College Physics 2013

Water in human body About two-thirds of your body mass consists of water. Determine the volume of water in a 70-kg person.

Determine the average density of Earth. What data did you use? What assumptions did you make?

Use data for the normal pressure and the density of air near Earth’s surface to estimate the height of the atmosphere, assuming it has uniform density. Indicate any additional assumptions you made. Are you on the low or high side of the real number?

A single-level home has a floor area of 200 $m^{2}$ with ceilings that are 2.6 $m$ high. Estimate the mass of the air in the house.

A diet decreases a person’s mass by 5%. Exercise creates muscle and reduces fat, thus increasing the person’s density by 2%. Determine the percent change in the person’s volume.

Pulsar density A pulsar, an extremely dense rotating star made of neutrons, has a density of $10^{18} kg/m^{3} .$ Determine the mass of a pulsar contained in a volume the size of your fist (about 200 $cm^{3} )$

A graduated cylinder sitting on a platform scale is filled in steps with oil. The mass of oil versus its volume is reported in Table 10.6. Make a mass-versus-volume graph for the oil and from the graph determine its density.

Use the graph lines in Figure P 10.8 to determine the densities of the three liquids in SI units. If you place them in one container, how will they position themselves? How does the density of each liquid change as its volume increases? As its mass decreases? Compare the masses of the three liquids when they occupy the same volume. Compare the volumes of the three liquids when they have the same mass.

Imagine that you have gelatin cut into three cubes: the side of cube A is a cm long, the side of cube B is double the side of A, and the side of cube C is three times the side of A. Compare the following properties of the cubes: (a) density, (b) volume, (c) surface area, (d) cross-sectional area, and (e) mass.

Determine the density of the material whose mass-versus- volume graph line is shown in Figure P 10.10. If you double the mass of this substance, what will happen to its density? What substance might this be?

An object made of material A has a mass of 90 kg and a volume of 0.45 $m^{3}$. If you cut the object in half, what would be the density of each half? If you cut the object into three pieces, what would be the density of each piece? What assumptions did you make?

You have a steel ball that has a mass of 6.0 kg and a volume of $3.0 \times 10^{-3} m^{3} .$ How can this be?

A material is made of molecules of mass $2.0 \times 10^{-26} kg$ . There are $2.3 \times 10^{29}$ of these molecules in a $2.0-m^{3}$ volume. What is the density of the material?

You compress all the molecules described in Problem 13 into 1.0 $m^{3} .$ Now what is the density of the material? What type of material could possibly behave this way?

Bowling balls are heavy. However, some bowling balls float in water. Use available resources to find the dimensions of a bowling ball and explain why some balls float while others do not.

Estimate the average density of a glass full of water and then the glass when the water is poured out (do not forget the air that now fills the glass instead of water).

Anita holds her physics textbook and complains that it is too heavy. Andrew says that her hand should exert no force on the book because the atmosphere pushes up on it and balances the downward pull of Earth on the book (the book’s weight). Jim disagrees. He says that the atmosphere presses down on things and that is why they feel heavy. Who is correct? Approximately how large is the force that the atmosphere exerts on the bottom of the book? Why does this force not balance the force exerted by Earth on the book?

Estimate the force exerted by Earth’s atmosphere on the state where you are taking your physics course.

The air pressure in the tires of a 980 -kg car is $3.0 \times 10^{5} N/m^{2} .$ Determine the average area of contact of each tire with the road.

Estimate the pressure that you exert on the floor while wearing hiking boots. Now estimate the pressure under each heel if you change into high-heeled shoes. Indicate any assumptions you made.

You are designing a hydraulic lift for a machine shop. The average mass of a car it needs to lift is about 1500 kg. What should be the specifications on the dimension of the pistons if you wish to exert a force on a smaller piston of not more than 500 N? How far down will you need to push the piston in order to lift the car 30 cm?

Venus pressure and underwater pressure Atmospheric pressure on Venus is $9.0 \times 10^{6} N/ m^{2} .$ How deep underwater on Earth would you have to go to feel the same pressure?

