Essential University Physics

Richard Wolfson

Chapter 6

Energy, Work, and Power - all with Video Answers

Educators

Chapter Questions

Problem 1

Give two examples of situations in which you might think you're doing work but in which, in the technical sense, you do no work.

Donald Albin

Donald Albin

Numerade Educator

Problem 2

If the scalar product of two nonzero vectors is zero, what can you conclude about their relative directions?

Donald Albin

Numerade Educator

Problem 3

Must you do work to whirl a ball around on the end of a string? Explain.

Donald Albin

Numerade Educator

Problem 4

If you pick up a suitcase and put it down, how much total work have you done on the suitcase? Does your answer change if you pick up the suitcase and drop it?

Donald Albin

Numerade Educator

Problem 5

You want to raise a piano a given height using a ramp. With a fixed, nonzero coefficient of friction, will you have to do more work if the ramp is steeper or more gradual? Explain.

Donald Albin

Numerade Educator

Problem 6

Does the gravitational force of the Sun do work on a planet in a circular orbit? On a comet in an elliptical orbit? Explain.

Donald Albin

Numerade Educator

Problem 7

A pendulum bob swings back and forth on the end of a string, describing a circular arc. Does the tension force in the string do any work?

Donald Albin

Numerade Educator

Problem 8

Does your car's kinetic energy change if you drive at constant speed for 1 hour?

Donald Albin

Numerade Educator

Problem 9

A watt-second is a unit of what quantity? Relate it to a more standard SI unit.

Donald Albin

Numerade Educator

Problem 10

A truck is moving northward at $55 \mathrm{mi} / \mathrm{h}$. Later, it's moving eastward at the same speed. Has its kinetic energy changed? Has work been done on the truck? Has a force acted on the truck? Explain.

Donald Albin

Numerade Educator

Problem 11

A news article reports that a new solar farm will produce 143 kilowatt-hours of electricity. Criticize this statement. What did the writer probably mean?

Donald Albin

Numerade Educator

Problem 12

Is it possible for you to do work on an object without changing the object's kinetic energy? Explain.

Donald Albin

Numerade Educator

Problem 13

How much work do you do as you exert a $75-\mathrm{N}$ force to push a shopping cart through a 12 -m-long supermarket aisle?

Donald Albin

Numerade Educator

Problem 14

If the coefficient of kinetic friction is $0.21,$ how much work do you do when you slide a $50-\mathrm{kg}$ box at constant speed across a $4.8-\mathrm{m}-$ wide room?

Donald Albin

Numerade Educator

Problem 15

A crane lifts a 650 -kg beam vertically upward 23 m and then swings it eastward $18 \mathrm{m}$. How much work does the crane do? Neglect friction, and assume the beam moves with constant speed.

Donald Albin

Numerade Educator

Problem 16

The world's highest waterfall, the Cherun-Meru in Venezuela, has a total drop of 980 m. How much work does gravity do on a cubic meter of water dropping down the Cherun-Meru?

Donald Albin

Numerade Educator

Problem 17

A meteorite plunges to Earth, embedding itself $75 \mathrm{cm}$ in the ground. If it does 140 MJ of work in the process, what average force does the meteorite exert on the ground?

Donald Albin

Numerade Educator

Problem 18

An elevator of mass $m$ rises a vertical distance $h$ with upward acceleration equal to one-tenth $g .$ Find an expression for the work the elevator cable does on the elevator.

Donald Albin

Numerade Educator

Problem 19

Show that the scalar product obeys the distributive law:
$\vec{A} \cdot(\vec{B}+\vec{C})=\vec{A} \cdot \vec{B}+\vec{A} \cdot \vec{C}$

Donald Albin

Numerade Educator

Problem 20

Find the work done by a force $\vec{F}=1.8 \hat{\imath}+2.2 \hat{\jmath} \mathrm{N}$ as it acts on an object moving from the origin to the point $56 \hat{\imath}+31 \hat{\jmath} \mathrm{m}$.

Donald Albin

Numerade Educator

Problem 21

To push a stalled car, you apply a $470-\mathrm{N}$ force at $17^{\circ}$ to the car's motion, doing $860 \mathrm{J}$ of work in the process. How far do you push the car?

