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Physics for Scientist and Engineers: A Strategic Approach

Randall Knight

Chapter 11

Work - all with Video Answers

Educators

Chapter Questions

02:34

Problem 1

Evaluate the dot product of the three pairs of vectors in (FIGURES CANNOT COPY)

Dale Sanford
Dale Sanford
Numerade Educator
02:58

Problem 2

Evaluate the dot product of the three pairs of vectors in (FIGURES CANNOT COPY)

Dale Sanford
Dale Sanford
Numerade Educator
02:00

Problem 3

Evaluate the dot product $\overrightarrow{\boldsymbol{A}} \cdot \overrightarrow{\boldsymbol{B}}$ if
a. $\vec{A}=3 \hat{i}-4 \hat{j}$ and $\vec{B}=-2 \hat{i}+6 \hat{j}$
b. $\vec{A}=2 \hat{i}+3 \hat{j}$ and $\vec{B}=6 \hat{i}-4 \hat{j}$

Dale Sanford
Dale Sanford
Numerade Educator
01:55

Problem 4

Evaluate the dot product $\vec{A} \cdot \vec{B}$ if
a. $\vec{A}=4 \hat{i}+2 \hat{j}$ and $\vec{B}=-3 \hat{i}-2 \hat{j}.$
b. $\vec{A}=-4 \hat{i}+2 \hat{j}$ and $\vec{B}=-\hat{i}-2 \hat{j}.$

Dale Sanford
Dale Sanford
Numerade Educator
04:08

Problem 5

What is the angle $\theta$ between vectors $\overrightarrow{\boldsymbol{A}}$ and $\overrightarrow{\boldsymbol{B}}$ in each part of Exercise $3 ?$

Dale Sanford
Dale Sanford
Numerade Educator
02:23

Problem 6

What is the angle $\theta$ between vectors $\vec{A}$ and $\vec{B}$ in each part of Exercise 47.

Mayukh Banik
Mayukh Banik
Numerade Educator
00:41

Problem 7

How much work is done by the force $\vec{F}=(6.0 \hat{\imath}-3.0 \hat{\jmath}) \mathrm{N}$ on a particle that moves through displacement (a) $\Delta \vec{r}=2.0 \hat{\imath} \mathrm{m}$ and (b) $\Delta \vec{r}=20 \hat{j} \mathrm{m} ?$

Mayukh Banik
Mayukh Banik
Numerade Educator
01:06

Problem 8

How much work is done by the force $\vec{F}=(-4,0 \hat{\imath}-6.0 \hat{\jmath}) \mathrm{N}$ on a particle that moves through displacement (a) $\Delta \vec{r}=3.0 \hat{\imath} \mathrm{m}$ and (b) $\Delta \vec{r}=(-3.0 \hat{\imath}+2.0 \hat{\jmath}) \mathrm{m} ?$

Mayukh Banik
Mayukh Banik
Numerade Educator
01:08

Problem 9

A 20 g particle is moving to the left at 30 m/s. How much net work must be done on the particle to cause it to move to the right at $30 \mathrm{m} / \mathrm{s} ?$

Mayukh Banik
Mayukh Banik
Numerade Educator
02:50

Problem 10

A $2.0 \mathrm{kg}$ book is lying on a $0.75-\mathrm{m}$ -high table. You pick it up and place it on a bookshelf 2.25 m above the floor.
a. How much work does gravity do on the book?
b. How much work does your hand do on the book?

Nishant Kumar
Nishant Kumar
Numerade Educator
02:05

Problem 11

The two ropes secn in RiGules FIGURE EX 11.11 are used to lower a $255 \mathrm{kg}$ piano $5.00 \mathrm{m}$ from a second-story window to the ground. How much work is done by each of the three forces? (FIGURE CANNOT COPY)

Mayukh Banik
Mayukh Banik
Numerade Educator
01:06

Problem 12

The three ropes shown in the bird's-eye view of FIGURE EX 11.12 are used to drag a crate 3.0 m across the floor. How much work is done by each of the three forces?

