50 km south. Find the magnitude and direction of the resultant displacement, using the method of components. In a vector-addition diagram (roughly to scale), show that the resultant displacement found from your…
You must design a device for shooting a small marble vertically upward. The marble is in a small cup that is attached to the rim of a wheel of radius 0.260 m; the cup is covered by a lid. The wheel starts from rest and rotates about a horizontal axis that is perpendicular to the wheel at its…
A roller in a printing press turns through an angle $\theta(t)$ given by $\theta(t) = \gamma t^2 - \beta t^3$, where $\gamma =$ 3.20 rad/s$^2$ and $\beta =$ 0.500 rad/s$^3$. (a) Calculate the angular velocity of the roller as a function of time. (b) Calculate the angular acceleration of the…
Vector $\overrightarrow{A}$ has $y$-component A$_y$ = $+$9.60 m. $\overrightarrow{A}$ makes anangle of 32.0$^{\circ}$ counterclockwise from the $+$$y$-axis. (a) What is the $x$-component of $\overrightarrow{A}$? (b) What is the magnitude of $\overrightarrow{A}$?
A uniform disk with radius $R =$ 0.400 m and mass 30.0 kg rotates in a horizontal plane on a frictionless vertical axle that passes through the center of the disk. The angle through which the disk has turned varies with time according to $\theta(t) =$ (1.10 rad/s)$t +$ (6.30 rad/s$^2)t^2$. What…
Let $\theta$ be the angle that the vector $\overrightarrow{A}$ makes with the $+$$x$-axis, measured counterclockwise from that axis. Find angle $\theta$ for a vector that has these components: (a) A$_x$ = 2.00 m, A$_y$ = $-$1.00 m; (b) A$_x$ = 2.00 m, A$_y$ = 1.00 m; (c) A$_x$ = $-$2.00 m,…
Compute the $x$- and $y$-components of the vectors $\overrightarrow{A}$, $\overrightarrow{B}$, $\overrightarrow{C}$,and $\overrightarrow{D}$ in Fig. E1.24.
A postal employee drives a delivery truck along the route shown in Fig. E1.25. Determine the magnitude and direction of the resultant displacement by drawing a scale diagram. (See also Exercise 1.32 for a different approach.)
An ice-cube tray of negligible mass contains 0.290 kg of water at 18.0$^\circ$C. How much heat must be removed to cool the water to 0.00$^\circ$C and freeze it? Express your answer in joules, calories, and Btu.
You are using water to dilute small amounts of chemicals in the laboratory, drop by drop. How many drops of water are in a 1.0-L bottle? ($Hint$: Start by estimating the diameter of a drop of water.)
How many times does a human heart beat during a person's lifetime? How many gallons of blood does it pump? (Estimate that the heart pumps 50 cm$^3$ of blood with each beat.)
How many gallons of gasoline are used in the United States in one day? Assume that there are two cars for every three people, that each car is driven an average of 10,000 miles per year, and that the average car gets 20 miles per gallon.
Express each approximation of $\pi$ to six significant figures: (a) 22/7 and (b) 355/113. (c) Are these approximations accurate to that precision?
A 25,000-kg subway train initially traveling at 15.5 m/s slows to a stop in a station and then stays there long enough for its brakes to cool. The station's dimensions are 65.0 m long by 20.0 m wide by 12.0 m high. Assuming all the work done by the brakes in stopping the train is transferred as…
A useful and easy-to-remember approximate value for the number of seconds in a year is $\pi$ \(\times\) 10$^7$. Determine the percent error in this approximate value. (There are 365.24 days in one year.)
A wheel of diameter 40.0 cm starts from rest and rotates with a constant angular acceleration of 3.00 rad/s$^2$. Compute the radial acceleration of a point on the rim for the instant the wheel completes its second revolution from the relationship (a) $a_{rad} = \omega^2r$ and (b) $a_{rad} =…
You are given a sample of metal and asked to determine its specific heat. You weigh the sample and find that its weight is 28.4 N. You carefully add $1.25 \times 10{^4}$ J of heat energy to the sample and find that its temperature rises 18.0 C$^\circ$. What is the sample's specific heat?
With a wooden ruler, you measure the length of a rectangular piece of sheet metal to be 12 mm. With micrometer calipers, you measure the width of the rectangle to be 5.98 mm. Use the correct number of significant figures: What is (a) the area of the rectangle; (b) the ratio of the rectangle's…
In very cold weather a significant mechanism for heat loss by the human body is energy expended in warming the air taken into the lungs with each breath. (a) On a cold winter day when the temperature is -20$^\circ$C, what amount of heat is needed to warm to body temperature (37$^\circ$C) the…
A glass flask whose volume is 1000.00 cm$^3$ at 0.0$^\circ$C is completely filled with mercury at this temperature. When flask and mercury are warmed to 55.0$^\circ$C, 8.95 cm$^3$ of mercury overflow. If the coefficient of volume expansion of mercury is $18.0 \times 10{^-}{^5} K{^-}{^1}$,…
Aluminum rivets used in airplane construction are made slightly larger than the rivet holes and cooled by "dry ice" (solid $CO_2$) before being driven. If the diameter of a hole is 4.500 mm, what should be the diameter of a rivet at 23.0$^\circ$C if its diameter is to equal that of the hole…
The angle $\theta$ through which a disk drive turns is given by $\theta(t) = a + bt - ct^3$, where $a$, $b$, and $c$ are constants, $t$ is in seconds, and $\theta$ is in radians. When $t =$ 0, $\theta =$ $\pi$/4 rad and the angular velocity is 2.00 rad/s. When $t =$ 1.50 s, the angular…
The pressure of a gas at the triple point of water is 1.35 atm. If its volume remains unchanged, what will its pressure be at the temperature at which $CO_2$ solidifies?
Convert the following Kelvin temperatures to the Celsius and Fahrenheit scales: (a) the midday temperature at the surface of the moon (400 K); (b) the temperature at the tops of the clouds in the atmosphere of Saturn (95 K); (c) the temperature at the center of the sun $(1.55 \times 10{^7} K)$.
According to the label on a bottle of salad dressing, the volume of the contents is 0.473 liter (L). Using only the conversions 1 (L) = 1000 cm$^3$ and 1 in. = 2.54 cm, express this volume in cubic inches.
The African bombardier beetle (Stenaptinus insignis) can emit a jet of defensive spray from the movable tip of its abdomen (Fig. P17.91). The beetle's body has reservoirs containing two chemicals; when the beetle is disturbed, these chemicals combine in a reaction chamber, producing a compound…
(a) By how much would the body temperature of the bicyclist in Problem 17.89 increase in an hour if he were unable to get rid of the excess heat? (b) Is this temperature increase large enough to be serious? To find out, how high a fever would it be equivalent to, in $^\circ$F? (Recall that the…
A fan blade rotates with angular velocity given by $\omega_z$($t$) $= \gamma - \beta t^2$, where $\gamma =$ 5.00 rad/s and $\beta =$ 0.800 rad/s$^3$. (a) Calculate the angular acceleration as a function of time. (b) Calculate the instantaneous angular acceleration $\alpha_z$ at $t =$ 3.00 s and…
The molar heat capacity of a certain substance varies with temperature according to the empirical equation $$C = 29.5 J/mol \cdot K + (8.20 \times 10{^-}{^3} J/mol \cdot K{^2})T$$ How much heat is necessary to change the temperature of 3.00 mol of this substance from 27$^\circ$C to…
(a) What angle in radians is subtended by an arc 1.50 m long on the circumference of a circle of radius 2.50 m? What is this angle in degrees? (b) An arc 14.0 cm long on the circumference of a circle subtends an angle of 128 $^\circ$. What is the radius of the circle? (c) The angle between…
CP A person of mass 70.0 kg is sitting in the bathtub. The bathtub is 190.0 cm by 80.0 cm; before the person got in, the water was 24.0 cm deep. The water is at 37.0$^\circ$C. Suppose that the water were to cool down spontaneously to form ice at 0.0$^\circ$C, and that all the energy released…
You cool a 100.0-g slug of red-hot iron (temperature 745$^\circ$C) by dropping it into an insulated cup of negligible mass containing 85.0 g of water at 20.0$^\circ$C. Assuming no heat exchange with the surroundings, (a) what is the final temperature of the water and (b) what is the final mass…
BIO Shivering. Shivering is your body's way of generating heat to restore its internal temperature to the normal 37$^\circ$C, and it produces approximately 290 W of heat power per square meter of body area. A 68-kg, 1.78-m-tall woman has approximately 1.8 m$^2$ of surface area. How long would…
A typical doughnut contains 2.0 g of protein, 17.0 g of carbohydrates, and 7.0 g of fat. Average food energy values are 4.0 kcal/g for protein and carbohydrates and 9.0 kcal/g for fat. (a) During heavy exercise, an average person uses energy at a rate of 510 kcal/h. How long would you have to…
A steel ring with a 2.5000-in. inside diameter at 20.0$^\circ$C is to be warmed and slipped over a brass shaft with a 2.5020-in. outside diameter at 20.0$^\circ$C. (a) To what temperature should the ring be warmed? (b) If the ring and the shaft together are cooled by some means such as liquid…
A sphere with radius $R =$ 0.200 m has density $\rho$ that decreases with distance $r$ from the center of the sphere according to $r =$ 3.00 $\times$ 103 kg/m$^3 -$ (9.00 $\times$ 103 kg/m$^4$)$r$. (a) Calculate the total mass of the sphere. (b) Calculate the moment of inertia of the sphere for…
A thin, uniform rod is bent into a square of side length $a$. If the total mass is $M$, find the moment of inertia about an axis through the center and perpendicular to the plane of the square. ($Hint$: Use the parallel-axis theorem.)