Donald Albin

Numerade Educator

Problem 22

Find the total work done by the force shown in Fig. 6.15 as the object on which it acts moves (a) from $x=0$ to $x=3 \mathrm{km}$ and (b) from $x=3 \mathrm{km}$ to $x=4 \mathrm{km}$.
(FIGURE CANT COPY)

Donald Albin

Numerade Educator

Problem 23

How much work does it take to stretch a spring with $k=200 \mathrm{N} / \mathrm{m}$
(a) $10 \mathrm{cm}$ from equilibrium and (b) from $10 \mathrm{cm}$ to $20 \mathrm{cm}$ from equilibrium?

Donald Albin

Numerade Educator

Problem 24

Uncompressed, the spring for an automobile suspension is $45 \mathrm{cm}$ long. It needs to be fitted into a space 32 cm long. If the spring constant is $3.8 \mathrm{kN} / \mathrm{m},$ how much work does a mechanic have to do to fit the spring?

Donald Albin

Numerade Educator

Problem 25

You do $8.5 \mathrm{J}$ of work to stretch a spring with $k=190 \mathrm{N} / \mathrm{m},$ starting with the spring unstretched. How far does the spring stretch?

Donald Albin

Numerade Educator

Problem 26

Spider silk is a remarkable elastic material. A particular strand has spring constant $70 \mathrm{mN} / \mathrm{m},$ and it stretches $9.6 \mathrm{cm}$ when a fly hits it. How much work did the fly's impact do on the silk strand?

Donald Albin

Numerade Educator

Problem 27

What's the kinetic energy of a $2.4 \times 10^{5}-\mathrm{kg}$ airplane cruising at $900 \mathrm{km} / \mathrm{h} ?$

Donald Albin

Numerade Educator

Problem 28

A cyclotron accelerates protons from rest to $21 \mathrm{Mm} / \mathrm{s}$. How much work does it do on each proton?

Donald Albin

Numerade Educator

Problem 29

At what speed must a 950 -kg subcompact car be moving to have the same kinetic energy as a $3.2 \times 10^{4}-\mathrm{kg}$ truck going $20 \mathrm{km} / \mathrm{h} ?$

Donald Albin

Numerade Educator

Problem 30

A $60-\mathrm{kg}$ skateboarder comes over the top of a hill at $5.0 \mathrm{m} / \mathrm{s}$ and reaches $10 \mathrm{m} / \mathrm{s}$ at the bottom. Find the total work done on the skateboarder between the top and bottom of the hill.

Donald Albin

Numerade Educator

Problem 31

After a tornado, a 0.50 -g drinking straw was found embedded $4.5 \mathrm{cm}$ in a tree. Subsequent measurements showed that the tree exerted a stopping force of $70 \mathrm{N}$ on the straw. What was the straw's speed?

Donald Albin

Numerade Educator

Problem 32

From what height would you have to drop a car for its impact to be equivalent to a 20 -mi/h collision?

Donald Albin

Numerade Educator

Problem 33

A typical human diet is $* 2000$ calories" per day, where the "calorie" describing food energy is actually 1 kilocalorie. Express 2000 kcal/day in watts.

Donald Albin

Numerade Educator

Problem 34

A horse plows a 200 -m-long furrow in 5.0 min, exerting a $750-\mathrm{N}$ force. Find its power output, measured in watts and in horsepower.

Donald Albin

Numerade Educator

Problem 35

A typical car battery stores about $1 \mathrm{~kW} \cdot \mathrm{h}$ of energy. What's its power output if it drains completely in (a) 1 minute,
(b) 1 hour, and (c) I day?

Donald Albin

Numerade Educator

Problem 36

A sprinter completes a 100 -m dash in $10.6 \mathrm{s}$, doing $22.4 \mathrm{kJ}$ of work. What's her average power output?

Donald Albin

Numerade Educator

Problem 37

How much work can a 3.5 -hp lawnmower engine do in 1 h?

Donald Albin

Numerade Educator

Problem 38

A 75 -kg long-jumper takes 3.1 s to reach a prejump speed of $10 \mathrm{m} / \mathrm{s} .$ What's his power output?

Donald Albin

Numerade Educator

Problem 39

Estimate your power output as you do deep knee bends at the rate of one per second.

Donald Albin

Numerade Educator

Problem 40

In midday sunshine, solar energy strikes Earth at the rate of about $1 \mathrm{kW} / \mathrm{m}^{2}$. How long would it take a perfectly efficient solar collector of $15-\mathrm{m}^{2}$ area to collect $40 \mathrm{kW} \cdot \mathrm{h}$ of energy? (Note: This is roughly the energy content of a gallon of gasoline.)