Mayukh Banik
Mayukh Banik
Numerade Educator
02:10

Problem 13

FIGURE EX11.13, is the velocity- versus-time graph for a $2.0 \mathrm{kg}$ object moving along the $x$ -axis. Determine the work done on the object during each of the five intervals $A B, B C, C D, D B,$ and $\mathrm{EF}.$ (GRAPH CANNOT COPY)

Mayukh Banik
Mayukh Banik
Numerade Educator
02:01

Problem 14

FIGURE EX11.14 is the force-versus-position graph for a particle moving along the $x$ -axis. Determine the work done on the particle during each of the three intervals $0-1 \mathrm{m}, 1-2 \mathrm{m},$ and $2-3 \mathrm{m}.$ (GRAPH CANNOT COPY)

Mayukh Banik
Mayukh Banik
Numerade Educator
03:37

Problem 15

A 500 g particle moving along the $x$ -axis experiences the force shown in FIGURE EX11.15 The particle's velocity is $2.0 \mathrm{m} / \mathrm{s}$ at $x=0 \mathrm{m} .$ What is its velocity at $x=1 \mathrm{m}, 2 \mathrm{m},$ and $3 \mathrm{m} ?$

Mayukh Banik
Mayukh Banik
Numerade Educator
02:55

Problem 16

A $2.0 \mathrm{kg}$ particle moving along the $x$ -axis experiences the force shown in FIGURE EX11.16 The particle's velocity is $4.0 \mathrm{m} / \mathrm{s}$ at $x=0 \mathrm{m} .$ What is its velocity at $x=2 \mathrm{m}$ and $4 \mathrm{m} ?$ (GRAPH CANNOT COPY)

Mayukh Banik
Mayukh Banik
Numerade Educator
01:16

Problem 17

A 500 g particle moving along the $x$ -axis experiences the force shown in FIGURE EX11.17, The particle goes from $v_{x}=2.0 \mathrm{m} / \mathrm{s}$ at $x=0 \mathrm{m}$ to $v_{x}=6.0 \mathrm{m} / \mathrm{s}$ at $x=2 \mathrm{m} .$ What is $F_{\max } ?$

Mayukh Banik
Mayukh Banik
Numerade Educator
03:01

Problem 18

A particle has the potential energy shown in FIGURE EX11.18 What is the $x$ -component of the force on the particle at $x=5$ $15,25,$ and $35 \mathrm{cm} ?$ (GRAPH CANNOT COPY)

Mayukh Banik
Mayukh Banik
Numerade Educator
02:01

Problem 19

A particle has the potential energy shown in FIGURE EX11.19, What is the $x$ -component of the force on the particle at $x=1 \mathrm{m}$ and $4 \mathrm{m} ?$

Mayukh Banik
Mayukh Banik
Numerade Educator
02:04

Problem 20

A particle moving along the $y$ -axis has the potential energy $U=4 y^{3} \mathrm{J},$ where $y$ is in $\mathrm{m}$
a. Graph the potential energy from $y=0$ m to $y=2$ m.
b. What is the $y$ -component of the force on the particle at $y=0 \mathrm{m}_{1} 1 \mathrm{m}_{1}$ and $2 \mathrm{m} ?$

Mayukh Banik
Mayukh Banik
Numerade Educator
02:28

Problem 21

A particle moving along the $x$ -axis has the potential energy $U=10 / x \mathrm{J},$ where $x$ is in $\mathrm{m}$
a. Graph the potential energy from $x=1$ m to $x=10$ m.
b. What is the $x$ -component of the force on the particle at $x=2 \mathrm{m}, 5 \mathrm{m},$ and $8 \mathrm{m} ?$

Mayukh Banik
Mayukh Banik
Numerade Educator
02:05

Problem 22

The mass of a carbon atom is $2.0 \times 10^{-26} \mathrm{kg}$.
a. What is the kinetic energy of a carbon atom moving with a speed of $500 \mathrm{m} / \mathrm{s} ?$
b. Two carbon atoms are joined by a spring-like carbon-carbon bond. The potential energy stored in the bond has the value you calculated in part a if the bond is stretched $0.050 \mathrm{nm}$. What is the bond's spring constant?

Mayukh Banik
Mayukh Banik
Numerade Educator
01:12

Problem 23

In Part IV you'll learn to calculate that 1 mole $(6.02 \times$ $10^{23}$ atoms) of helium atoms in the gas phase has $3700 \mathrm{J}$ of microscopic kinetic energy at room temperature. If we assume that all atoms move with the same speed, what is that speed? The mass of a helium atom is $6.68 \times 10^{-27} \mathrm{kg}.$

Mayukh Banik
Mayukh Banik
Numerade Educator
02:26

Problem 24

A 1500 kg car traveling at $20 \mathrm{m} / \mathrm{s}$ skids to a halt.
a. Describe the energy transfers and transformations occurring during the skid.
b. What is the change in the combined thermal energy of the car and the road surface?

Mayukh Banik
Mayukh Banik
Numerade Educator
02:48

Problem 25

A 20 kg child slides down a 3.0 -m-high playground slide. She starts from rest, and her speed at the bottom is $2.0 \mathrm{m} / \mathrm{s}$
a. Describe the energy transfers and transformations occurring during the slide.
b. What is the change in the combined thermal energy of the slide and the seat of her pants?