Human Rotational Energy. A dancer is spinning at 72 rpm about an axis through her center with her arms outstretched ($\textbf{Fig. P9.83}$). From biomedical measurements, the typical distribution of mass in a human body is as follows: Head: 7.0% Arms: 13% (for both) Trunk and legs:…
In $\textbf{Fig. P9.80}$, the cylinder and pulley turn without friction about stationary horizontal axles that pass through their centers. A light rope is wrapped around the cylinder, passes over the pulley, and has a 3.00-kg box suspended from its free end. There is no slipping between the…
In the system shown in Fig. 9.17, a 12.0-kg mass is released from rest and falls, causing the uniform 10.0-kg cylinder of diameter 30.0 cm to turn about a frictionless axle through its center. How far will the mass have to descend to give the cylinder 480 J of kinetic energy?
A thin, light wire is wrapped around the rim of a wheel as shown in Fig. E9.45. The wheel rotates about a stationary horizontal axle that passes through the center of the wheel. The wheel has radius 0.180 m and moment of inertia for rotation about the axle of $I =$ 0.480 kg $\cdot$ m$^2$. A…
The pulley in $\textbf{Fig. P9.76}$ has radius 0.160 m and moment of inertia 0.380 kg $\cdot$ m$^2$. The rope does not slip on the pulley rim. Use energy methods to calculate the speed of the 4.00-kg block just before it strikes the floor.
A surveyor's 30.0-m steel tape is correct at 20.0$^\circ$C. The distance between two points, as measured by this tape on a day when its temperature is 5.00$^\circ$C, is 25.970 m. What is the true distance between the points?
You are making pesto for your pasta and have a cylindrical measuring cup 10.0 cm high made of ordinary glass [$\beta = 2.7 \times 10{^-}{^5}(C^\circ){^-}{^1}]$ that is filled with olive oil [$\beta = 6.8 \times 10{^-}{^4}(C^\circ){^-}{^1}$] to a height of 3.00 mm below the top of the cup.…
A physics student of mass 43.0 kg is standing at the edge of the flat roof of a building, 12.0 m above the sidewalk. An unfriendly dog is running across the roof toward her. Next to her is a large wheel mounted on a horizontal axle at its center. The wheel, used to lift objects from the ground…
A uniform, solid disk with mass $m$ and radius $R$ is pivoted about a horizontal axis through its center. A small object of the same mass $m$ is glued to the rim of the disk. If the disk is released from rest with the small object at the end of a horizontal radius, find the angular speed when…
How I Scales. If we multiply all the design dimensions of an object by a scaling factor $f$, its volume and mass will be multiplied by $f ^3$. (a) By what factor will its moment of inertia be multiplied? (b) If a $\frac{1}{48}$-scale model has a rotational kinetic energy of 2.5 J, what will be…
CP CALC A 250-kg weight is hanging from the ceiling by a thin copper wire. In its fundamental mode, this wire vibrates at the frequency of concert A (440 Hz). You then increase the temperature of the wire by 40 C$^\circ$. (a) By how much will the fundamental frequency change? Will it increase…
Suppose that a steel hoop could be constructed to fit just around the earth's equator at 20.0$^\circ$C. What would be the thickness of space between the hoop and the earth if the temperature of the hoop were increased by 0.500 C$^\circ$?
The hot glowing surfaces of stars emit energy in the form of electromagnetic radiation. It is a good approximation to assume e = 1 for these surfaces. Find the radii of the following stars (assumed to be spherical): (a) Rigel, the bright blue star in the constellation Orion, which radiates…
What is the rate of energy radiation per unit area of a blackbody at (a) 273 K and (b) 2730 K?
You are asked to design a cylindrical steel rod 50.0 cm long, with a circular cross section, that will conduct 190.0 J/s from a furnace at 400.0$^\circ$C to a container of boiling water under 1 atmosphere. What must the rod’s diameter be?
BIO Conduction Through the Skin. The blood plays an important role in removing heat from the body by bringing this energy directly to the surface where it can radiate away. Nevertheless, this heat must still travel through the skin before it can radiate away. Assume that the blood is brought to…
An electric kitchen range has a total wall area of 1.40 m$^2$ and is insulated with a layer of fiberglass 4.00 cm thick. The inside surface of the fiberglass has a temperature of 175$^\circ$C, and its outside surface is at 35.0$^\circ$C. The fiberglass has a thermal conductivity of 0.040 W /m…
It has been argued that power plants should make use of off-peak hours (such as late at night) to generate mechanical energy and store it until it is needed during peak load times, such as the middle of the day. One suggestion has been to store the energy in large flywheels spinning on…
A carpenter builds an exterior house wall with a layer of wood 3.0 cm thick on the outside and a layer of Styrofoam insulation 2.2 cm thick on the inside wall surface. The wood has $k$ = 0.080 W/m $\cdot$ K, and the Styrofoam has $k$ = 0.027 W /m $\cdot$ K. The interior surface temperature is…
A computer disk drive is turned on starting from rest and has constant angular acceleration. If it took 0.0865 s for the drive to make its $second$ complete revolution, (a) how long did it take to make the first complete revolution, and (b) what is its angular acceleration, in rad/s$^2$?
The motor of a table saw is rotating at 3450 rev/min. A pulley attached to the motor shaft drives a second pulley of half the diameter by means of a V-belt. A circular saw blade of diameter 0.208 m is mounted on the same rotating shaft as the second pulley. (a) The operator is careless and the…
Suppose that the rod in Fig. 17.24a is made of copper, is 45.0 cm long, and has a cross-sectional area of 1.25 cm$^2$. Let T$_H$ = 100.0$^\circ$C and T$_C $= 0.0$^\circ$C. (a) What is the final steady-state temperature gradient along the rod? (b) What is the heat current in the rod in the final…
A vessel whose walls are thermally insulated contains 2.40 kg of water and 0.450 kg of ice, all at 0.0$^\circ$C. The outlet of a tube leading from a boiler in which water is boiling at atmospheric pressure is inserted into the water. How many grams of steam must condense inside the vessel (also…
A 4.00-kg silver ingot is taken from a furnace, where its temperature is 750.0$^\circ$C, and placed on a large block of ice at 0.0$^\circ$C. Assuming that all the heat given up by the silver is used to melt the ice, how much ice is melted?
An insulated beaker with negligible mass contains 0.250 kg of water at 75.0$^\circ$C. How many kilograms of ice at $-$20.0$^\circ$C must be dropped into the water to make the final temperature of the system 40.0$^\circ$C?
You are designing a rotating metal flywheel that will be used to store energy. The flywheel is to be a uniform disk with radius 25.0 cm. Starting from rest at $t =$ 0, the flywheel rotates with constant angular acceleration 3.00 rad/s$^2$ about an axis perpendicular to the flywheel at its…
Evaporation of sweat is an important mechanism for temperature control in some warm-blooded animals. (a) What mass of water must evaporate from the skin of a 70.0-kg man to cool his body 1.00 C$^\circ$? The heat of vaporization of water at body temperature (37$^\circ$C) is $2.42 \times 10{^6}…
A disk of radius 25.0 cm is free to turn about an axle perpendicular to it through its center. It has very thin but strong string wrapped around its rim, and the string is attached to a ball that is pulled tangentially away from the rim of the disk ($\textbf{Fig. P9.59}$). The pull…
What is the amount of heat input to your skin when it receives the heat released (a) by 25.0 g of steam initially at 100.0$^\circ$C, when it is cooled to skin temperature (34.0$^\circ$C)? (b) By 25.0 g of water initially at 100.0$^\circ$C, when it is cooled to 34.0$^\circ$C? (c) What does this…
What must the initial speed of a lead bullet be at 25.0$^\circ$C so that the heat developed when it is brought to rest will be just sufficient to melt it? Assume that all the initial mechanical energy of the bullet is converted to heat and that no heat flows from the bullet to its surroundings.…
An open container holds 0.550 kg of ice at -15.0$^\circ$C. The mass of the container can be ignored. Heat is supplied to the container at the constant rate of 800.0 J/min for 500.0 min. (a) After how many minutes does the ice start to melt? (b) After how many minutes, from the time when the…
A slender rod with length $L$ has a mass per unit length that varies with distance from the left end, where $x =$ 0, according to $dm/dx = \gamma x$, where g has units of kg/m$^2$. (a) Calculate the total mass of the rod in terms of $\gamma$ and $L$. (b) Use Eq. (9.20) to calculate the moment…
How much heat is required to convert 18.0 g of ice at -10.0$^\circ$C to steam at 100.0$^\circ$C? Express your answer in joules, calories, and Btu.
In the situation described in Exercise 17.42, the man's metabolism will eventually return the temperature of his body (and of the soft drink that he consumed) to 37.0$^\circ$C. If his body releases energy at a rate of $7.00 \times 10{^3} kJ/$day (the basal metabolic rate, or BMR), how long does…
BIO Before going in for his annual physical, a 70.0-kg man whose body temperature is 37.0$^\circ$C consumes an entire 0.355-L can of a soft drink (mostly water) at 12.0$^\circ$C. (a) What will his body temperature be after equilibrium is attained? Ignore any heating by the man’s metabolism. The…
A thin uniform rod of mass $M$ and length $L$ is bent at its center so that the two segments are now perpendicular to each other. Find its moment of inertia about an axis perpendicular to its plane and passing through (a) the point where the two segments meet and (b) the midpoint of the line…
A thin, rectangular sheet of metal has mass $M$ and sides of length $a$ and $b$. Use the parallel-axis theorem to calculate the moment of inertia of the sheet for an axis that is perpendicular to the plane of the sheet and that passes through one corner of the sheet.
In a container of negligible mass, 0.200 kg of ice at an initial temperature of -40.0$^\circ$C is mixed with a mass m of water that has an initial temperature of 80.0$^\circ$C. No heat is lost to the surroundings. If the final temperature of the system is 28.0$\circ$C, what is the mass m of the…
About what axis will a uniform, balsa-wood sphere have the same moment of inertia as does a thin-walled, hollow, lead sphere of the same mass and radius, with the axis along a diameter?
Find the moment of inertia of a hoop (a thin-walled, hollow ring) with mass $M$ and radius $R$ about an axis perpendicular to the hoop’s plane at an edge.