Donald Albin

Numerade Educator

Problem 41

It takes about $20 \mathrm{kJ}$ to melt an ice cube. A typical microwave oven produces 900 W of microwave power. How long will it take a typical microwave to melt the ice cube?

Donald Albin

Numerade Educator

Problem 42

Which consumes more energy, a 1.2 -k $\mathrm{W}$ hair dryer used for 10 min or a $7-W$ night-light left on for 24 h?

Donald Albin

Numerade Educator

Problem 43

You slide a box of books at constant speed up a $30^{\circ}$ ramp, applying a force of $200 \mathrm{N}$ directed up the slope. The coefficient of sliding friction is $0.18 .$ (a) How much work have you done when the box has risen 1 m vertically? (b) What's the mass of the box?

Donald Albin

Numerade Educator

Problem 44

Two people push a stalled car at its front doors, each applying a $280-\mathrm{N}$ force at $25^{\circ}$ to the forward direction, as shown in Fig. 6.16 How much work does each person do in pushing the car $5.6 \mathrm{m} ?$
(FIGURE CANT COPY)

Donald Albin

Numerade Educator

Problem 45

You're at the gym, doing arm raises. With each rep, you lift a $20-\mathrm{N}$ weight $55 \mathrm{cm} .$ (a) How many raises must you do before you've expended 200 kcal of work (see Exercise 33 )? (b) If your workout takes 1.0 min, what's your average power output?

Donald Albin

Numerade Educator

Problem 46

A locomotive does $7.9 \times 10^{11} \mathrm{J}$ of work in pulling a $3.4 \times 10^{6}-\mathrm{kg}$ train $180 \mathrm{km}$. Find the average force in the coupling between the locomotive and the rest of the train.

Donald Albin

Numerade Educator

Problem 47

You pull a box 23 m horizontally, using the rope shown in Fig. 6.17 If the rope tension is $120 \mathrm{N},$ and if the rope does $2500 \mathrm{J}$ of work on the box, what angle $\theta$ does the rope make with the horizontal?
(FIGURE CANT COPY)

Donald Albin

Numerade Educator

Problem 48

(a) Find the scalar products $\hat{\imath} \cdot \hat{\imath}, \hat{\jmath} \cdot \hat{\jmath},$ and $\hat{k} \cdot \hat{k} .$ (b).Find $\hat{i} \cdot \hat{j}, \hat{j} \cdot \hat{k},$ and $\hat{k} \cdot \hat{\imath} .$ (c) Use the distributive law to multiply out the scalar product of two arbitrary vectors $\vec{A}=A_{x} \hat{\imath}+A_{y} \hat{\jmath}+A_{z} \hat{k}$ and $\vec{B}=B_{x} \hat{\imath}+B_{y} \hat{\jmath}+B_{z} \hat{k},$ and use the results of (a) and (b) to verify Equation 6.4.

Donald Albin

Numerade Educator

Problem 49

(a) Find the scalar product of the vectors $a \hat{\imath}+b \hat{\jmath}$ and $b \hat{\imath}-a \hat{\jmath}$ where $a$ and $b$ are arbitrary constants. (b) What's the angle between the two vectors?

Donald Albin

Numerade Educator

Problem 50

Looking to cut costs, the airline you work for asks you to investigate the efficiency of the tractors that push aircraft away from the gates. One model is supposed to do no more than 10 MJ of work in pushing a 747 aircraft $25 \mathrm{m}$. If the tractor exerts a $0.42-\mathrm{MN}$ force, does it meet its specifications?

Donald Albin

Numerade Educator

Problem 51

How much work does a force $\vec{F}=67 \hat{\imath}+23 \hat{\jmath}+55 \hat{k} \mathrm{N}$ do as it acts on a body moving in a straight line from $\vec{r}_{1}=16 \hat{\imath}+31 \hat{\jmath} \mathrm{m}$ to $\vec{r}_{2}=21 \hat{\imath}+10 \hat{\jmath}+14 \hat{k} \mathrm{m} ?$

Donald Albin

Numerade Educator

Problem 52

A force $\vec{F}$ acts in the $x$ -direction, its magnitude given by $F=a x^{2}$ where $x$ is in meters and $a=5.0 \mathrm{N} / \mathrm{m}^{2} .$ Find the work done by this force as it acts on a particle moving from $x=0$ to $x=6.0 \mathrm{m}$.