Estimate the force that air exerts on your forehead. Describe the assumptions you made.

A cylindrical iron plunger is held against the ceiling, and the air is pumped from inside it. A 72-kg person hangs by a rope from the plunger (Figure P 10.24). List the quantities that you can determine about the situation and determine them. Make assumptions if necessary.

You have a rubber pad with a handle attached to it (Figure P 10.25). If you press the pad firmly on a smooth table, it is impossible to lift it off the table. Why? What force would you need to exert on the handle to lift it? The surface area of the pad is 0.023 $m^{2}$

You vacuum up a small piece of paper on the floor. Draw a force diagram for the paper just as it is being lifted up into the vacuum cleaner.

A child’s toy arrow has a suction cup on one end. When the arrow hits the wall, it sticks. Draw a force diagram for the arrow stuck on the wall and estimate the magnitudes of the forces exerted on it when it is in equilibrium. The mass of the arrow is about 10 g. Why are the words “suction cup” not appropriate?

The Titanic rests 4 km (2.5 miles) below the surface of the ocean. What physical quantities can you determine using this information?

You have three reservoirs (Figure P 10.29). Rank the pressures at the bottom of each and explain your rankings. Then rank the net force that the water exerts on the bottom of each reservoir. Explain your rankings.

A bucket filled to the top with water has a piece of ice floating in it. (a) Will the pressure on the bottom of the bucket change when the ice melts? Explain. (b)Will the level of water rise when the ice melts? Explain.

Water reservoir and faucet The pressure at the top of the water in a city's gravity-fed reservoir is $1.0 \times 10^{5} N /m^{2} .$ Determine the pressure at the faucet of a home 42 $m$ below the reservoir.

An old story tells of a Dutch boy who used his fist to plug a 2.0-cm-diameter hole in a dike that was 3.0 m below sea level, thus preventing the flooding of part of Holland. What physical quantities can you determine from this information? Determine them.

Estimate the pressure of the blood in your brain and in your feet when standing, relative to the average pressure of the blood in your heart of $1.3 \times 10^{4}-N/m^{2}$ above atmospheric pressure.

A glucose solution of density 1050 $kg/m^{3}$ is transferred from a collapsible bag through a tube and syringe into the vein of a person’s arm. The pressure in the arm exceeds the atmospheric pressure by 1400 $N/m^{2}$. How high above the arm must the top of the liquid in the bottle be so that the pressure in the glucose solution at the needle exceeds the pressure of the blood in the arm? Ignore the pressure drop across the needle and tubing due to viscous forces.

Determine the change in air pressure as you climb from elevation of 1650 m at the timberline of Mount Rainier to its 4392-m summit, assuming an average air density of 0.82 $kg/m^{3} .$ Will the real change be more or less than the one you calculated? Explain.

Estimate the pressure change of the blood in the brain of a giraffe when it lifts its head from the grass to eat a leaf on an overhead tree. Without special valves in its circulatory system, the giraffe could easily faint when lifting its head.

Your car slides off an embankment into a pond. Estimate the force you must exert on the door to open
it if the top of the door is 0.5 m below the surface. Describe in detail how you might escape without opening the door.

You are drinking water through a straw in an open glass. Select a small volume of water in the straw as a system and draw a force diagram for the water in- side this volume that explains why the water goes up the straw.

While you are drinking through the straw, the pressure in your mouth is 30 mm Hg below atmospheric pressure. What is the maximum length of a straw in an open glass that you can use to drink a fruit drink of density 1200 $kg /m^{3} ?$

Your office has a 0.020 $m^{3}$ cylindrical container of drinking water. The radius of the container is about 14 cm. When the container is full, what is the pressure that the water exerts on the sides of the container halfway down from the top? All the way down?