BIO Treatment for a Stroke. One suggested treatment for a person who has suffered a stroke is immersion in an ice-water bath at 0$^circ$C to lower the body temperature, which prevents damage to the brain. In one set of tests, patients were cooled until their internal temperature reached…
A 500.0-g chunk of an unknown metal, which has been in boiling water for several minutes, is quickly dropped into an insulating Styrofoam beaker containing 1.00 kg of water at room temperature (20.0$^\circ$C). After waiting and gently stirring for 5.00 minutes, you observe that the water’s…
You have 750 g of water at 10.0$^\circ$C in a large insulated beaker. How much boiling water at 100.0$^\circ$C must you add to this beaker so that the final temperature of the mixture will be 75$^\circ$C?
A uniform 2.00-m ladder of mass 9.00 kg is leaning against a vertical wall while making an angle of 53.0$^\circ$ with the floor. A worker pushes the ladder up against the wall until it is vertical. What is the increase in the gravitational potential energy of the ladder?
CP A 15.0-g bullet traveling horizontally at 865 m/s passes through a tank containing 13.5 kg of water and emerges with a speed of 534 m/s. What is the maximum temperature increase that the water could have as a result of this event?
A thin, light wire is wrapped around the rim of a wheel ($\textbf{Fig. E9.45}$). The wheel rotates without friction about a stationary horizontal axis that passes through the center of the wheel. The wheel is a uniform disk with radius $R$ = 0.280 m. An object of mass $m$ = 4.20 kg is suspended…
A technician measures the specific heat of an unidentified liquid by immersing an electrical resistor in it. Electrical energy is converted to heat transferred to the liquid for 120 s at a constant rate of 65.0 W. The mass of the liquid is 0.780 kg, and its temperature increases from…
A bucket of mass $m$ is tied to a massless cable that is wrapped around the outer rim of a frictionless uniform pulley of radius $R$, similar to the system shown in Fig. E9.43. In terms of the stated variables, what must be the moment of inertia of the pulley so that it always has half as much…
A frictionless pulley has the shape of a uniform solid disk of mass 2.50 kg and radius 20.0 cm. A 1.50-kg stone is attached to a very light wire that is wrapped around the rim of the pulley ($\textbf{Fig. E9.43}$), and the system is released from rest. (a) How far must the stone fall so that…
A light, flexible rope is wrapped several times around a $hollow$ cylinder, with a weight of 40.0 N and a radius of 0.25 m, that rotates without friction about a fixed horizontal axis. The cylinder is attached to the axle by spokes of a negligible moment of inertia. The cylinder is initially at…
CP While painting the top of an antenna 225 m in height, a worker accidentally lets a 1.00-L water bottle fall from his lunchbox. The bottle lands in some bushes at ground level and does not break. If a quantity of heat equal to the magnitude of the change in mechanical energy of the water goes…
Energy is to be stored in a 70.0-kg flywheel in the shape of a uniform solid disk with radius $R =$ 1.20 m. To prevent structural failure of the flywheel, the maximum allowed radial acceleration of a point on its rim is 3500 m/s$^2$. What is the maximum kinetic energy that can be stored in the…
The flywheel of a gasoline engine is required to give up 500 J of kinetic energy while its angular velocity decreases from 650 rev/min to 520 rev/min. What moment of inertia is required?
A hollow spherical shell has mass 8.20 kg and radius 0.220 m. It is initially at rest and then rotates about a stationary axis that lies along a diameter with a constant acceleration of 0.890 rad/s$^2$. What is the kinetic energy of the shell after it has turned through 6.00 rev?
A compound disk of outside diameter 140.0 cm is made up of a uniform solid disk of radius 50.0 cm and area density 3.00 g/cm$^2$ surrounded by a concentric ring of inner radius 50.0 cm, outer radius 70.0 cm, and area density 2.00 g/cm$^2$. Find the moment of inertia of this object about an axis…
BIO While running, a 70-kg student generates thermal energy at a rate of 1200 W. For the runner to maintain a constant body temperature of 37$^\circ$C, this energy must be removed by perspiration or other mechanisms. If these mechanisms failed and the energy could not flow out of the student’s…
An airplane propeller is 2.08 m in length (from tip to tip) with mass 117 kg and is rotating at 2400 rpm (rev/min) about an axis through its center. You can model the propeller as a slender rod. (a) What is its rotational kinetic energy? (b) Suppose that, due to weight constraints, you had to…
A wagon wheel is constructed as shown in Fig. E9.33. The radius of the wheel is $0.300 \mathrm{~m}$ and the rim has mass $1.40 \mathrm{~kg}$. Each of the eight spokes that lie along a diameter and are $0.300 \mathrm{~m}$ long has mass $0.280 \mathrm{~kg}$. What is the moment of inertia of the…
In an effort to stay awake for an all-night study session, a student makes a cup of coffee by first placing a 200-W electric immersion heater in 0.320 kg of water. (a) How much heat must be added to the water to raise its temperature from 20.0$^\circ$C to 80.0$^\circ$C? (b) How much time is…
You are a project manager for a manufacturing company. One of the machine parts on the assembly line is a thin, uniform rod that is 60.0 cm long and has mass 0.400 kg. (a) What is the moment of inertia of this rod for an axis at its center, perpendicular to the rod? (b) One of your engineers…
An aluminum tea kettle with mass 1.10 kg and containing 1.80 kg of water is placed on a stove. If no heat is lost to the surroundings, how much heat must be added to raise the temperature from 20.0$^\circ$C to 85.0$^\circ$C?
Steel train rails are laid in 12.0-m-long segments placed end to end. The rails are laid on a winter day when their temperature is -9.0$^\circ$C. (a) How much space must be left between adjacent rails if they are just to touch on a summer day when their temperature is 33.0$^\circ$C? (b) If the…
Four small spheres, each of which you can regard as a point of mass 0.200 kg, are arranged in a square 0.400 m on a side and connected by extremely light rods ($\textbf{Fig. E9.28}$). Find the moment of inertia of the system about an axis (a) through the center of the square, perpendicular to…
According to the shop manual, when drilling a 12.7-mm-diameter hole in wood, plastic, or aluminum, a drill should have a speed of 1250 rev/min. For a 12.7-mm-diameter drill bit turning at a constant 1250 rev/min, find (a) the maximum linear speed of any part of the bit and (b) the maximum…
A machinist bores a hole of diameter 1.35 cm in a steel plate that is at 25.0$^\circ$C. What is the cross-sectional area of the hole (a) at 25.0$^\circ$C and (b) when the temperature of the plate is increased to 175$^\circ$C? Assume that the coefficient of linear expansion remains constant over…
An advertisement claims that a centrifuge takes up only $0.127 \mathrm{~m}$ of bench space but can produce a radial acceleration of $3000 \mathrm{~g}$ at 5000 rev $/ \mathrm{min}$. Calculate the required radius of the centrifuge. Is the claim realistic?
A geodesic dome constructed with an aluminum framework is a nearly perfect hemisphere; its diameter measures $55.0 \mathrm{~m}$ on a winter day at a temperature of $-15^{\circ} \mathrm{C}$. How much more interior space does the dome have in the summer, when the temperature is $35^{\circ}…
A copper cylinder is initially at 20.0$^\circ$C. At what temperature will its volume be 0.150% larger than it is at 20.0$^\circ$C?
One of the tallest buildings in the world is the Taipei 101 in Taiwan, at a height of 1671 feet. Assume that this height was measured on a cool spring day when the temperature was 15.5$^\circ$C. You could use the building as a sort of giant thermometer on a hot summer day by carefully measuring…
The Humber Bridge in England has the world's longest single span, 1410 m. Calculate the change in length of the steel deck of the span when the temperature increases from -5.0$^\circ$C to 18.0$^\circ$C.
Using Appendix F, along with the fact that the earth spins on its axis once per day, calculate (a) the earth’s orbital angular speed (in rad/s) due to its motion around the sun, (b) its angular speed (in rad/s) due to its axial spin, (c) the tangential speed of the earth around the sun…
Like the Kelvin scale, the Rankine scale is an absolute temperature scale: Absolute zero is zero degrees Rankine (0$^\circ$R). However, the units of this scale are the same size as those of the Fahrenheit scale rather than the Celsius scale. What is the numerical value of the triple-point…
At $t =$ 0 a grinding wheel has an angular velocity of 24.0 rad/s. It has a constant angular acceleration of 30.0 rad/s$^2$ until a circuit breaker trips at $t =$ 2.00 s. From then on, it turns through 432 rad as it coasts to a stop at constant angular acceleration. (a) Through what total angle…
An experimenter using a gas thermometer found the pressure at the triple point of water (0.01$^\circ$C) to be $4.80 \times 10{^4} Pa$ and the pressure at the normal boiling point (100$^\circ$C) to be $6.50 \times 10{^4} Pa$. (a) Assuming that the pressure varies linearly with temperature, use…
A high-speed flywheel in a motor is spinning at 500 rpm when a power failure suddenly occurs. The flywheel has mass 40.0 kg and diameter 75.0 cm. The power is off for 30.0 s, and during this time the flywheel slows due to friction in its axle bearings. During the time the power is off, the…
A circular saw blade 0.200 m in diameter starts from rest. In 6.00 s it accelerates with constant angular acceleration to an angular velocity of 140 rad/s. Find the angular acceleration and the angle through which the blade has turned.
(a) Derive Eq. (9.12) by combining Eqs. (9.7) and (9.11) to eliminate $t$. (b) The angular velocity of an airplane propeller increases from 12.0 rad/s to 16.0 rad/s while turning through 7.00 rad. What is the angular acceleration in rad/s$^2$?
An electric fan is turned off, and its angular velocity decreases uniformly from 500 rev/min to 200 rev/min in 4.00 s. (a) Find the angular acceleration in rev/s$^2$ and the number of revolutions made by the motor in the 4.00-s interval. (b) How many more seconds are required for the fan to…
You put a bottle of soft drink in a refrigerator and leave it until its temperature has dropped 10.0 K. What is its temperature change in (a) F$^\circ$ and (b) C$^\circ$?