Nishant Kumar

Numerade Educator

Problem 53

A certain amount of work is required to stretch spring A a certain distance. Twice as much work is required to stretch spring B half that distance. Compare the spring constants of the two.

Donald Albin

Numerade Educator

Problem 54

A force with magnitude $F=a \sqrt{x}$ acts in the $x$ -direction, where $a=9.5 \mathrm{N} / \mathrm{m}^{1 / 2} .$ Calculate the work this force does as it acts on an object moving from (a) $x=0$ to $x=3.0 \mathrm{m} ;$ (b) $3.0 \mathrm{m}$ to $6.0 \mathrm{m}$ and (c) $6.0 \mathrm{m}$ to $9.0 \mathrm{m}$.

Donald Albin

Numerade Educator

Problem 55

The force exerted by a rubber band is given approximately by $$F=F_{0}\left[\frac{L_{0}-x}{L_{0}}-\frac{L_{0}^{2}}{\left(L_{0}+x\right)^{2}}\right]$$,where $L_{0}$ is the unstretched length, $x$ is the stretch, and $F_{0}$ is a constant. Find an expression for the work needed to stretch the rubber band a distance $x$.

Donald Albin

Numerade Educator

Problem 56

You put your little sister (mass $m$ ) on a swing whose chains have length $L$ and pull slowly back until the swing makes an angle $\phi$ with the vertical. Show that the work you do is $m g L(1-\cos \phi)$.

Donald Albin

Numerade Educator

Problem 57

Two unknown elementary particles pass through a detection chamber. If they have the same kinetic energy and their mass ratio is $4: 1,$ what's the ratio of their speeds?

Donald Albin

Numerade Educator

Problem 58

A tractor tows a plane from its airport gate, doing 8.7 MJ of work. The link from the plane to the tractor makes a $22^{\circ}$ angle with the plane's motion, and the tension in the link is $0.41 \mathrm{MN}$. How far does the tractor move the plane?

Prabhat Tyagi

Numerade Educator

Problem 59

E. coli bacteria swim by means of flagella that rotate about 100 so times per second. A typical $E .$ coli bacterium swims at $22 \mu \mathrm{m} / \mathrm{s}$ its flagella exerting a force of $0.57 \mathrm{pN}$ to overcome the resistance due to its liquid environment. (a) What's the bacterium's power output? (b) How much work would it do in traversing the $25-\mathrm{mm}$ width of a microscope slide?

Donald Albin

Numerade Educator

Problem 60

On February $15,2013,$ an asteroid moving at $19 \mathrm{km} / \mathrm{s}$ entered Earth's atmosphere over Chelyabinsk, Russia, and exploded at an altitude of more than $20 \mathrm{km}$. This was the largest object known to have entered the atmosphere in over a century. The asteroid's kinetic energy just before entering the atmosphere was estimated as the energy equivalent of 500 kilotons of the explosive TNT. (Kilotons [kt] and megatons [Mt] are energy units used to describe the explosive yields of nuclear weapons, and you'll find the energy equivalent of $1 \mathrm{Mt}$ in Appendix $C$ ). What was the approximate mass of the Chelyabinsk asteroid?

Donald Albin

Numerade Educator

Problem 61

An elevator ascends from the ground floor to the 10 th floor, a height of $41 \mathrm{m},$ in 35 s. If the mass of the elevator and passengers is $840 \mathrm{kg},$ what's the power necessary to lift the elevator? (Your answer is greater than the actual power needed because elevators are counter weighted, thus reducing the work the motor needs to do.)

Donald Albin

Numerade Educator

Problem 62

You're asked to assess the reliability of a nuclear power plant, as measured by the capacity factor-the ratio of the energy it actually produces to what it could produce if it operated all the time. The plant is rated at $840 \mathrm{MW}$ of electrical power output, and in a full year it produces $6.8 \times 10^{9} \mathrm{kW} \cdot$ h of electrical energy. What's its capacity factor?

Donald Albin

Numerade Educator

Problem 63

A force pointing in the $x$ -direction is given by $F=F_{0}\left(x / x_{0}\right)^{2}$ where $F_{0}$ and $x_{0}$ are constants and $x$ is position. Find an expression for the work done by this force as it acts on an object moving from $x=0$ to $x=x_{0}$.