Estimate the net force on your $0.5-cm^{2}$ eardrum that air exerts on the inside and the outside after you drive from Denver, Colorado (elevation 1609 m) to the top of Pikes Peak (elevation 4301 m). Assume that the air pressure inside and out are balanced when you leave Denver and that the average density of the air is 0.80 $kg/m^{3}$. What other assumptions did you make?

You now go snorkeling. What is the pressure on your eardrum when you are 2.4 m under the water, assuming the pressure was equalized before the dive?

Water and oil are poured into opposite sides of an open U-shaped tube. The oil and water meet at the exact center of the U at the bottom of the tube. If the column of oil of density 900 $kg/m^{3}$
is 16 cm high on one side, how high is the water on the other side?

Examine the photo of Hoover Dam (Figure P 10.44). What do you notice about its vertical structure? Explain why a dam is thicker at the bottom than at the top.

A test tube of length L and cross-sectional area A is submerged in water with the open end down so that the edge of the tube is a distance h below the surface. The water goes up into the tube so its height inside the tube is $l.$ Describe how you can use this information to decide whether the air that was initially in the tube obeys Boyle’s law. List your assumptions.

The reading of a barometer in your room is 780 mm Hg. What does this mean? What is the pressure in pascals?

How long would Torricelli's barometer have had to be if he had used oil of density 950 $kg/m^{3}$ instead of mercury?

Sometimes gas pressure is measured with a device called a liquid manometer (Figure P 10.48). Explain how this instrument can be used to measure the pressure of gas in a bulb attached to one of the tubes.

You use a liquid manometer with water to measure the pressure inside a rubber bulb. Before you squeeze the bulb, the water is at the same level in both legs of the tube. After you squeeze the bulb,
the water in the opposite leg rises 20 cm with respect to the leg connected to the bulb (Figure P 10.49). What is the pressure in the bulb? What assumptions did you make? How will the answer change if the assumptions are not valid?

In a mercury-filled manometer (Figure P 10.50), the open end is inserted into a container of gas and the closed end of the tube is evacuated. The difference in the height of the mercury is 80 mm. The radius of the connecting tube is 0.50 cm. (a) Determine the pressure inside the container in newtons per square meter. (b) An identical manometer has a connecting tube that is twice as wide. If the difference in the height of the mercury is the same, then what is the pressure in the container?

A liquid manometer contains two liquids. Liquid A on the left side is $h$ meters higher $(h<<1.0 m$ than the liquid on the right side. What do you know about those two liquids? What assumptions did you make? If the assumptions were not true, how would the answer be different?

Examine the reading of the manometer that you use to measure the pressure inside car tires. What are the units? Does the manometer measure the absolute pressure of the air inside the tires or gauge pressure? How do you know?

Marjory thinks that the mass of a liquid above a certain level should affect the pressure at this level. Describe how you will test her idea.

Draw a force diagram for an object that is floating at the surface of a liquid.

Draw a cubic object that is completely submerged in a fluid but not resting on the bottom of the container. Then draw arrows to represent the forces exerted by the fluid on the top, sides, and bottom of the object. Make the arrows the correct relative lengths. What is the direction of the total force exerted by the fluid on the object?

Draw a force diagram for a helium balloon that you just released. Then draw a force diagram for an air-filled balloon that you just released.

You are holding a brick that is completely submerged in water. Draw a force diagram for the brick. Why does it feel lighter in water than when you hold it in the air?

This textbook says that the upward force that a fluid exerts on a submerged object is equal in magnitude to the product of the density of the fluid, the gravitational constant g, and the volume of the submerged part of the object. Where did this equation come from?

This textbook says that the upward force that a fluid exerts on a submerged object is equal in magnitude to the product of the density of the fluid, the gravitational constant g, and the volume of the submerged part of the object. Design an experiment to test this expression, including a prediction about the outcome of the experiment.

You have four objects at rest, each of the same volume. Object A is partially submerged, and objects B, C, and D are totally submerged in the same container of liquid, as shown in Figure P 10.60. Draw a force diagram for each object. Rank the densities of the objects from least to greatest and indicate whether any objects have the same density.