A wheel is rotating about an axis that is in the $z$-direction.The angular velocity $\omega_z$ is $-$6.00 rad/s at $t =$ 0, increases linearly with time, and is $+$4.00 rad/s at $t =$ 7.00 s. We have taken counterclockwise rotation to be positive. (a) Is the angular acceleration during this…
(a) On January 22, 1943, the temperature in Spearfish, South Dakota, rose from -4.0$^\circ$F to 45.0$^\circ$F in just 2 minutes. What was the temperature change in Celsius degrees? (b) The temperature in Browning, Montana, was 44.0$^\circ$F on January 23, 1916. The next day the temperature…
BIO Temperatures in Biomedicine. (a) Normal body temperature. The average normal body temperature measured in the mouth is 310 K. What would Celsius and Fahrenheit thermometers read for this temperature? (b) Elevated body temperature. During very vigorous exercise, the body’s temperature can go…
An airplane propeller is rotating at 1900 rpm (rev/min). (a) Compute the propeller's angular velocity in rad/s. (b) How many seconds does it take for the propeller to turn through 35 $^\circ$?
Convert the following Celsius temperatures to Fahrenheit: (a) -62.8$^\circ$C, the lowest temperature ever recorded in North America (February 3, 1947, Snag, Yukon); (b) 56.7$^\circ$C, the highest temperature ever recorded in the United States (July 10, 1913, Death Valley, California); (c)…
A flask contains a mixture of neon (Ne), krypton (Kr), and radon (Rn) gases. Compare (a) the average kinetic energies of the three types of atoms and (b) the root-mean-square speeds. (Hint: Appendix D shows the molar mass (in g/mol) of each element under the chemical symbol for that element.)
(a) What is the total translational kinetic energy of the air in an empty room that has dimensions 8.00 m $\times$ 12.00 m $\times$ 4.00 m if the air is treated as an ideal gas at 1.00 atm? (b) What is the speed of a 2000-kg automobile if its kinetic energy equals the translational kinetic…
Consider an ideal gas at 27$^\circ$C and 1.00 atm. To get some idea how close these molecules are to each other, on the average, imagine them to be uniformly spaced, with each molecule at the center of a small cube. (a) What is the length of an edge of each cube if adjacent cubes touch but do…
If the energy of the $H_{2}$ covalent bond is -4.48 eV, what wavelength of light is needed to break that molecule apart? In what part of the electromagnetic spectrum does this light lie?
In a gas at standard conditions, what is the length of the side of a cube that contains a number of molecules equal to the population of the earth (about 7 $\times$ 10$^9$ people)?
Modern vacuum pumps make it easy to attain pressures of the order of 10${^-}{^1}{^3}$ atm in the laboratory. Consider a volume of air and treat the air as an ideal gas. (a) At a pressure of 9.00$\times$ 10${^-}{^1}{^4}$ atm and an ordinary temperature of 300.0 K, how many molecules are present…
A large organic molecule has a mass of 1.41$\times$ 10${^-}{^2}{^1}$ kg. What is the molar mass of this compound?
At an altitude of 11,000 m (a typical cruising altitude for a jet airliner), the air temperature is -56.5$^\circ$C and the air density is 0.364 kg/m$^3$. What is the pressure of the atmosphere at that altitude? (Note: The temperature at this altitude is not the same as at the surface of the…
(a) Calculate the mass of nitrogen present in a volume of 3000 cm$^3$ if the gas is at 22.0$^\circ$C and the absolute pressure of 2.00$\times$ 10${^-}{^1}{^3}$ atm is a partial vacuum easily obtained in laboratories. (b) What is the density (in kg/m$^3$) of the N$_2$ ?
Calculate the net torque about point O for the two forces applied as in $\textbf{Fig. E10.2.}$ The rod and both forces are in the plane of the page.
Calculate the torque (magnitude and direction) about point $O$ due to the force $F$ in each of the cases sketched in $\textbf{Fig. E10.1.}$ In each case, both the force $F$ and the rod lie in the plane of the page, the rod has length 4.00 m, and the force has magnitude $F =$ 10.0 N.
With the assumption that the air temperature is a uniform 0.0$^\circ$C, what is the density of the air at an altitude of 1.00 km as a percentage of the density at the surface?
With the assumptions of Example 18.4 (Section 18.1), at what elevation above sea level is air pressure 90% of the pressure at sea level?
A metal tank with volume 3.10 L will burst if the absolute pressure of the gas it contains exceeds 100 atm. (a) If 11.0 mol of an ideal gas is put into the tank at 23.0$^\circ$C, to what temperature can the gas be warmed before the tank ruptures? Ignore the thermal expansion of the tank. (b)…
A small block has constant acceleration as it slides down a frictionless incline. The block is released from rest at the top of the incline, and its speed after it has traveled 6.80 m to the bottom of the incline is 3.80 m/s. What is the speed of the block when it is 3.40 m from the top of the…
The graph in $\textbf{Fig. E2.31}$ shows the velocity of a motorcycle police officer plotted as a function of time. (a) Find the instantaneous acceleration at $t =$ 3 s, $t =$ 7 s, and $t =$ 11 s. (b) How far does the officer go in the first 5 s? The first 9 s? The first 13 s?
During an auto accident, the vehicle's air bags deploy and slow down the passengers more gently than if they had hit the windshield or steering wheel. According to safety standards, air bags produce a maximum acceleration of $60 g$ that lasts for only $36 \mathrm{~ms}$ (or less). How far (in…
A car's velocity as a function of time is given by $v_x(t) = \alpha + \beta t^2$, where $\alpha =$ 3.00 m/s and $\beta =$ 0.100 m/s$^3$. (a) Calculate the average acceleration for the time interval $t =$ 0 to $t =$ 5.00 s. (b) Calculate the instantaneous acceleration for $t =$ 0 and $t =$ 5.00…
On a compact disc (CD), music is coded in a pattern of tiny pits arranged in a track that spirals outward toward the rim of the disc. As the disc spins inside a CD player, the track is scanned at a constant $linear$ speed of $v =$ 1.25m/s. Because the radius of the track varies as it spirals…
If a certain amount of ideal gas occupies a volume $V$ at STP on earth, what would be its volume (in terms of $V$) on Venus, where the temperature is 1003$^\circ$C and the pressure is 92 atm?
A dog in an open field runs 12.0 m east and then 28.0 m in a direction 50.0$^{\circ}$ west of north. In what direction and how far must the dog then run to end up 10.0 m south of her original starting point?
A fence post is 52.0 m from where you are standing, in a direction 37.0$^{\circ}$ north of east. A second fence post is due south from you. How far are you from the second post if the distance between the two posts is 68.0 m?
An ideal gas has a density of 1.33 $\times$ 10${^-}{^6}$ g/cm$^3$ at 1.00 $\times$ 10${^-}{^3}$ atm and 20.0$^\circ$C. Identify the gas.
You decide to go to your favorite neighborhood restaurant. You leave your apartment, take the elevator 10 flights down (each flight is 3.0 m), and then walk 15 m south to the apartment exit. You then proceed 0.200 km east, turn north, and walk 0.100 km to the entrance of the restaurant. (a)…
An empty cylindrical canister 1.50 m long and 90.0 cm in diameter is to be filled with pure oxygen at 22.0$^\circ$C to store in a space station. To hold as much gas as possible, the absolute pressure of the oxygen will be 21.0 atm. The molar mass of oxygen is 32.0 g/mol. (a) How many moles of…
An explorer in Antarctica leaves his shelter during a whiteout. He takes 40 steps northeast, next 80 steps at 60$^{\circ}$ north of west, and then 50 steps due south. Assume all of his steps are equal in length. (a) Sketch, roughly to scale, the three vectors and their resultant. (b) Save the…
A large cylindrical tank contains 0.750 m$^3$ of nitrogen gas at 27$^\circ$C and 7.50 $\times$ 10${^3}$Pa (absolute pressure). The tank has a tight-fitting piston that allows the volume to be changed. What will be the pressure if the volume is decreased to 0.410 m$^3$ and the temperature is…
As a test of orienteering skills, your physics class holds a contest in a large, open field. Each contestant is told to travel 20.8 m due north from the starting point, then 38.0 m due east, and finally 18.0 m in the direction 33.0$^{\circ}$ west of south. After the specified displacements, a…
A Jaguar XK8 convertible has an eight-cylinder engine. At the beginning of its compression stroke, one of the cylinders contains 499 cm$^3$ of air at atmospheric pressure (1.01 $\times$ 10${^5}$ Pa) and a temperature of 27.0$^\circ$C. At the end of the stroke, the air has been compressed to a…
You have several identical balloons. You experimentally determine that a balloon will break if its volume exceeds 0.900 L. The pressure of the gas inside the balloon equals air pressure (1.00 atm). (a) If the air inside the balloon is at a constant 22.0$^\circ$C and behaves as an ideal gas,…
(a) Calculate the density of the atmosphere at the surface of Mars (where the pressure is 650 Pa and the temperature is typically 253 $K$, with a $CO_2$ atmosphere), Venus (with an average temperature of 730 $K$ and pressure of 92 atm, with a $CO_2$ atmosphere), and Saturn's moon Titan (where…
Calculate the moment of inertia of a uniform solid cone about an axis through its center ($\textbf{Fig. P9.90}$). The cone has mass $M$ and altitude $h$. The radius of its circular base is $R$.
As noted in Exercise 1.26, a spelunker is surveying a cave. She follows a passage 180 m straight west, then 210 m in a direction 45$^{\circ}$ east of south, and then 280 m at 30$^{\circ}$ east of north. After a fourth displacement, she finds herself back where she started. Use the method of…
You are rebuilding a 1965 Chevrolet. To decide whether to replace the flywheel with a newer, lighter-weight one, you want to determine the moment of inertia of the original, 35.6-cm-diameter flywheel. It is not a uniform disk, so you can't use $I =$ \( \frac{1}{2} \) $MR^2$ to calculate the…
Two workers pull horizontally on a heavy box, but one pulls twice as hard as the other. The larger pull is directed at 21.0$^{\circ}$ west of north, and the resultant of these two pulls is 460.0 N directly northward. Use vector components to find the magnitude of each of these pulls and the…
A cylindrical tank has a tight-fitting piston that allows the volume of the tank to be changed. The tank originally contains 0.110 m$^3$ of air at a pressure of 0.355 atm. The piston is slowly pulled out until the volume of the gas is increased to 0.390 m$^3$. If the temperature remains…
BIO Biological tissues are typically made up of 98% water. Given that the density of water is 1.0 \(\times\) 10$^3$ kg/m$^3$, estimate the mass of (a) the heart of an adult human; (b) a cell with a diameter of 0.5 $\mu$m; (c) a honeybee.