Mayukh Banik
Mayukh Banik
Numerade Educator
01:48

Problem 26

A system loses $400 \mathrm{J}$ of potential energy. In the process, it does $400 \mathrm{J}$ of work on the environment and the thermal energy increases by $100 \mathrm{J}$. Show this process on an energy bar chart.

Mayukh Banik
Mayukh Banik
Numerade Educator
01:47

Problem 27

A system gains 500 J of kinetic energy while losing $200 \mathrm{J}$ of potential energy. The thermal energy increases 100 J. Show this process on an energy bar chart.

Mayukh Banik
Mayukh Banik
Numerade Educator
01:15

Problem 28

How much work is done by the environment in the process shown in FIGURE EX11.28 Is energy transferred from the environment to the system or from the system to the environment? (GRAPH CANNOT COPY)

Mayukh Banik
Mayukh Banik
Numerade Educator
02:05

Problem 29

A cable with $20.0 \mathrm{N}$ of tension pulls straight up on a $1.02 \mathrm{kg}$ block that is initially at rest. What is the block's speed after being lifted $2.00 \mathrm{m} ?$ Solve this problem using work and energy.

Mayukh Banik
Mayukh Banik
Numerade Educator
01:09

Problem 30

a. How much work does an elevator motor do to lift a $1000 \mathrm{kg}$ clevator a hcight of $100 \mathrm{m} ?$
b. How much power must the motor supply to do this in 50 s
at constant speed?

Mayukh Banik
Mayukh Banik
Numerade Educator
02:00

Problem 31

a. How much work must you do to push a $10 \mathrm{kg}$ block of steel across a steel table at a steady speed of $1.0 \mathrm{m} / \mathrm{s}$ for $3.0 \mathrm{s} ?$
b. What is your power output while doing so?

Mayukh Banik
Mayukh Banik
Numerade Educator
01:48

Problem 32

At midday, solar energy strikes the earth with an intensity of about $1 \mathrm{kW} / \mathrm{m}^{2} .$ What is the area of a solar collector that could collect 150 MJ of energy in 1 hr? This is roughly the energy content of 1 gallon of gasoline.

Mayukh Banik
Mayukh Banik
Numerade Educator
01:02

Problem 33

I Which consumes more energy, a $1.2 \mathrm{kW}$ hair dryer used for 10 min or a $10 \mathrm{W}$ night light left on for $24 \mathrm{hr} ?$

Mayukh Banik
Mayukh Banik
Numerade Educator
00:42

Problem 34

The electric company bills you in "kilowatt hours," abbrevi-ated k Wh.
a. Is this energy, power, or force? Explain.
b. Monthly electric use for a typical household is $500 \mathrm{kWh}$. What is this in basic SI units?

Mayukh Banik
Mayukh Banik
Numerade Educator
03:55

Problem 35

A $50 \mathrm{kg}$ sprinter, starting from rest, runs $50 \mathrm{m}$ in $7.0 \mathrm{s}$ at constant acceleration.
a. What is the magnitude of the horizontal force acting on the sprinter?
b. What is the sprinter's power output at $2.0 \mathrm{s}, 4.0 \mathrm{s},$ and $6.0 \mathrm{s} ?$

Mayukh Banik
Mayukh Banik
Numerade Educator
02:27

Problem 36

A particle moves from A to D in FIGURE P11.36while experiencing force $\overrightarrow{\boldsymbol{F}}=(6 \hat{\imath}+8 \hat{\jmath}) \mathrm{N} .$ How much
work does the force do if the particle follows path (a) ABD, (b) ACD, and (c) AD? Is this a conservative force? Explain. (GRAPH CANNOT COPY)

Mayukh Banik
Mayukh Banik
Numerade Educator
05:03

Problem 37

A 100 g particle experiences the one-dimensional, conservative force $F_{x}$ shown in FIGURE P11.37. (GRAPH CANNOT COPY)
a. Draw a graph of the potential energy $U$ from $x=0$ m to $x=5 \mathrm{m} .$ Let the zero of the potential energy be at $x=0 \mathrm{m}$ Hint: Think about the definition of potential energy and the geometric interpretation of the work done by a varying force.
b. The particle is shot toward the right from $x=1.0$ m with a speed of $25 \mathrm{m} / \mathrm{s}$. What is the particle's mechanical energy?
c. Draw the total energy line on your graph of part a.
d. Where is the particle's turning point?