Does air affect what a scale reads? A 60 -kg woman with a density of 980 $kg / m^{3}$ stands on a bathroom scale. Determine the reduction of the scale reading due to air.

When analyzing a sample of ore, a geologist finds that it weighs 2.00 N in air and 1.13 N when immersed in water. What is the density of the ore? What assumptions did you make to answer the question? If the assumptions are not correct, how would the answer be different?

A pin through a hole in the middle supports a meter stick. Two identical blocks hang from strings at an equal distance from the center so the stick is balanced. What happens to the stick if one block is submerged in water of density 1000 $kg/ m^{3}$ and the other block in kerosene of density 850 $kg/m^{3}$ ?

A meter stick is supported by a pin through a hole in the middle. (a) Two blocks made of the same material but different sizes hang from strings at different positions in such a way that the stick balances. What happens when the blocks hang entirely submerged in beakers of water? (b) Next you hang two blocks of different masses but the same volume at different positions so the stick balances. What happens when these blocks hang completely submerged in beakers of water? Support your answer for each part using force diagrams with arrows drawn with the correct relative lengths.

Goose on a lake A 3.6 -kg goose floats on a lake with 40$\%$ of its body below the $1000-kg/ m^{3}$ water level. Determine the density of the goose.

Floating in seawater A person of density of $\rho_{1}$ floats in seawater of density $\rho_{2} .$ What fraction of the person's body is
? Explain.

Floating in seawater A person of density of 980 $kg/m^{3}$ floats in seawater of density 1025 $kg/m^{3} .$ What can you determine using this information? Determine it.

(a) Determine the force that a vertical string exerts on a 0.80-kg rock of density of 3300 $kg / m^{3}$ when it is fully submerged in water of density 1000 $kg /m^{3} .(b)$ If the force exerted by the string supporting the rock increases by 12% when the rock is submerged in a different fluid, what is that fluid’s density? (c) If the density of another rock of the same volume is 12% greater, what happens to the buoyant force the water exerts on it?

Snorkeling A 60 -kg snorkeler (including snorkel, mask, and other gear) displaces 0.058 $m^{3}$ of water when 1.2 $m$ under the surface. Determine the magnitude of the buoyant force exerted by the $1025-kg /m^{3}$ seawater on the person. Will the person sink or drift upward?

A helium balloon of volume 0.12 $m^{3}$ has a total mass (the helium plus the balloon) of 0.12 $kg$ . Determine the buoyant force exerted on the balloon by the air if the air has density 1.13 $kg /m^{3}$ . Determine the initial acceleration of the balloon when released.

A bucket filled to the top with water has a piece of ice floating in it. Will the pressure on the bottom change when the ice melts? Justify your answer.

A protein molecule of mass 1.1 $\times 10^{-22} kg$ and density $1.3 \times 10^{3} kg/m^{3}$ is placed in a vertical tube of water of density 1000 $kg / m^{3} .$ (a) Draw a motion diagram and a force diagram at the moment immediately after the molecule is released. (b) Determine the initial acceleration of the protein.

How can you determine if a steel ball of known radius is hollow? List the equipment that you will need for the experiment, and describe the procedure and calculations. Can you determine how big the hollow part is if present in the ball?

A crown is made of gold and silver. The scale reads its mass as 3.0 $kg$ when in air and 2.75 $kg$ when in water. Determine the masses of the gold and the silver in the crown. The density of gold is $19,300 kg/ m^{3}$ and that of silver is $10,500 kg/m^{3}$ .

Wood raft Logs of density 600 $kg /m^{3}$ are used to build a raft. What is the weight of the maximum load that can be sup- ported by a raft built from 300 $kg$ of of logs?

A cylinder has radius R. How high should a column of liquid be so that the magnitude of the force averaged over the side wall surface area that the liquid exerts on the wall equals the magnitude of the force that the liquid exerts on the bottom surface of the cylinder? Explain.

A log is L long and d in diameter. What is the mass of a person who can stand on the log without getting her feet wet?