To measure the specific heat in the liquid phase of a newly developed cryoprotectant, you place a sample of the new cryoprotectant in contact with a cold plate until the solution's temperature drops from room temperature to its freezing point. Then you measure the heat transferred to the cold…
As you eat your way through a bag of chocolate chip cookies, you observe that each cookie is a circular disk with a diameter of 8.50 $\pm$ 0.02 cm and a thickness of 0.050 $\pm$ 0.005 cm. (a) Find the average volume of a cookie and the uncertainty in the volume. (b) Find the ratio of the…
In another experiment, you place a layer of this cryoprotectant between one 10 cm $\times$ 10 cm cold plate maintained at -40$^\circ$C and a second cold plate of the same size maintained at liquid nitrogen's boiling temperature (77 K). Then you measure the rate of heat transfer. Another lab…
The density of air under standard laboratory conditions is 1.29 kg/m$^3$, and about 20% of that air consists of oxygen. Typically, people breathe about \(\frac{1}{2}\) L of air per breath. (a) How many grams of oxygen does a person breathe in a day? (b) If this air is stored uncompressed in a…
Careful measurements show that the specific heat of the solid phase depends on temperature (Fig. P17.117). How will the actual time needed for this cryoprotectant to come to equilibrium with the cold plate compare with the time predicted by using the values in the table? Assume that all values…
You are analyzing the motion of a large flywheel that has radius 0.800 m. In one test run, the wheel starts from rest and turns with constant angular acceleration. An accelerometer on the rim of the flywheel measures the magnitude of the resultant acceleration $a$ of a point on the rim of the…
You place 35 g of this cryoprotectant at 22$^\circ$C in contact with a cold plate that is maintained at the boiling temperature of liquid nitrogen (77 K). The cryoprotectant is thermally insulated from everything but the cold plate. Use the values in the table to determine how much heat will be…
In January 2006 astronomers reported the discovery of a planet, comparable in size to the earth, orbiting another star and having a mass about 5.5 times the earth's mass. It is believed to consist of a mixture of rock and ice, similar to Neptune. If this planet has the same density as Neptune…
An acre has a length of one furlong (\(\frac{1}{8}\) mi) and a width one-tenth of its length. (a) How many acres are in a square mile? (b) How many square feet are in an acre? See Appendix E. (c) An acre-foot is the volume of water that would cover 1 acre of flat land to a depth of 1 foot. How…
For the two vectors $\overrightarrow{A}$ and $\overrightarrow{B}$ in Fig. E1.39, find (a) the scalar product $\overrightarrow{A}$ $\cdot$ $\overrightarrow{B}$; (b) the magnitude and direction of the vector product $\overrightarrow{A}$ \(\times\) $\overrightarrow{B}$.
For the two vectors $\overrightarrow{A}$ and $\overrightarrow{D}$ in Fig. E1.24, find the magnitude and direction of (a) the vector product $\overrightarrow{A}$ \(\times\) $\overrightarrow{D}$; (b) the vector product $\overrightarrow{D}$ \(\times\) $\overrightarrow{A}$.
For the two vectors in Fig. E1.35, find the magnitude and direction of (a) the vector product $\overrightarrow{A}$ \(\times\) $\overrightarrow{B}$; (b) the vector product $\overrightarrow{B}$ \(\times\) $\overrightarrow{A}$.
During your mechanical engineering internship, you are given two uniform metal bars $A$ and $B$, which are made from different metals, to determine their thermal conductivities. Measuring the bars, you determine that both have length 40.0 cm and uniform cross-sectional area 2.50 cm$^2$. You…
For the vectors $\overrightarrow{A}$, $\overrightarrow{B}$, and $\overrightarrow{C}$ in Fig. E1.24, find the scalar products (a) $\overrightarrow{A}$ $\cdot$ $\overrightarrow{B}$; (b) $\overrightarrow{B}$ $\cdot$ $\overrightarrow{C}$; (c) $\overrightarrow{A}$ $\cdot$ $\overrightarrow{C}$.
(a) Find the scalar product of the vectors $\overrightarrow{A}$ and $\overrightarrow{B}$ given in Exercise 1.38. (b) Find the angle between these two vectors.
At a chemical plant where you are an engineer, a tank contains an unknown liquid. You must determine the liquid's specific heat capacity. You put 0.500 kg of the liquid into an insulated metal cup of mass 0.200 kg. Initially the liquid and cup are at 20.0$^\circ$C. You add 0.500 kg of water…
Given two vectors $\overrightarrow{A}$ = $-$2.00$\hat{\imath}$ $+$ 3.00$\hat{\jmath}$ $+$ 4.00$\hat{k}$ and $\overrightarrow{B}$ = 3.00$\hat{\imath}$ $+$ 1.00$\hat{\jmath}$ $-$ 3.00$\hat{k}$, (a) find the magnitude of each vector; (b) use unit vectors to write an expression for the vector…
As a physicist, you put heat into a 500.0-g solid sample at the rate of 10.0 kJ/min while recording its temperature as a function of time. You plot your data as shown in Fig. P17.111. (a) What is the latent heat of fusion for this solid? (b) What are the specific heats of the liquid and solid…
The icecaps of Greenland and Antarctica contain about 1.75% of the total water (by mass) on the earth's surface; the oceans contain about 97.5%, and the other 0.75% is mainly groundwater. Suppose the icecaps, currently at an average temperature of about -30$^\circ$C, somehow slid into the ocean…
You have probably seen people jogging in extremely hot weather. There are good reasons not to do this! When jogging strenuously, an average runner of mass 68 kg and surface area 1.85 m$^2$ produces energy at a rate of up to 1300 W, 80% of which is converted to heat. The jogger radiates heat but…
A metal sphere with radius 3.20 cm is suspended in a large metal box with interior walls that are maintained at 30.0$^\circ$C. A small electric heater is embedded in the sphere. Heat energy must be supplied to the sphere at the rate of 0.660 J/s to maintain the sphere at a constant temperature…
A physicist uses a cylindrical metal can 0.250 m high and 0.090 m in diameter to store liquid helium at 4.22 K; at that temperature the heat of vaporization of helium is $2.09 \times 10{^4} J/kg$. Completely surrounding the metal can are walls maintained at the temperature of liquid nitrogen,…
The Kinetic Energy of Running. Using Problem 9.81 as a guide, apply it to a person running at 12 km/h, with his arms and legs each swinging through $\pm$30$^\circ$ in \( \frac{1}{2} \) s. As before, assume that the arms and legs are kept straight.
(a) When the air temperature is below 0$^\circ$C, the water at the surface of a lake freezes to form an ice sheet. Why doesn't freezing occur throughout the entire volume of the lake? (b) Show that the thickness of the ice sheet formed on the surface of a lake is proportional to the square root…
If a person of mass $M$ simply moved forward with speed $V$, his kinetic energy would be \( \frac{1}{2} \)$MV^2$. However, in addition to possessing a forward motion, various parts of his body (such as the arms and legs) undergo rotation. Therefore, his total kinetic energy is the sum of the…
A brass rod 12.0 cm long, a copper rod 18.0 cm long, and an aluminum rod 24.0 cm long-each with cross-sectional area 2.30 cm$^3$-are welded together end to end to form a rod 54.0 cm long, with copper as the middle section. The free end of the brass section is maintained at 100.0$^\circ$C, and…
Rods of copper, brass, and steel-each with crosssectional area of 2.00 cm$^2$-are welded together to form a Y-shaped figure. The free end of the copper rod is maintained at 100.0$^\circ$C, and the free ends of the brass and steel rods at 0.0$^\circ$C. Assume that there is no heat loss from the…
Write each vector in Fig. E1.24 in terms of the unit vectors $\hat{\imath}$ and $\hat{\jmath}$.
In a container of negligible mass, 0.0400 kg of steam at 100$^\circ$C and atmospheric pressure is added to 0.200 kg of water at 50.0$^\circ$C. (a) If no heat is lost to the surroundings, what is the final temperature of the system? (b) At the final temperature, how many kilograms are there of…
The pulley in $\textbf{Fig. P9.75}$ has radius $R$ and a moment of inertia $I$. The rope does not slip over the pulley, and the pulley spins on a frictionless axle. The coefficient of kinetic friction between block $A$ and the tabletop is $\mu_k$ . The system is released from rest, and block…
You have 1.50 kg of water at 28.0$^\circ$C in an insulated container of negligible mass. You add 0.600 kg of ice that is initially at -22.0$^\circ$C. Assume that no heat exchanges with the surroundings. (a) After thermal equilibrium has been reached, has all of the ice melted? (b) If all of the…
In a household hot-water heating system, water is delivered to the radiators at 70.0$^\circ$C (158.0$^\circ$F) and leaves at 28.0$^\circ$C (82.4$^\circ$F). The system is to be replaced by a steam system in which steam at atmospheric pressure condenses in the radiators and the condensed steam…
Exactly one turn of a flexible rope with mass $m$ is wrapped around a uniform cylinder with mass $M$ and radius $R$. The cylinder rotates without friction about a horizontal axle along the cylinder axis. One end of the rope is attached to the cylinder. The cylinder starts with angular speed…
A uniform disk has radius $R$$_0$ and mass $M$$_0$. Its moment of inertia for an axis perpendicular to the plane of the disk at the disk's center is \( \frac{1}{2} \)$M_0R_0^2$. You have been asked to halve the disk's moment of inertia by cutting out a circular piece at the center of the disk.…
A metal wire, with density $\rho$ and Young's modulus $Y$, is stretched between rigid supports. At temperature $T$, the speed of a transverse wave is found to be $\upsilon_1$. When the temperature is increased to $T$ + $\Delta$$T$, the speed decreases to $\upsilon_2$ < $\upsilon_1$. Determine…
(a) Equation (17.12) gives the stress required to keep the length of a rod constant as its temperature changes. Show that if the length is permitted to change by an amount $\Delta$$L$ when its temperature changes by $\Delta$$T$, the stress is equal to $${F A} = Y({\Delta L \over L_0} - a \Delta…
A disoriented physics professor drives 3.25 km north, then 2.20 km west, and then 1.50 km south. Find the magnitude and direction of the resultant displacement, using the method of components. In a vector-addition diagram (roughly to scale), show that the resultant displacement found from your…
You must design a device for shooting a small marble vertically upward. The marble is in a small cup that is attached to the rim of a wheel of radius 0.260 m; the cup is covered by a lid. The wheel starts from rest and rotates about a horizontal axis that is perpendicular to the wheel at its…
A roller in a printing press turns through an angle $\theta(t)$ given by $\theta(t) = \gamma t^2 - \beta t^3$, where $\gamma =$ 3.20 rad/s$^2$ and $\beta =$ 0.500 rad/s$^3$. (a) Calculate the angular velocity of the roller as a function of time. (b) Calculate the angular acceleration of the…
Vector $\overrightarrow{A}$ has $y$-component A$_y$ = $+$9.60 m. $\overrightarrow{A}$ makes anangle of 32.0$^{\circ}$ counterclockwise from the $+$$y$-axis. (a) What is the $x$-component of $\overrightarrow{A}$? (b) What is the magnitude of $\overrightarrow{A}$?