Mayukh Banik
Mayukh Banik
Numerade Educator
04:14

Problem 38

A 10 g particle has the potential energy shown in FIGURE $P 11.38$.
a. Draw a force-versus-position graph from $x=0 \mathrm{cm}$ to $x=8 \mathrm{cm}$
b. How much work does the force do as the particle moves from $x=2 \mathrm{cm}$ to $x=6 \mathrm{cm} ?$
c. What speed does the particle need at $x=2 \mathrm{cm}$ to arrive at $x=6 \mathrm{cm}$ with a speed of $10 \mathrm{m} / \mathrm{s} ?$

Mayukh Banik
Mayukh Banik
Numerade Educator
03:18

Problem 39

a. FIGURE P1 1.39 a shows the force $F_{x}$ exerted on a particle that moves along the $x$ -axis. Draw a graph of the particle's potential energy as a function of position $x$ Let $U$ be zero at $x=0$ m.
b. FIGURE P11.396 shows the potential energy $U$ of a particle that moves along the $x$ -axis. Draw a graph of the force $F_{x}$ as a function of position $x$

Mayukh Banik
Mayukh Banik
Numerade Educator
11:30

Problem 40

FIGURE P11.40, is the velocity-versus-time graph of a $500 \mathrm{g}$ particle that starts at $x=0 \mathrm{m}$ and moves along the $x$ -axis. Draw graphs of the following by calculating and plotting numerical values at $t=0,1,2,3,$ and $4 \mathrm{s}$ Then sketch lines or curves of the appropriate shape between the points. Make sure you include appropriate scales on both axes of each graph. (GRAPH CANNOT COPY)
a. Acceleration versus time.
b. Position versus time.
c. Kinetic energy versus time.
d. Force versus time.
e. Use your $F_{x}$ -versus-t graph to determine the impulse delivered to the particle during the time interval $0-2 s$ and also the interval $2-4$ s.
I. Use the impulse-momentum theorem to determine the particle's velocity at $t=2 \mathrm{s}$ and at $t=4 \mathrm{s}$. Do your results agree with the velocity graph?
g. Now draw a graph of force versus position. This requires no calculations; just think carefully about what you learned in parts a to d.
h. Use your $F_{x}$ -versus- $x$ graph to determine the work done on the particle during the time interval $0-2 s$ and also the interval $2-4 s$
i. Use the work-kinetic energy theorem to determine the particle's velocity at $t=2 \mathrm{s}$ and at $t=4 \mathrm{s}$. Do your results agree with the velocity graph?

Eric Mockensturm
Eric Mockensturm
Numerade Educator
05:03

Problem 41

A $1000 \mathrm{kg}$ clevator accelerates upward at $1.0 \mathrm{m} / \mathrm{s}^{2}$ for $10 \mathrm{m}$ starting from rest.
a. How much work does gravity do on the elevator?
b. How much work does the tension in the elevator cable do on the elevator?
c. Use the work-kinetic energy theorem to find the kinetic energy of the clevator as it reaches $10 \mathrm{m}$.
d. What is the speed of the elevator as it reaches $10 \mathrm{m} ?$

Dale Sanford
Dale Sanford
Numerade Educator
01:48

Problem 42

Bob can throw a $500 \mathrm{g}$ rock with a speed of $30 \mathrm{m} / \mathrm{s}$. He moves his hand forward $1.0 \mathrm{m}$ while doing so.
a. How much work does Bob do on the rock?
b. How much force, assumed to be constant, does Bob apply to the rock?
c. What is Bob's maximum power output as he throws the rock?

Mayukh Banik
Mayukh Banik
Numerade Educator
02:31

Problem 43

Doug pushes a $5.0 \mathrm{kg}$ crate up a 2.0 -m-high $20^{\circ}$ frictionless slope by pushing it with a constant horizontal force of $25 \mathrm{N}$ What is the speed of the crate as it reaches the top of the slope?
a. Solve this problem using work and energy. Solve this problem using Newton's laws.

Mayukh Banik
Mayukh Banik
Numerade Educator
03:09

Problem 44

Sam, whose mass is $75 \mathrm{kg}$, straps on his skis and starts down a 50-m-high, $20^{\circ}$ frictionless slope. A strong headwind exerts a horizontal force of $200 \mathrm{N}$ on him as he skies. Find Sam's speed at the bottom (a) using work and energy, (b) using Newton's laws.

Mayukh Banik
Mayukh Banik
Numerade Educator
03:44

Problem 45

Susan's $10 \mathrm{kg}$ baby brother Paul sits on a mat. Susan pulls the mat across the floor using a rope that is angled $30^{\circ}$ above the floor. The tension is a constant $30 \mathrm{N}$ and the coefficient of friction is $0.20 .$ Use work and energy to find Paul's speed after being pulled 3.0 $\mathrm{m}$.

Mayukh Banik
Mayukh Banik
Numerade Educator
02:04

Problem 46

A horizontal spring with spring constant $100 \mathrm{N} / \mathrm{m}$ is compressed $20 \mathrm{cm}$ and used to launch a $2.5 \mathrm{kg}$ box across a frictionless, horizontal surface. After the box travels some distance, the surface becomes rough. The coefficient of kinctic friction of the box on the surface is $0.15 .$ Use work and energy to find how far the box slides across the rough surface before stopping.