Donald Albin

Numerade Educator

Problem 64

A force pointing in the $x$ -direction is given by $F=a x^{3 / 2},$ where $a=0.75 \mathrm{N} / \mathrm{m}^{3 / 2} .$ Find the work done by this force as it acts on an object moving from $x=0$ to $x=14 \mathrm{m}$.

Donald Albin

Numerade Educator

Problem 65

Two vectors have equal magnitude, and their scalar product is one-third the square of their magnitude. Find the angle between them.

Donald Albin

Numerade Educator

Problem 66

At what rate can a half-horsepower well pump deliver water to a tank $60 \mathrm{m}$ above the water level in the well? Give your answer in $\mathrm{kg} / \mathrm{s}$ and gal/min.

Donald Albin

Numerade Educator

Problem 67

The rate at which the United States imports oil, expressed in terms of the energy content of the imported oil, is about 600 GW. Using the "Energy Content of Fuels" table in Appendix C, convert this figure to gallons per day.

Donald Albin

Numerade Educator

Problem 68

By measuring oxygen uptake, sports physiologists have found that long-distance runners' power output is given approximately by $P=m(b v-c),$ where $m$ and $v$ are the runner's mass and speed, and $b$ and $c$ are constants given by $b=4.27 \mathrm{J} / \mathrm{kg} \cdot \mathrm{m}$ and $c=1.83$ W/kg. Determine the work done by a 54 -kg runner who runs a 10 -km race at $5.2 \mathrm{m} / \mathrm{s}$.

Donald Albin

Numerade Educator

Problem 69

You're writing performance specifications for a new car model. The 1750 -kg car delivers energy to its drive wheels at the rate of $35 \mathrm{kW} .$ Neglecting air resistance, what do you list for the greatest speed at which it can climb a $4.5^{\circ}$ slope?

Donald Albin

Numerade Educator

Problem 70

A $1400-\mathrm{kg}$ car ascends a mountain road at a steady $60 \mathrm{km} / \mathrm{h}$ against a $450-\mathrm{N}$ force of air resistance. If the engine supplies energy to the drive wheels at the rate of $38 \mathrm{kW},$ what's the slope angle of the road?

Donald Albin

Numerade Educator

Problem 71

You do $2.2 \mathrm{kJ}$ of work pushing a $78-\mathrm{kg}$ trunk at constant speed $3.1 \mathrm{m}$ along a ramp inclined upward at $22^{\circ} .$ What's the frictional coefficient between trunk and ramp?

Donald Albin

Numerade Educator

Problem 72

(a) Find the work done in lifting 1 L of blood (mass 1 kg) from the foot to the head of a 1.7 -m-tall person. (b) If blood circulates through the body at the rate of $5.0 \mathrm{L} / \mathrm{min}$, estimate the heart's power output. (Your answer underestimates the power by a factor of about 5 because it neglects fluid friction and other factors.)

Donald Albin

Numerade Educator

Problem 73

(a) What power is needed to push a 95 -kg crate at $0.62 \mathrm{m} / \mathrm{s}$ along a horizontal floor where the coefficient of friction is $0.78 ?$ (b) How much work is done in pushing the crate $11 \mathrm{m} ?$

Donald Albin

Numerade Educator

Problem 74

You mix flour into bread dough, exerting a $45-\mathrm{N}$ force on the spoon, which you move at $0.29 \mathrm{m} / \mathrm{s} .$ (a) What power do you supply? (b) How much work do you do if you stir for 1.0 min?

Donald Albin

Numerade Educator

Problem 75

A machine does work at a rate given by $P=c t^{2},$ where $c=18 \mathrm{W} / \mathrm{s}^{2}$ and $t$ is time. Find the work done between $t=10 \mathrm{s}$ and $t=20 \mathrm{s}$.

Donald Albin

Numerade Educator

Problem 76

A typical bumblebee has mass 0.25 mg. It beats its wings 100 times per second, and the wings undergo an average displacement of about $1.5 \mathrm{mm}$. When the bee is hovering over a flower, the average force between wings and air must support the bee's weight. Estimate the average power the bee expends in hovering.