A uniform disk with radius $R =$ 0.400 m and mass 30.0 kg rotates in a horizontal plane on a frictionless vertical axle that passes through the center of the disk. The angle through which the disk has turned varies with time according to $\theta(t) =$ (1.10 rad/s)$t +$ (6.30 rad/s$^2)t^2$. What…
Let $\theta$ be the angle that the vector $\overrightarrow{A}$ makes with the $+$$x$-axis, measured counterclockwise from that axis. Find angle $\theta$ for a vector that has these components: (a) A$_x$ = 2.00 m, A$_y$ = $-$1.00 m; (b) A$_x$ = 2.00 m, A$_y$ = 1.00 m; (c) A$_x$ = $-$2.00 m,…
Compute the $x$- and $y$-components of the vectors $\overrightarrow{A}$, $\overrightarrow{B}$, $\overrightarrow{C}$,and $\overrightarrow{D}$ in Fig. E1.24.
A postal employee drives a delivery truck along the route shown in Fig. E1.25. Determine the magnitude and direction of the resultant displacement by drawing a scale diagram. (See also Exercise 1.32 for a different approach.)
An ice-cube tray of negligible mass contains 0.290 kg of water at 18.0$^\circ$C. How much heat must be removed to cool the water to 0.00$^\circ$C and freeze it? Express your answer in joules, calories, and Btu.
You are using water to dilute small amounts of chemicals in the laboratory, drop by drop. How many drops of water are in a 1.0-L bottle? ($Hint$: Start by estimating the diameter of a drop of water.)
How many times does a human heart beat during a person's lifetime? How many gallons of blood does it pump? (Estimate that the heart pumps 50 cm$^3$ of blood with each beat.)
How many gallons of gasoline are used in the United States in one day? Assume that there are two cars for every three people, that each car is driven an average of 10,000 miles per year, and that the average car gets 20 miles per gallon.
Express each approximation of $\pi$ to six significant figures: (a) 22/7 and (b) 355/113. (c) Are these approximations accurate to that precision?
A 25,000-kg subway train initially traveling at 15.5 m/s slows to a stop in a station and then stays there long enough for its brakes to cool. The station's dimensions are 65.0 m long by 20.0 m wide by 12.0 m high. Assuming all the work done by the brakes in stopping the train is transferred as…
A useful and easy-to-remember approximate value for the number of seconds in a year is $\pi$ \(\times\) 10$^7$. Determine the percent error in this approximate value. (There are 365.24 days in one year.)
A wheel of diameter 40.0 cm starts from rest and rotates with a constant angular acceleration of 3.00 rad/s$^2$. Compute the radial acceleration of a point on the rim for the instant the wheel completes its second revolution from the relationship (a) $a_{rad} = \omega^2r$ and (b) $a_{rad} =…
You are given a sample of metal and asked to determine its specific heat. You weigh the sample and find that its weight is 28.4 N. You carefully add $1.25 \times 10{^4}$ J of heat energy to the sample and find that its temperature rises 18.0 C$^\circ$. What is the sample's specific heat?
With a wooden ruler, you measure the length of a rectangular piece of sheet metal to be 12 mm. With micrometer calipers, you measure the width of the rectangle to be 5.98 mm. Use the correct number of significant figures: What is (a) the area of the rectangle; (b) the ratio of the rectangle's…
In very cold weather a significant mechanism for heat loss by the human body is energy expended in warming the air taken into the lungs with each breath. (a) On a cold winter day when the temperature is -20$^\circ$C, what amount of heat is needed to warm to body temperature (37$^\circ$C) the…
A glass flask whose volume is 1000.00 cm$^3$ at 0.0$^\circ$C is completely filled with mercury at this temperature. When flask and mercury are warmed to 55.0$^\circ$C, 8.95 cm$^3$ of mercury overflow. If the coefficient of volume expansion of mercury is $18.0 \times 10{^-}{^5} K{^-}{^1}$,…
Aluminum rivets used in airplane construction are made slightly larger than the rivet holes and cooled by "dry ice" (solid $CO_2$) before being driven. If the diameter of a hole is 4.500 mm, what should be the diameter of a rivet at 23.0$^\circ$C if its diameter is to equal that of the hole…
The angle $\theta$ through which a disk drive turns is given by $\theta(t) = a + bt - ct^3$, where $a$, $b$, and $c$ are constants, $t$ is in seconds, and $\theta$ is in radians. When $t =$ 0, $\theta =$ $\pi$/4 rad and the angular velocity is 2.00 rad/s. When $t =$ 1.50 s, the angular…
The pressure of a gas at the triple point of water is 1.35 atm. If its volume remains unchanged, what will its pressure be at the temperature at which $CO_2$ solidifies?
Convert the following Kelvin temperatures to the Celsius and Fahrenheit scales: (a) the midday temperature at the surface of the moon (400 K); (b) the temperature at the tops of the clouds in the atmosphere of Saturn (95 K); (c) the temperature at the center of the sun $(1.55 \times 10{^7} K)$.
According to the label on a bottle of salad dressing, the volume of the contents is 0.473 liter (L). Using only the conversions 1 (L) = 1000 cm$^3$ and 1 in. = 2.54 cm, express this volume in cubic inches.
The African bombardier beetle (Stenaptinus insignis) can emit a jet of defensive spray from the movable tip of its abdomen (Fig. P17.91). The beetle's body has reservoirs containing two chemicals; when the beetle is disturbed, these chemicals combine in a reaction chamber, producing a compound…
(a) By how much would the body temperature of the bicyclist in Problem 17.89 increase in an hour if he were unable to get rid of the excess heat? (b) Is this temperature increase large enough to be serious? To find out, how high a fever would it be equivalent to, in $^\circ$F? (Recall that the…
A fan blade rotates with angular velocity given by $\omega_z$($t$) $= \gamma - \beta t^2$, where $\gamma =$ 5.00 rad/s and $\beta =$ 0.800 rad/s$^3$. (a) Calculate the angular acceleration as a function of time. (b) Calculate the instantaneous angular acceleration $\alpha_z$ at $t =$ 3.00 s and…
The molar heat capacity of a certain substance varies with temperature according to the empirical equation $$C = 29.5 J/mol \cdot K + (8.20 \times 10{^-}{^3} J/mol \cdot K{^2})T$$ How much heat is necessary to change the temperature of 3.00 mol of this substance from 27$^\circ$C to…
(a) What angle in radians is subtended by an arc 1.50 m long on the circumference of a circle of radius 2.50 m? What is this angle in degrees? (b) An arc 14.0 cm long on the circumference of a circle subtends an angle of 128 $^\circ$. What is the radius of the circle? (c) The angle between…
CP A person of mass 70.0 kg is sitting in the bathtub. The bathtub is 190.0 cm by 80.0 cm; before the person got in, the water was 24.0 cm deep. The water is at 37.0$^\circ$C. Suppose that the water were to cool down spontaneously to form ice at 0.0$^\circ$C, and that all the energy released…
You cool a 100.0-g slug of red-hot iron (temperature 745$^\circ$C) by dropping it into an insulated cup of negligible mass containing 85.0 g of water at 20.0$^\circ$C. Assuming no heat exchange with the surroundings, (a) what is the final temperature of the water and (b) what is the final mass…
BIO Shivering. Shivering is your body's way of generating heat to restore its internal temperature to the normal 37$^\circ$C, and it produces approximately 290 W of heat power per square meter of body area. A 68-kg, 1.78-m-tall woman has approximately 1.8 m$^2$ of surface area. How long would…
A typical doughnut contains 2.0 g of protein, 17.0 g of carbohydrates, and 7.0 g of fat. Average food energy values are 4.0 kcal/g for protein and carbohydrates and 9.0 kcal/g for fat. (a) During heavy exercise, an average person uses energy at a rate of 510 kcal/h. How long would you have to…
A steel ring with a 2.5000-in. inside diameter at 20.0$^\circ$C is to be warmed and slipped over a brass shaft with a 2.5020-in. outside diameter at 20.0$^\circ$C. (a) To what temperature should the ring be warmed? (b) If the ring and the shaft together are cooled by some means such as liquid…
A sphere with radius $R =$ 0.200 m has density $\rho$ that decreases with distance $r$ from the center of the sphere according to $r =$ 3.00 $\times$ 103 kg/m$^3 -$ (9.00 $\times$ 103 kg/m$^4$)$r$. (a) Calculate the total mass of the sphere. (b) Calculate the moment of inertia of the sphere for…
A thin, uniform rod is bent into a square of side length $a$. If the total mass is $M$, find the moment of inertia about an axis through the center and perpendicular to the plane of the square. ($Hint$: Use the parallel-axis theorem.)