Mayukh Banik
Mayukh Banik
Numerade Educator
01:00

Problem 47

A baggage handler throws a $15 \mathrm{kg}$ suitcase horizontally along the floor of an airplane luggage compartment with an initial speed of $1.2 \mathrm{m} / \mathrm{s}$. The suitcase slides $2.0 \mathrm{m}$ before stopping. Use work and energy to find the suitcase's coefficient of kinetic friction on the floor.

Mayukh Banik
Mayukh Banik
Numerade Educator
03:54

Problem 48

Truck brakes can fail if they get too hot. In some mountainous areas, ramps of loose gravel are constructed to stop runaway trucks that have lost their brakes. The combination of a slight upward slope and a large coefficient of rolling resistance as the truck tires sink into the gravel brings the truck safely to a halt. Suppose a gravel ramp slopes upward at $6.0^{\circ}$ and the coefficient of friction is $0.40 .$ Use work and energy to find the length of a ramp that will stop a 15,000 kg truck that enters the ramp atM $35 \mathrm{m} / \mathrm{s}(\approx 75 \mathrm{mph}).$

Mayukh Banik
Mayukh Banik
Numerade Educator
01:18

Problem 49

A freight company uses a compressed spring to shoot 2.0 $\mathrm{kg}$ packages up a 1.0 -m-high frictionless ramp into a truck, as FIGURE P11.49 . (FIGURE CANNOT COPY)
a. What is the speed of the package when it reaches the truck?
b. A careless worker spills his soda on the ramp. This creates a 50-cm-long sticky spot with a coefficient of kinetic friction 0.30. Will the next package make it into the truck?

Mayukh Banik
Mayukh Banik
Numerade Educator
04:51

Problem 50

Use work and energy to find the speed of the $2.0 \mathrm{kg}$ block in FIGURE P11.50 just before it hits the floor if (a) the table is frictionless and if (b) the coefficient of kinetic friction of the $3.0 \mathrm{kg}$ block is 0.15

Mayukh Banik
Mayukh Banik
Numerade Educator
06:12

Problem 51

An $8.0 \mathrm{kg}$ crate is pulled $5.0 \mathrm{m}$ up a $30^{\circ}$ incline by a rope angled $18^{\circ}$ above the incline. The tension in the rope is $120 \mathrm{N}$, and the crate's coefficient of kinctic friction on the incline is 0.25.
a. How much work is done by tension, by gravity, and by the normal force?
b. What is the increase in thermal energy of the crate and incline?

Mayukh Banik
Mayukh Banik
Numerade Educator
03:10

Problem 52

A $10.2 \mathrm{kg}$ weather rocket generates a thrust of $200 \mathrm{N}$. The rocket, pointing upward, is clamped to the top of a vertical spring. The bottom of the spring, whose spring constant is
$500 \mathrm{N} / \mathrm{m},$ is anchored to the ground.
a. Initially, before the engine is ignited, the rocket sits at rest on top of the spring. How much is the spring compressed?
b. After the engine is ignited, what is the rocket's speed when the spring has stretched $40 \mathrm{cm} ?$ For comparison, what would be the rocket's speed after traveling this distance if it weren't attached to the spring?

Mayukh Banik
Mayukh Banik
Numerade Educator
03:21

Problem 53

A 50 kg ice skater is gliding along the ice, heading due north at $4.0 \mathrm{m} / \mathrm{s} .$ The ice has a small coefficient of static friction, to prevent the skater from slipping sideways, but $\mu_{\mathbf{k}}=0 .$ Suddenly, a wind from the northeast exerts a force of $4.0 \mathrm{N}$ on the skater.
a. Use work and energy to find the skater's speed after gliding $100 \mathrm{m}$ in this wind.
b. What is the minimum value of $\mu$, that allows her to continue moving straight north?

Mayukh Banik
Mayukh Banik
Numerade Educator
03:41

Problem 54

a. A $50 \mathrm{g}$ ice cube can slide without friction up and down a $30^{\circ}$ slope. The ice cube is pressed against a spring at the bottom of the slope, compressing the spring $10 \mathrm{cm} .$ The spring constant is $25 \mathrm{N} / \mathrm{m}$. When the ice cube is released, what total distance will it travel up the slope before reversing direction?
b. The ice cube is replaced by a 50 g plastic cube whose coefficient of kinetic friction is $0.20 .$ How far will the plastic cube travel up the slope?