Donald Albin

Numerade Educator

Problem 77

You're trying to decide whether to buy an energy-efficient $225-\mathrm{W}$ $\sim$ refrigerator for \$ 1150$ or a standard $425-\mathrm{W}$ model for $\$ 850 dollars The standard model will run $20 \%$ of the time, but better insulation means the energy-efficient model will run $11 \%$ of the time. If electricity costs $9.5 \phi / \mathrm{kW} \cdot \mathrm{h}$, how long would you have to own the energy-efficient model to make up the difference in cost? Neglect interest you might earn on your money.

Donald Albin

Numerade Educator

Problem 78

Your friend does five reps with a barbell, on each rep lifting $45 \mathrm{kg} 0.50 \mathrm{m} .$ She claims the work done is enough to "burn off' a chocolate bar with energy content $230 \mathrm{kcal}$ (see Exercise 33 ). Is that true? If not, how many lifts would it take?

Donald Albin

Numerade Educator

Problem 79

A machine delivers power at a decreasing rate $P=P_{0} t_{0}^{2} /\left(t+t_{0}\right)^{2}$ where $P_{0}$ and $t_{0}$ are constants. The machine starts at $t=0$ and runs forever. Show that it nevertheless does only a finite amount of work, equal to $P_{0} t_{0}$.

Donald Albin

Numerade Educator

Problem 80

A locomotive accelerates a freight train of total mass $M$ from rest, applying constant power $P$. Determine the speed and position of the train as functions of time, assuming all the power goes to increasing the train's kinetic energy.

Donald Albin

Numerade Educator

Problem 81

A force given by $F=b / \sqrt{x}$ acts in the $x$ -direction, where $b$ is a constant with the units $\mathrm{N} \cdot \mathrm{m}^{1 / 2} .$ Show that even though the force becomes arbitrarily large as $x$ approaches zero, the work done in moving from $x_{1}$ to $x_{2}$ remains finite even as $x_{1}$ approaches zero. Find an expression for that work in the limit $x_{1} \rightarrow 0$.

Donald Albin

Numerade Educator

Problem 82

You're assisting a cardiologist in planning a stress test for a $75-\mathrm{kg}$ patient. The test involves rapid walking on an inclined treadmill, and the patient is to reach a peak power output of 350 W. If the patient's maximum walking speed is $8.0 \mathrm{km} / \mathrm{h},$ what should be the treadmill's inclination angle?

Donald Albin

Numerade Educator

Problem 83

You're an engineer for a company that makes bungee-jump cords, and you're asked to develop a formula for the work involved in stretching cords to double their length. Your cords have force distance relations described by $F=-\left(k x+b x^{2}+c x^{3}+d x^{4}\right)$ where $k, b, c,$ and $d$ are constants. (a) Given a cord with unstretched length $L_{0},$ what's your formula? (b) Evaluate the work done in doubling the stretch of a 10 -m cord with $k=420 \mathrm{N} / \mathrm{m}$ $b=-86 \mathrm{N} / \mathrm{m}^{2}, c=12 \mathrm{N} / \mathrm{m}^{3},$ and $d=-0.50 \mathrm{N} / \mathrm{m}^{4}$.

Donald Albin

Numerade Educator

Problem 84

You push an object of mass $m$ slowly, partway up a loop-the-loop track of radius $R,$ starting from the bottom, and ending at a height $h<R$ above the bottom. The coefficient of friction between the object and the track is a constant $\mu .$ Show that the work you do against friction is $\mu m g \sqrt{2 h R-h^{2}}$.

Donald Albin

Numerade Educator

Problem 85

A particle moves from the origin to the point $x=3 \mathrm{m}, y=6 \mathrm{m}$ along the curve $y=a x^{2}-b x,$ where $a=2 \mathrm{m}^{-1}$ and $b=4 .$ It's subject to a force $c x y \hat{\imath}+d \hat{\jmath},$ where $c=10 \mathrm{N} / \mathrm{m}^{2}$ and $d=15 \mathrm{N}$.Calculate the work done by the force.

Donald Albin

Numerade Educator

Problem 86

Repeat Problem 85 for the following cases: (a) the particle moves first along the $x$ -axis from the origin to the point $(3 \mathrm{m}, 0)$ and then parallel to the $y$ -axis until it reaches $(3 \mathrm{m}, 6 \mathrm{m}) ;$ (b) it moves first along the $y$ -axis from the origin to the point $(0,6 \mathrm{m})$ and then parallel to the $x$ -axis until it reaches $(3 \mathrm{m}, 6 \mathrm{m})$.