Human Rotational Energy. A dancer is spinning at 72 rpm about an axis through her center with her arms outstretched ($\textbf{Fig. P9.83}$). From biomedical measurements, the typical distribution of mass in a human body is as follows: Head: 7.0% Arms: 13% (for both) Trunk and legs:…
In $\textbf{Fig. P9.80}$, the cylinder and pulley turn without friction about stationary horizontal axles that pass through their centers. A light rope is wrapped around the cylinder, passes over the pulley, and has a 3.00-kg box suspended from its free end. There is no slipping between the…
In the system shown in Fig. 9.17, a 12.0-kg mass is released from rest and falls, causing the uniform 10.0-kg cylinder of diameter 30.0 cm to turn about a frictionless axle through its center. How far will the mass have to descend to give the cylinder 480 J of kinetic energy?
A thin, light wire is wrapped around the rim of a wheel as shown in Fig. E9.45. The wheel rotates about a stationary horizontal axle that passes through the center of the wheel. The wheel has radius 0.180 m and moment of inertia for rotation about the axle of $I =$ 0.480 kg $\cdot$ m$^2$. A…
The pulley in $\textbf{Fig. P9.76}$ has radius 0.160 m and moment of inertia 0.380 kg $\cdot$ m$^2$. The rope does not slip on the pulley rim. Use energy methods to calculate the speed of the 4.00-kg block just before it strikes the floor.
A surveyor's 30.0-m steel tape is correct at 20.0$^\circ$C. The distance between two points, as measured by this tape on a day when its temperature is 5.00$^\circ$C, is 25.970 m. What is the true distance between the points?
You are making pesto for your pasta and have a cylindrical measuring cup 10.0 cm high made of ordinary glass [$\beta = 2.7 \times 10{^-}{^5}(C^\circ){^-}{^1}]$ that is filled with olive oil [$\beta = 6.8 \times 10{^-}{^4}(C^\circ){^-}{^1}$] to a height of 3.00 mm below the top of the cup.…
A physics student of mass 43.0 kg is standing at the edge of the flat roof of a building, 12.0 m above the sidewalk. An unfriendly dog is running across the roof toward her. Next to her is a large wheel mounted on a horizontal axle at its center. The wheel, used to lift objects from the ground…
A uniform, solid disk with mass $m$ and radius $R$ is pivoted about a horizontal axis through its center. A small object of the same mass $m$ is glued to the rim of the disk. If the disk is released from rest with the small object at the end of a horizontal radius, find the angular speed when…
How I Scales. If we multiply all the design dimensions of an object by a scaling factor $f$, its volume and mass will be multiplied by $f ^3$. (a) By what factor will its moment of inertia be multiplied? (b) If a $\frac{1}{48}$-scale model has a rotational kinetic energy of 2.5 J, what will be…
CP CALC A 250-kg weight is hanging from the ceiling by a thin copper wire. In its fundamental mode, this wire vibrates at the frequency of concert A (440 Hz). You then increase the temperature of the wire by 40 C$^\circ$. (a) By how much will the fundamental frequency change? Will it increase…
Suppose that a steel hoop could be constructed to fit just around the earth's equator at 20.0$^\circ$C. What would be the thickness of space between the hoop and the earth if the temperature of the hoop were increased by 0.500 C$^\circ$?
The hot glowing surfaces of stars emit energy in the form of electromagnetic radiation. It is a good approximation to assume e = 1 for these surfaces. Find the radii of the following stars (assumed to be spherical): (a) Rigel, the bright blue star in the constellation Orion, which radiates…
What is the rate of energy radiation per unit area of a blackbody at (a) 273 K and (b) 2730 K?
You are asked to design a cylindrical steel rod 50.0 cm long, with a circular cross section, that will conduct 190.0 J/s from a furnace at 400.0$^\circ$C to a container of boiling water under 1 atmosphere. What must the rod’s diameter be?
BIO Conduction Through the Skin. The blood plays an important role in removing heat from the body by bringing this energy directly to the surface where it can radiate away. Nevertheless, this heat must still travel through the skin before it can radiate away. Assume that the blood is brought to…
An electric kitchen range has a total wall area of 1.40 m$^2$ and is insulated with a layer of fiberglass 4.00 cm thick. The inside surface of the fiberglass has a temperature of 175$^\circ$C, and its outside surface is at 35.0$^\circ$C. The fiberglass has a thermal conductivity of 0.040 W /m…
It has been argued that power plants should make use of off-peak hours (such as late at night) to generate mechanical energy and store it until it is needed during peak load times, such as the middle of the day. One suggestion has been to store the energy in large flywheels spinning on…
A carpenter builds an exterior house wall with a layer of wood 3.0 cm thick on the outside and a layer of Styrofoam insulation 2.2 cm thick on the inside wall surface. The wood has $k$ = 0.080 W/m $\cdot$ K, and the Styrofoam has $k$ = 0.027 W /m $\cdot$ K. The interior surface temperature is…
A computer disk drive is turned on starting from rest and has constant angular acceleration. If it took 0.0865 s for the drive to make its $second$ complete revolution, (a) how long did it take to make the first complete revolution, and (b) what is its angular acceleration, in rad/s$^2$?
Suppose that the rod in Fig. 17.24a is made of copper, is 45.0 cm long, and has a cross-sectional area of 1.25 cm$^2$. Let T$_H$ = 100.0$^\circ$C and T$_C $= 0.0$^\circ$C. (a) What is the final steady-state temperature gradient along the rod? (b) What is the heat current in the rod in the final…
A vessel whose walls are thermally insulated contains 2.40 kg of water and 0.450 kg of ice, all at 0.0$^\circ$C. The outlet of a tube leading from a boiler in which water is boiling at atmospheric pressure is inserted into the water. How many grams of steam must condense inside the vessel (also…
A 4.00-kg silver ingot is taken from a furnace, where its temperature is 750.0$^\circ$C, and placed on a large block of ice at 0.0$^\circ$C. Assuming that all the heat given up by the silver is used to melt the ice, how much ice is melted?
An insulated beaker with negligible mass contains 0.250 kg of water at 75.0$^\circ$C. How many kilograms of ice at $-$20.0$^\circ$C must be dropped into the water to make the final temperature of the system 40.0$^\circ$C?
You are designing a rotating metal flywheel that will be used to store energy. The flywheel is to be a uniform disk with radius 25.0 cm. Starting from rest at $t =$ 0, the flywheel rotates with constant angular acceleration 3.00 rad/s$^2$ about an axis perpendicular to the flywheel at its…
Evaporation of sweat is an important mechanism for temperature control in some warm-blooded animals. (a) What mass of water must evaporate from the skin of a 70.0-kg man to cool his body 1.00 C$^\circ$? The heat of vaporization of water at body temperature (37$^\circ$C) is $2.42 \times 10{^6}…
A disk of radius 25.0 cm is free to turn about an axle perpendicular to it through its center. It has very thin but strong string wrapped around its rim, and the string is attached to a ball that is pulled tangentially away from the rim of the disk ($\textbf{Fig. P9.59}$). The pull…
What is the amount of heat input to your skin when it receives the heat released (a) by 25.0 g of steam initially at 100.0$^\circ$C, when it is cooled to skin temperature (34.0$^\circ$C)? (b) By 25.0 g of water initially at 100.0$^\circ$C, when it is cooled to 34.0$^\circ$C? (c) What does this…
What must the initial speed of a lead bullet be at 25.0$^\circ$C so that the heat developed when it is brought to rest will be just sufficient to melt it? Assume that all the initial mechanical energy of the bullet is converted to heat and that no heat flows from the bullet to its surroundings.…
An open container holds 0.550 kg of ice at -15.0$^\circ$C. The mass of the container can be ignored. Heat is supplied to the container at the constant rate of 800.0 J/min for 500.0 min. (a) After how many minutes does the ice start to melt? (b) After how many minutes, from the time when the…
A slender rod with length $L$ has a mass per unit length that varies with distance from the left end, where $x =$ 0, according to $dm/dx = \gamma x$, where g has units of kg/m$^2$. (a) Calculate the total mass of the rod in terms of $\gamma$ and $L$. (b) Use Eq. (9.20) to calculate the moment…
How much heat is required to convert 18.0 g of ice at -10.0$^\circ$C to steam at 100.0$^\circ$C? Express your answer in joules, calories, and Btu.
In the situation described in Exercise 17.42, the man's metabolism will eventually return the temperature of his body (and of the soft drink that he consumed) to 37.0$^\circ$C. If his body releases energy at a rate of $7.00 \times 10{^3} kJ/$day (the basal metabolic rate, or BMR), how long does…
BIO Before going in for his annual physical, a 70.0-kg man whose body temperature is 37.0$^\circ$C consumes an entire 0.355-L can of a soft drink (mostly water) at 12.0$^\circ$C. (a) What will his body temperature be after equilibrium is attained? Ignore any heating by the man’s metabolism. The…
A thin, rectangular sheet of metal has mass $M$ and sides of length $a$ and $b$. Use the parallel-axis theorem to calculate the moment of inertia of the sheet for an axis that is perpendicular to the plane of the sheet and that passes through one corner of the sheet.
In a container of negligible mass, 0.200 kg of ice at an initial temperature of -40.0$^\circ$C is mixed with a mass m of water that has an initial temperature of 80.0$^\circ$C. No heat is lost to the surroundings. If the final temperature of the system is 28.0$\circ$C, what is the mass m of the…
About what axis will a uniform, balsa-wood sphere have the same moment of inertia as does a thin-walled, hollow, lead sphere of the same mass and radius, with the axis along a diameter?
Find the moment of inertia of a hoop (a thin-walled, hollow ring) with mass $M$ and radius $R$ about an axis perpendicular to the hoop’s plane at an edge.
BIO Treatment for a Stroke. One suggested treatment for a person who has suffered a stroke is immersion in an ice-water bath at 0$^circ$C to lower the body temperature, which prevents damage to the brain. In one set of tests, patients were cooled until their internal temperature reached…
A 500.0-g chunk of an unknown metal, which has been in boiling water for several minutes, is quickly dropped into an insulating Styrofoam beaker containing 1.00 kg of water at room temperature (20.0$^\circ$C). After waiting and gently stirring for 5.00 minutes, you observe that the water’s…
You have 750 g of water at 10.0$^\circ$C in a large insulated beaker. How much boiling water at 100.0$^\circ$C must you add to this beaker so that the final temperature of the mixture will be 75$^\circ$C?