A ferryboat is 12 m long and 8 m wide. Two cars, each of mass 1600 kg, ride on the boat for transport across the lake. How much farther does the boat sink into the water?

Estimate the fraction of the volume of an iceberg that is underwater.

A life preserver is manufactured to support a 70-kg person with 20% of his volume out of the water. If the density of the life preserver is 100 $kg/ m^{3}$ and it is completely submerged, what must its volume be? List your assumptions.

Compare the density of water at $0^{\circ} C$ to the density of ice at $0^{\circ} C$ . Suggest possible explanations in terms of the molecular arrangements inside the liquid and solid forms of water that would account for the difference. If necessary, use extra re- sources to help answer the question.

The radius of a collapsing star destined to become a pulsar decreases by 10% while at the same time 12% of its mass escapes. Determine the percent change in its density.

You are getting a flu shot. Estimate the average pressure of the fluid entering your arm during the shot. Indicate any assumptions you made. Compare this to the pressure of your shoes on the ground when standing.

Explain qualitatively and quantitatively how we drink through a straw. Make sure you can account for the water going up the length of the straw.

The Trieste research submarine traveled 10.9 km below the ocean surface while exploring the Mariana Trench in the South Pacific, the deepest place in the ocean. Determine the force needed to prevent a 0.10-m-diameter window on the side of the submarine from imploding. The density of the water is 1025 $kg / m^{3}$

Pascal placed a long 0.20-cm-radius tube in a wine barrel of radius 0.24 m. He sealed the barrel where the tube entered it. When he added wine of density 1050 $kg/m^{3}$ to the tube so the column of wine was 8.0 $m$ high, the cover of the barrel burst off the top of the barrel. What was the net force that caused the cover to come off?

Experimentally determine the maximum distance you can suck water up a straw. Use this number to determine the pressure in your lungs above or below atmospheric pressure while you are sucking. Be sure to indicate any assumptions you made and show clearly how you reached your conclusion.

Atmospheric pressure on Venus is $92 \times 10^{5} N/m^{2} .$ Suppose that NASA is planning to land a 1.0 -m-radius spherical research vehicle on Venus. (a) Determine the force on each square centimeter of its surface. (b) What is the buoyant force exerted by the atmosphere on the spherical vehicle?

You have an empty water bottle. Predict how much mass you need to add to it to make it float half-submerged. Then add the calculated mass and explain any discrepancy that you found. How did you make your prediction?

A 1.0-kg fish of density 1025 $kg/m^{3}$ is in water of the same density. The fish's bladder contains $10 cm^{3}$ of air. The bladder compresses to $4 cm^{3},$ reducing its volume by $6 cm^{3} .$ Now what is the density of the fish? Will it sink or rise? Explain.

When a 27,000-kg fighter airplane lands on the deck of the aircraft carrier Nimitz, the carrier sinks 0.25 cm deeper into the water. Determine the cross-sectional area of the carrier.

To determine the density of an object and an unknown liquid, it is first weighed in air, then in water, and then in an unknown liquid. The readings of the scale are $T_{1}, T_{2},$ and $T_{3}$ respectively. Suggest a method of using these data to determine the density of the object and of the liquid. Decide what additional equipment and measurements you would need to make to test whether the results of the first method are correct.

Two upward-moving balloons carry equal loads. The first balloon has an upward acceleration of $(g / 3) .$ The second balloon moves up at constant speed. The density of the gas inside both balloons is one-third the density of air. The volume of the first balloon is $V_{1}$ . What is the volume of the second balloon? The masses of the balloons are the same.

Derive an equation for determining the unknown density of a liquid by measuring the magnitude of a force $T_{S}$ on $O$ that a string needs to exert on a hanging object of unknown mass m and density r to support it when the object is submerged in the liquid. string needs to exert on a hanging object of unknown mass $m$ and density $\rho$ to support it when the object is submerged in the liquid.

The pressure of the water when Musimu was 209.6 m below the surface was closest to which of the following?