Mayukh Banik
Mayukh Banik
Numerade Educator
03:37

Problem 55

A $5.0 \mathrm{kg}$ box slides down a 5.0 -m-high frictionless hill, starting from rest, across a 2.0 -m-wide horizontal surface, then hits a horizontal spring with spring constant $500 \mathrm{N} / \mathrm{m}$. The other end of the spring is anchored against a wall. The ground under the spring is frictionless, but the 2.0 -m-wide horizontal surface is rough. The coefficient of kinetic friction of the box on this surface is 0.25.
a. What is the speed of the box just before reaching the rough surface?
b. What is the speed of the box just before hitting the spring?
c. How far is the spring compressed?
d. Including the first crossing, how many complete trips will the box make across the rough surface before coming to rest?

Mayukh Banik
Mayukh Banik
Numerade Educator
02:26

Problem 56

The spring shown in FIGURE P1 1.56 is compressed $50 \mathrm{cm}$ and used to launch a $100 \mathrm{kg}$ physics student. The track is frictionless until it starts up the incline. The student's coefficient of kinetic friction on the $30^{\circ}$ incline is 0.15. (FIGURE CANNOT COPY)
a. What is the student's speed just after losing contact with the spring?
b. How far up the incline does the student go?

Mayukh Banik
Mayukh Banik
Numerade Educator
02:22

Problem 57

A block of mass $m$ starts from rest at height $h .$ It slides down a frictionless incline, across a rough horizontal surface of length
L, then up a frictionless incline. The coefficient of kinctic friction on the rough surface is $\mu_{\mathbf{k}}$
a. What is the block's speed at the bottom of the first incline?
b. How high does the block go on the second incline? Give your answers in terms of $m, h, L, \mu_{\mathbf{k}},$ and $g.$

Mayukh Banik
Mayukh Banik
Numerade Educator
01:51

Problem 58

Show that Hooke's law for an ideal spring is a conservative force. To do so, first calculate the work done by the spring as it expands from A to B. Then calculate the work done by the spring as it expands from A to point C, which is beyond B, then returns from C to B.

Mayukh Banik
Mayukh Banik
Numerade Educator
05:07

Problem 59

A clever engineer designs a "sprong" that obeys the force law $F_{x}=-q\left(x-x_{0}\right)^{3},$ where $x_{0}$ is the equilibrium position of the end of the sprong and $q$ is the sprong constant. For simplicity, we'll let $x_{0}=0$ m. Then $F_{x}=-q x^{3}.$
a. What are the units of $q ?$
b. Draw a graph of $F_{x}$ versus $x$
c. Find an expression for the potential energy of a stretched or compressed sprong.
d. A sprong-loaded toy gun shoots a $20 \mathrm{g}$ plastic ball. What is the launch speed if the sprong constant is $40,000,$ with the units you found in part $a$, and the sprong is compressed $10 \mathrm{cm} ?$ Assume the barrel is frictionless.

Eric Mockensturm
Eric Mockensturm
Numerade Educator
05:16

Problem 60

A particle of mass $m$ starts from $x_{0}=0$ m with $v_{0}>0$ m/s. The particle experiences the variable force $F_{x}=F_{0} \sin (c x)$ as it moves to the right along the $x$ -axis, where $F_{0}$ and $c$ are constants.
a. What are the units of $F_{0} ?$
b. What are the units of $c ?$
c. At what position $x_{\max }$ does the force first reach a maximum value? Your answer will be in terms of the constants $F_{0}$ and $c$ and perhaps other numerical constants.
d. Sketch a graph of $F$ versus $x$ from $x_{0}$ to $x_{\max }$
c. What is the particle's velocity as it reaches $x_{\max } ?$ Give your answer in terms of $m, v_{0}, F_{0},$ and $c .$

Mayukh Banik
Mayukh Banik
Numerade Educator
01:21

Problem 61

a. Estimate the height in meters of the two flights of stairs that go from the first to the third floor of a building.
b. Estimate how long it takes you to run up these two flights of stairs.
c. Estimate your power output in both watts and horsepower while running up the stairs.

Mayukh Banik
Mayukh Banik
Numerade Educator
00:53

Problem 62

A $5.0 \mathrm{kg}$ cat leaps from the floor to the top of a $95-\mathrm{cm}$ -high table. If the cat pushes against the floor for 0.20 s to accomplish this feat, what was her average power output during the pushoff period?

Mayukh Banik
Mayukh Banik
Numerade Educator
03:00

Problem 63

A 2.0 hp electric motor on a water well pumps water from $10 \mathrm{m}$ below the surface. The density of water is $1.0 \mathrm{kg}$ per liter. How many liters of water does the motor pump in 1 hr?