A uniform 2.00-m ladder of mass 9.00 kg is leaning against a vertical wall while making an angle of 53.0$^\circ$ with the floor. A worker pushes the ladder up against the wall until it is vertical. What is the increase in the gravitational potential energy of the ladder?
CP A 15.0-g bullet traveling horizontally at 865 m/s passes through a tank containing 13.5 kg of water and emerges with a speed of 534 m/s. What is the maximum temperature increase that the water could have as a result of this event?
A thin, light wire is wrapped around the rim of a wheel ($\textbf{Fig. E9.45}$). The wheel rotates without friction about a stationary horizontal axis that passes through the center of the wheel. The wheel is a uniform disk with radius $R$ = 0.280 m. An object of mass $m$ = 4.20 kg is suspended…
A technician measures the specific heat of an unidentified liquid by immersing an electrical resistor in it. Electrical energy is converted to heat transferred to the liquid for 120 s at a constant rate of 65.0 W. The mass of the liquid is 0.780 kg, and its temperature increases from…
A frictionless pulley has the shape of a uniform solid disk of mass 2.50 kg and radius 20.0 cm. A 1.50-kg stone is attached to a very light wire that is wrapped around the rim of the pulley ($\textbf{Fig. E9.43}$), and the system is released from rest. (a) How far must the stone fall so that…
A light, flexible rope is wrapped several times around a $hollow$ cylinder, with a weight of 40.0 N and a radius of 0.25 m, that rotates without friction about a fixed horizontal axis. The cylinder is attached to the axle by spokes of a negligible moment of inertia. The cylinder is initially at…
CP While painting the top of an antenna 225 m in height, a worker accidentally lets a 1.00-L water bottle fall from his lunchbox. The bottle lands in some bushes at ground level and does not break. If a quantity of heat equal to the magnitude of the change in mechanical energy of the water goes…
The flywheel of a gasoline engine is required to give up 500 J of kinetic energy while its angular velocity decreases from 650 rev/min to 520 rev/min. What moment of inertia is required?
A hollow spherical shell has mass 8.20 kg and radius 0.220 m. It is initially at rest and then rotates about a stationary axis that lies along a diameter with a constant acceleration of 0.890 rad/s$^2$. What is the kinetic energy of the shell after it has turned through 6.00 rev?
A compound disk of outside diameter 140.0 cm is made up of a uniform solid disk of radius 50.0 cm and area density 3.00 g/cm$^2$ surrounded by a concentric ring of inner radius 50.0 cm, outer radius 70.0 cm, and area density 2.00 g/cm$^2$. Find the moment of inertia of this object about an axis…
BIO While running, a 70-kg student generates thermal energy at a rate of 1200 W. For the runner to maintain a constant body temperature of 37$^\circ$C, this energy must be removed by perspiration or other mechanisms. If these mechanisms failed and the energy could not flow out of the student’s…
An airplane propeller is 2.08 m in length (from tip to tip) with mass 117 kg and is rotating at 2400 rpm (rev/min) about an axis through its center. You can model the propeller as a slender rod. (a) What is its rotational kinetic energy? (b) Suppose that, due to weight constraints, you had to…
A wagon wheel is constructed as shown in Fig. E9.33. The radius of the wheel is $0.300 \mathrm{~m}$ and the rim has mass $1.40 \mathrm{~kg}$. Each of the eight spokes that lie along a diameter and are $0.300 \mathrm{~m}$ long has mass $0.280 \mathrm{~kg}$. What is the moment of inertia of the…
In an effort to stay awake for an all-night study session, a student makes a cup of coffee by first placing a 200-W electric immersion heater in 0.320 kg of water. (a) How much heat must be added to the water to raise its temperature from 20.0$^\circ$C to 80.0$^\circ$C? (b) How much time is…
You are a project manager for a manufacturing company. One of the machine parts on the assembly line is a thin, uniform rod that is 60.0 cm long and has mass 0.400 kg. (a) What is the moment of inertia of this rod for an axis at its center, perpendicular to the rod? (b) One of your engineers…
An aluminum tea kettle with mass 1.10 kg and containing 1.80 kg of water is placed on a stove. If no heat is lost to the surroundings, how much heat must be added to raise the temperature from 20.0$^\circ$C to 85.0$^\circ$C?
Steel train rails are laid in 12.0-m-long segments placed end to end. The rails are laid on a winter day when their temperature is -9.0$^\circ$C. (a) How much space must be left between adjacent rails if they are just to touch on a summer day when their temperature is 33.0$^\circ$C? (b) If the…
Four small spheres, each of which you can regard as a point of mass 0.200 kg, are arranged in a square 0.400 m on a side and connected by extremely light rods ($\textbf{Fig. E9.28}$). Find the moment of inertia of the system about an axis (a) through the center of the square, perpendicular to…
According to the shop manual, when drilling a 12.7-mm-diameter hole in wood, plastic, or aluminum, a drill should have a speed of 1250 rev/min. For a 12.7-mm-diameter drill bit turning at a constant 1250 rev/min, find (a) the maximum linear speed of any part of the bit and (b) the maximum…
A machinist bores a hole of diameter 1.35 cm in a steel plate that is at 25.0$^\circ$C. What is the cross-sectional area of the hole (a) at 25.0$^\circ$C and (b) when the temperature of the plate is increased to 175$^\circ$C? Assume that the coefficient of linear expansion remains constant over…
An advertisement claims that a centrifuge takes up only $0.127 \mathrm{~m}$ of bench space but can produce a radial acceleration of $3000 \mathrm{~g}$ at 5000 rev $/ \mathrm{min}$. Calculate the required radius of the centrifuge. Is the claim realistic?
A geodesic dome constructed with an aluminum framework is a nearly perfect hemisphere; its diameter measures $55.0 \mathrm{~m}$ on a winter day at a temperature of $-15^{\circ} \mathrm{C}$. How much more interior space does the dome have in the summer, when the temperature is $35^{\circ}…
One of the tallest buildings in the world is the Taipei 101 in Taiwan, at a height of 1671 feet. Assume that this height was measured on a cool spring day when the temperature was 15.5$^\circ$C. You could use the building as a sort of giant thermometer on a hot summer day by carefully measuring…
The Humber Bridge in England has the world's longest single span, 1410 m. Calculate the change in length of the steel deck of the span when the temperature increases from -5.0$^\circ$C to 18.0$^\circ$C.
Using Appendix F, along with the fact that the earth spins on its axis once per day, calculate (a) the earth’s orbital angular speed (in rad/s) due to its motion around the sun, (b) its angular speed (in rad/s) due to its axial spin, (c) the tangential speed of the earth around the sun…
Like the Kelvin scale, the Rankine scale is an absolute temperature scale: Absolute zero is zero degrees Rankine (0$^\circ$R). However, the units of this scale are the same size as those of the Fahrenheit scale rather than the Celsius scale. What is the numerical value of the triple-point…
At $t =$ 0 a grinding wheel has an angular velocity of 24.0 rad/s. It has a constant angular acceleration of 30.0 rad/s$^2$ until a circuit breaker trips at $t =$ 2.00 s. From then on, it turns through 432 rad as it coasts to a stop at constant angular acceleration. (a) Through what total angle…
An experimenter using a gas thermometer found the pressure at the triple point of water (0.01$^\circ$C) to be $4.80 \times 10{^4} Pa$ and the pressure at the normal boiling point (100$^\circ$C) to be $6.50 \times 10{^4} Pa$. (a) Assuming that the pressure varies linearly with temperature, use…
A high-speed flywheel in a motor is spinning at 500 rpm when a power failure suddenly occurs. The flywheel has mass 40.0 kg and diameter 75.0 cm. The power is off for 30.0 s, and during this time the flywheel slows due to friction in its axle bearings. During the time the power is off, the…
A circular saw blade 0.200 m in diameter starts from rest. In 6.00 s it accelerates with constant angular acceleration to an angular velocity of 140 rad/s. Find the angular acceleration and the angle through which the blade has turned.
(a) Derive Eq. (9.12) by combining Eqs. (9.7) and (9.11) to eliminate $t$. (b) The angular velocity of an airplane propeller increases from 12.0 rad/s to 16.0 rad/s while turning through 7.00 rad. What is the angular acceleration in rad/s$^2$?
You put a bottle of soft drink in a refrigerator and leave it until its temperature has dropped 10.0 K. What is its temperature change in (a) F$^\circ$ and (b) C$^\circ$?
A wheel is rotating about an axis that is in the $z$-direction.The angular velocity $\omega_z$ is $-$6.00 rad/s at $t =$ 0, increases linearly with time, and is $+$4.00 rad/s at $t =$ 7.00 s. We have taken counterclockwise rotation to be positive. (a) Is the angular acceleration during this…
(a) On January 22, 1943, the temperature in Spearfish, South Dakota, rose from -4.0$^\circ$F to 45.0$^\circ$F in just 2 minutes. What was the temperature change in Celsius degrees? (b) The temperature in Browning, Montana, was 44.0$^\circ$F on January 23, 1916. The next day the temperature…
BIO Temperatures in Biomedicine. (a) Normal body temperature. The average normal body temperature measured in the mouth is 310 K. What would Celsius and Fahrenheit thermometers read for this temperature? (b) Elevated body temperature. During very vigorous exercise, the body’s temperature can go…
An airplane propeller is rotating at 1900 rpm (rev/min). (a) Compute the propeller's angular velocity in rad/s. (b) How many seconds does it take for the propeller to turn through 35 $^\circ$?
Convert the following Celsius temperatures to Fahrenheit: (a) -62.8$^\circ$C, the lowest temperature ever recorded in North America (February 3, 1947, Snag, Yukon); (b) 56.7$^\circ$C, the highest temperature ever recorded in the United States (July 10, 1913, Death Valley, California); (c)…
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