Donald Albin

Numerade Educator

Problem 87

The world's fastest elevator, in Taiwan's Taipei 101 skyscraper (Fig. $6.18),$ ascends at the rate of $1010 \mathrm{m} / \mathrm{min} .$ Counterweights balance the weight of the elevator car, so the motor doesn't have to lift the car's weight. If the motor produces 330 kW of power, what's the maximum number of $67-\mathrm{kg}$ people the elevator can accommodate? (Your answer somewhat overestimates the actual rated load of 24 people.)
(FIGURE CANT COPY)

Donald Albin

Numerade Educator

Problem 88

An experimental measurement of the force required to stretch a "slingshot is given in the table below. Plot the force-distance curve for this slingshot and use graphical integration to determine the work done in stretching the slingshot the full 40 -cm distance.$$\begin{array}{cc}\hline \text { Stretch }(\mathrm{cm}) & \text { Force }(\mathrm{N}) \\\hline 0 & 0 \\5.00 & 0.885 \\10.0 & 1.89 \\15.0 & 3.05 \\20.0 & 4.48 \\25.0 & 6.44 \\30.0 & 8.22 \\35.0 & 9.95 \\40.0 & 12.7 \\\hline\end{array}$$

Donald Albin

Numerade Educator

Problem 89

You're an expert witness in a medical malpractice lawsuit. A hospital patient's leg slipped off a stretcher and his heel hit the floor. The defense attorney for the hospital claims the leg, with mass $8 \mathrm{kg}$, hit the floor with a force equal to the weight of the leg-about $80 \mathrm{N}$ - and any damage was due to a prior injury. You argue that the leg and heel dropped freely for $0.7 \mathrm{m}$, then hit the floor and stopped in $2 \mathrm{cm} .$ What do you tell the jury about the force on the heel?

Donald Albin

Numerade Educator

Problem 90

The energy in a batted baseball comes from the power delivered while the bat is in contact with the ball. The most powerful hitters can supply some 10 horsepower during the brief contact time, propelling the ball to over 100 miles per hour. Figure 6.19 shows data taken from a particular hit, giving the power the bat delivers to the ball as a function of time.
(FIGURE CANT COPY)
Which of the following is greatest at the peak of the curve?
a. the ball's kinetic energy
b. the ball's speed
c. the rate at which the bat supplies energy to the ball
d. the total work the bat has done on the ball

Donald Albin

Numerade Educator

Problem 91

The energy in a batted baseball comes from the power delivered while the bat is in contact with the ball. The most powerful hitters can supply some 10 horsepower during the brief contact time, propelling the ball to over 100 miles per hour. Figure 6.19 shows data taken from a particular hit, giving the power the bat delivers to the ball as a function of time.
(FIGURE CANT COPY)
The ball has its maximum speed at about
a. $85 \mathrm{ms}$
b. $145 \mathrm{ms}$
c. $185 \mathrm{ms}$
d. whenever the force is greatest.

Donald Albin

Numerade Educator

Problem 92

The energy in a batted baseball comes from the power delivered while the bat is in contact with the ball. The most powerful hitters can supply some 10 horsepower during the brief contact time, propelling the ball to over 100 miles per hour. Figure 6.19 shows data taken from a particular hit, giving the power the bat delivers to the ball as a function of time.
(FIGURE CANT COPY)
As a result of being hit, the ball's kinetic energy increases by about
a. $550 \mathrm{J}$
b. $1.3 \mathrm{kJ}$
c. $7.0 \mathrm{kJ}$
d. You can't tell because you don't know its speed coming from the pitcher.

Donald Albin

Numerade Educator

Problem 93

The energy in a batted baseball comes from the power delivered while the bat is in contact with the ball. The most powerful hitters can supply some 10 horsepower during the brief contact time, propelling the ball to over 100 miles per hour. Figure 6.19 shows data taken from a particular hit, giving the power the bat delivers to the ball as a function of time.
(FIGURE CANT COPY)
The force on the ball is greatest approximately
a. at $185 \mathrm{ms}$
b. at the peak in Fig. 6.19
c. before the peak in Fig. 6.19
d. after the peak in Fig. 6.19 but before 185 ms.

Donald Albin

Numerade Educator