Mayukh Banik
Mayukh Banik
Numerade Educator
03:37

Problem 64

In a hydroelectric dam, water falls $25 \mathrm{m}$ and then spins a turbine to generate electricity.
a. What is $\Delta U$ of $1.0 \mathrm{kg}$ of water?
b. Suppose the dam is $80 \%$ efficient at converting the water's potential energy to electrical energy. How many kilograms of water must pass through the turbines cach second to generate 50 MW of electricity? This is a typical value for a small hydroelectric dam.

Mayukh Banik
Mayukh Banik
Numerade Educator
01:12

Problem 65

The force required to tow a water skier at speed $v$ is proportional to the speed. That is, $F_{\text {tow }}=A v,$ where $A$ is a proportionality constant. If a speed of 2.5 mph requires 2 hp. how much power is required to tow a water skier at 7.5 mph?

Mayukh Banik
Mayukh Banik
Numerade Educator
02:21

Problem 66

Estimate the maximum speed of a horse. Assume that a horse is $1.8 \mathrm{m}$ tall and $0.5 \mathrm{m}$ wide.

Susan Hallstrom
Susan Hallstrom
Numerade Educator
02:51

Problem 67

The engine in a $1500 \mathrm{kg}$ car has a maximum power output of $200 \mathrm{hp},$ but $25 \%$ of the power is $10 \mathrm{st}$ before reaching the drive wheels. The car has a front profile that is 1.6 m wide and $1.4 \mathrm{m}$ high. The coefficient of rolling friction is $0.02 .$ What is the car's top speed? Is this answer reasonable?

Mayukh Banik
Mayukh Banik
Numerade Educator
05:00

Problem 68

A Porsche 944 Turbo has a rated engine power of 217 hp. $30 \%$ of the power is lost in the drive train, and $70 \%$ reaches the wheels. The total mass of the car and driver is $1480 \mathrm{kg}$, and twothirds of the weight is over the drive wheels. a. What is the maximum acceleration of the Porsche on a concrete surface where $\mu_{\mathrm{s}}=1.00 ?$ Hint: What force pushes the car forward?
b. What is the speed of the Porsche at maximum power output?
c. If the Porsche accelerates at $a_{\max }$, how long does it take until it reaches the maximum power output?

Mayukh Banik
Mayukh Banik
Numerade Educator
02:20

Problem 69

You are given the equation(s) used to solve a problem. For each of these, you are toIn Problems 69 through 72 you are given the equation(s) used to solve a problem. For each of these, you are to a. Write a realistic problem for which this is the correct equation(s).
b. Draw a pictorial representation. c. Finish the solution of the problem.
$$\begin{array}{l} \frac{1}{2}(2.0 \mathrm{kg})(4.0 \mathrm{m} / \mathrm{s})^{2}+0 \\
+(0.15)(2.0 \mathrm{kg})\left(9.8 \mathrm{m} / \mathrm{s}^{2}\right)(2.0 \mathrm{m})=0+0+T(2.0 \mathrm{m}) \end{array}$$

Mayukh Banik
Mayukh Banik
Numerade Educator
02:06

Problem 70

You are given the equation(s) used to solve a problem. For each of these, you are toIn Problems 69 through 72 you are given the equation(s) used to solve a problem. For each of these, you are to a. Write a realistic problem for which this is the correct equation(s).
b. Draw a pictorial representation. c. Finish the solution of the problem.
$$\begin{array}{l}-\frac{1}{2}(20 \mathrm{kg}) v_{1}^{2}+0 \\
+(0.15)(20 \mathrm{kg})\left(9.8 \mathrm{m} / \mathrm{s}^{2}\right) \cos 40^{\circ}\left((2.5 \mathrm{m}) / \sin 40^{\circ}\right) \\ =0+(20 \mathrm{kg})\left(9.8 \mathrm{m} / \mathrm{s}^{2}\right)(2.5 \mathrm{m})+0 \end{array}$$

Mayukh Banik
Mayukh Banik
Numerade Educator
01:35

Problem 71

You are given the equation(s) used to solve a problem. For each of these, you are toIn Problems 69 through 72 you are given the equation(s) used to solve a problem. For each of these, you are to a. Write a realistic problem for which this is the correct equation(s).
b. Draw a pictorial representation. c. Finish the solution of the problem.
$$\begin{array}{l}F_{\text {push }}-(0.20)(30 \mathrm{kg})\left(9.8 \mathrm{m} / \mathrm{s}^{2}\right)=0 \\75 \mathrm{W}=F_{\text {push }} v\end{array}$$