$\begin{array}{ll}{\text { (a) } 2 \mathrm{atm}} & {\text { (b) } 3 \text { atm }} & {\text { (c) } 21 \text { atm }} \\ {\text { (d) } 22 \mathrm{atm}} & {\text { (e) } 200 \mathrm{atm}}\end{array}$

Assuming Musimu weighs 670 N (150 lb) and is 1.6 m tall, 0.30 m wide, and 0.15 m thick, which answer below is closest to the magnitude of the force that the deep water exerted on one side of his body?

(a) 0
(b) 670 $N(130 lb)$
(c) 15,000 N (3000 lb)
(d) $10^{5} N(20,000 lb)$
(e) $10^{6} N(200,000 lb)$

Musimu's training allows him to hold up to $9 L=9000 cm^{3}$ of air when in a 1 atm environment. Which answer below is closest to the volume of that air if at pressure 22 atm?

$\begin{array}{ll}{\text { (a) } 100 \mathrm{cm}^{3}} & {\text { (b) } 200 \mathrm{cm}^{3}} & {\text { (c) } 400 \mathrm{cm}^{3}} \\ {\text { (d) } 9000 \mathrm{cm}^{3}} & {\text { (e) } 2 \times 10^{5} \mathrm{cm}^{3}}\end{array}$

As Musimu descends, the buoyant force that the water exerts on him

(a) remains approximately constant.
(b) increases a lot because the pressure is so much greater.
(c) decreases significantly because his body is being compressed and made much smaller.
(d) is zero for the entire dive.
(e) There is not enough information to answer the question.

Why don’t his lungs, heart, and chest completely collapse?

(a) The return balloon helps counteract the external pressure.
(b) There is no external force pushing directly on the organs.
(c) The sled that helps him descend protects the front of his body.
(d) Blood plasma moves from his extremities to his chest and the organs in it.
(e) The air originally in the lungs is transferred to the vital organs.

Using the dimensions in Question 96, which answer below is closest to the buoyant force that the water exerts on Musimu (without his sled or his return balloon)? Assume that the density of water is 1000 $kg / m^{3}$

$\begin{array}{ll}{\text { (a) } 200 \mathrm{N}} & {\text { (b) } 400 \mathrm{N}} & {\text { (c) } 700 \mathrm{N}} \\ {\text { (d) } 1000 \mathrm{N}} & {\text { (e) } 2 \times 10^{6} \mathrm{N}}\end{array}$

When is water denser?

(a) When liquid at $0^{\circ} C$
(b) When solid ice at $0^{\circ} C$
(c) Water is always 1000 $kg/m^{3}$.
(d) When it is near room temperature.

Why does water freeze from the top down?

(a) The denser water at $0^{\circ} C$ sinks below the ice.
(b) The less dense ice at $0^{\circ} C$ rises above the liquid water at $0^{\circ} C$
(c) The solid ice is denser than the liquid, just like for metals.
(d) a and b
(e) a, b, and c

Using Newton’s second law, expressions for buoyant force and other forces, and the densities of liquid and solid water at $0^{\circ} C$, find the fraction of an iceberg or an ice cube that is under liquid water.

$\begin{array}{ll}{\text { (a) } 0.84} & {\text { (b) } 0.88} & {\text { (c) } 0.92} \\ {\text { (d) } 0.96} & {\text { (e) } 1.00}\end{array}$

A swimming pool at $0^{\circ} C$ has a very large chunk of ice floating in it-like an iceberg in the ocean. When the ice melts, what happens to the level of the water at the edge of the pool?

(a) It rises. (b) It stays the same.
(c) It drops. (d) It depends on the size of the chunk.

Which of the following are benefits of the decrease in the density of water when it freezes?

(a) Fish and plants can survive winters without being frozen.
(b) Over time, soil is formed from sedimentary rocks.
(c) Water pipes when frozen in the winter do not burst.
(d) Two of the above three.
(e) All of the first three.