Mayukh Banik
Mayukh Banik
Numerade Educator
01:50

Problem 72

You are given the equation(s) used to solve a problem. For each of these, you are toIn Problems 69 through 72 you are given the equation(s) used to solve a problem. For each of these, you are to a. Write a realistic problem for which this is the correct equation(s).
b. Draw a pictorial representation. c. Finish the solution of the problem.
$$\begin{array}{l}T-(1500 \mathrm{kg})\left(9.8 \mathrm{m} / \mathrm{s}^{2}\right)=(1500 \mathrm{kg})\left(1.0 \mathrm{m} / \mathrm{s}^{2}\right) \\ P=T(2.0 \mathrm{m} / \mathrm{s})\end{array}$$

Mayukh Banik
Mayukh Banik
Numerade Educator
03:36

Problem 73

You've taken a summer job at a water park. In one stunt, a water skier is going to glide up the $2.0-\mathrm{m}$ -high frictionless ramp shown in FIGURE CP11.T3, then sail over a 5.0 -m-wide tank filled with hungry sharks. You will be driving the boat that pulls her to the ramp. She'll drop the tow rope at the base of the ramp just as you veer away. What minimum speed must you have as you reach the ramp in order for her to live to do this again tomorrow? (FIGURE CANNOT COPY)

Mayukh Banik
Mayukh Banik
Numerade Educator
04:37

Problem 74

The spring in Ficure CP 11.74 has a spring constant of $1000 \mathrm{N} / \mathrm{m}$. It is compressed $15 \mathrm{cm},$ then launches a $200 \mathrm{g}$ block. The horizontal surface is frictionless, but the block's coefficient of kinetic friction on the incline is $0.20 .$ What distance $d$ does the block sail through the air? (FIGURE CANNOT COPY)

Eric Mockensturm
Eric Mockensturm
Numerade Educator
06:45

Problem 75

As a hobby, you like to participate in reenactments of Civil War battles. Civil War cannons were "muzzle loaded," meaning that the gunpowder and the cannonball were inserted into the output end of the muzzle, then tamped into place with a long plunger. To recreate the authenticity of muzzle-loaded cannons, but without the danger of real cannons, Civil War buffs have invented a spring-powered cannon that fires a $1.0 \mathrm{kg}$ plastic ball. A spring, with spring constant $3000 \mathrm{N} / \mathrm{m},$ is mounted at the back of the barrel. You place a ball in the barrel, then use a long plunger to press the ball against the spring and lock the spring into place, ready for firing. In order for the latch to catch, the ball has to be moving at a speed of at least $2.0 \mathrm{m} / \mathrm{s}$ when the spring has been compressed $30 \mathrm{cm} .$ The coefficient of friction of the ball in the barrel is $0.30 .$ The plunger doesn't touch the sides of the barrel.
a. If you push the plunger with a constant force, what is the minimum force that you must use to compress and latch the spring? You can assume that no effort was required to push the ball down the barrel to where it first contacts the spring.
b. What is the cannon's muzzle velocity if the ball travels a total distance of $1.5 \mathrm{m}$ to the end of the barrel?

Eric Mockensturm
Eric Mockensturm
Numerade Educator
07:14

Problem 76

The equation mgy for gravitational potential energy is valid only for objects near the surface of a planet. Consider two very large objects of mass $m_{1}$ and $m_{2},$ such as stars or planets, whose centers are separated by the large distance $r$. These two large objects exert gravitational forces on each other. You'll learn in Chapter 13 that the gravitational potential energy is $$U=-\frac{G m_{1} m_{2}}{r}$$ where $G=6.67 \times 10^{-11} \mathrm{Nm}^{2} / \mathrm{kg}^{2}$ is called the gravitational constant.
a. Sketch a graph of $U$ versus $r$. The mathematical difficulty at $r=0$ is not a physically significant problem because the masses will collide before they get that close together.
b. What separation $r$ has been chosen as the point of zero potential energy? Does this make sense? Explain.
c. Two stars are at rest $1.0 \times 10^{14} \mathrm{m}$ apart. This is about 10 times the diameter of the solar system. The first star is the size of our sun, with a mass of $2.0 \times 10^{30} \mathrm{kg}$ and a radius of $7.0 \times 10^{8} \mathrm{m} .$ The second star has mass $8.0 \times 10^{30} \mathrm{kg}$ and radius of $11.0 \times 10^{8} \mathrm{m} .$ Gravitational forces pull the two stars together. What is the speed of each star at the moment of impact?

Eric Mockensturm
Eric Mockensturm
Numerade Educator
03:58

Problem 77

A gardener pushes a $12 \mathrm{kg}$ lawnmower whose handle is tilted up
$37^{\circ}$ above horizontal. The lawnmower's coefficient of rolling friction is $0.15 .$ How much power does the gardener have to supply to push the lawnmower at a constant speed of $1.2 \mathrm{m} / \mathrm{s} ?$ Assume his push is parallel to the handle.

Mayukh Banik
Mayukh Banik
Numerade Educator