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Please do questions, 10, 24, 81, and 86

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PROBLEMS AND CONCEPTUAL EXERCISES

245

4. IPA 4.1-kg block is attached to a spring with a force constant

of 550 N/m, as shown in Figure 8-17. (a) Find the work done by

the spring on the block as the block moves from A to B along

paths 1 and 2. (b) How do your results depend on the mass of

the block? Specifically, if you increase the mass, does the work

done by the spring increase, decrease, or stay the same? (As-

sume the system is frictionless.)

urnen

9. As an Acapulco cliff diver drops to the water from a height of

46 m, his gravitational potential energy decreases by 25,000 J.

What is the diver’s weight in newtons?

10. Find the gravitational potential energy of an 88-kg person

standing atop Mt. Everest at an altitude of 8848 m. Use sea level

as the location for y=0.

11. Jeopardy! Contestants on the game show Jeopardy! depress

spring-loaded buttons to “buzz in” and provide the question

corresponding to the revealed answer. The force constant on

these buttons is about 130 N/m. Estimate the amount of energy

it takes-at a minimum–to buzz in.

12… BIO The Wing of the Hawkmoth Experiments performed

on the wing of a hawkmoth (Manduca sexta) show that it de-

flects by a distance of x = 4.8 mm when a force of magnitude

F – 3.0 mN is applied at the tip, as indicated in Figure 8-19.

Treating the wing as an ideal spring, find (a) the force constant

of the wing and (b) the energy stored in the wing when it is de-

flected. (c) What force must be applied to the tip of the wing to

store twice the energy found in part (b)?

A

B

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-2.0 cm

20 cm

1.0 cm

FIGURE 8-17 Problems 4 and 6

5. . IP (a) Calculate the work done by gravity as a 5.2-kg object is

moved from A to B in Figure 8-18 along paths 1 and 2. (b) How

do your results depend on the mass of the block? Specifically, if

you increase the mass, does the work done by gravity increase,

decrease, or stay the same?

Side View

A

50 m

S.We

10 m

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A FIGURE 8-20 Problems 17,

34, 35, and 74

SECTION 8-3 CONSERVATION OF MECHANICAL

ENERGY

18. CE Predict/Explain You throw a ball upward and let it fall to

the ground. Your friend drops an identical ball straight down to

the ground from the same height. Is the change in kinetic en-

ergy of your ball greater than, less than or equal to the change

in kinetic energy of your friend’s ball? (b) Choose the best

explanation from among the following:

I. Your friend’s ball converts all its initial energy into kinetic

energy

II. Your ball is in the air longer, which results in a greater

change in kinetic energy

III. The change in gravitational potential energy is the same for

each ball, which means the change in kinetic energy must

be the same also

19. CE Suppose the situation described in Conceptual Check

point 8-2 is repeated on the fictional planet Epsilon, where

the acceleration due to gravity is less than it is on the Earth.

(a) Would the height of a hill on Epsilon that causes a reduction

in speed from 4 m/s to be greater than, less than or equal to the

height of the corresponding hill on Earth? Explain. (b) Consider

the hill on Epsilon discussed in part (a). If the initial speed at the

bottom of the hill is 5 m/s, will the final speed at the top of the

hill be greater than, less than or equal to 3 m/s? Explain.

20. CE Predict/Explain When a ball of mass m is dropped from

rest from a height, its kinetic energy just before landing is K.

Now, suppose a second ball of mass 4m is dropped from rest

from a height h/4. (a) Just before ball 2 lands, is its kinetic en-

ergy 4K, 2K, K, K/2, or K/42 (b) Choose the best explanation from

among the following:

1. The two balls have the same initial energy.

FIGURE 8-21 Problems 22 and 23

23. CE Referring to Problem 22, suppose the object is released from

rest at a point halfway between the points F and G. Rank the

other points in the figure in increasing order of the object’s speed,

if the object can reach that point. Indicate ties where appropriate.

24. At an amusement park, a swimmer uses a water slide to enter

the main pool. If the swimmer starts at rest, slides without fric-

tion, and descends through a vertical height of 2.31 m, what is

her speed at the bottom of the slide?

25. In the previous problem, find the swimmer’s speed at the bot-

tom of the slide if she starts with an initial speed of 0.840 m/s.

26. IP A player passes a 0.600-kg basketball downcourt for a fast

break. The ball leaves the player’s hands with a speed of 8.30 m/s

and slows down to 7.10 m/s at its highest point. (a) Ignoring air

resistance, how high above the release point is the ball when it

is at its maximum height? (b) How would doubling the ball’s

mass affect the result in part (a)? Explain.

27… CE Three balls are thrown upward with the same initial

speed do, but at different angles relative to the horizontal, as

shown in Figure 8Ã¢â‚¬â€œ22. Ignoring air resistance, indicate which of

the following statements is correct: At the dashed level, (A) ball

3 has the lowest speed; (B) ball 1 has the lowest speed; (C) all

three balls have the same speed; (D) the speed of the balls de-

pends on their mass.

Sie

FIGURE 8-22 Problem 27

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TUM VELIC

following calculations. Find (a) the distance through which the

81. A skateboarder starts at point A in Figure 8-27 and rises to a

strip is flexed and (b) the force constant of the strip.

height of 2.64 m above the top of the ramp at point B. What was

the skateboarder’s initial speed at point A?

73. . IP A pendulum bob with a mass of 0.13 kg is attached to a

string with a length of 0.95 m. We choose the potential energy to

be zero when the string makes an angle of 90Ã‚Â° with the vertical.

(a) Find the potential energy of this system when the string

makes an angle of 45Ã‚Â° with the vertical. (b) is the magnitude of

the change in potential energy from an angle of 90Ã‚Â° to 45Ã‚Â°

2.64 m

greater than, less than, or the same as the magnitude of the

change from 45Ã‚Â° to 0Ã‚Â°? Explain. (c) Calculate the potential en

ergy of the system when the string is vertical

74. . Suppose the pendulum bob in Figure 8-20 has a mass of

0.25 kg. (a) How much work does gravity do on the bob as it

moves from point A to point B? (b) From point B to point A?

(c) How much work does the string do on the bob as it moves

from point A to point B? (d) From point B to point A?

75. Ã¢â‚¬Â¢ An 1865-kg airplane starts at rest on an airport runway at

sea level. (a) What is the change in mechanical energy of the air-

FIGURE 8-27 Problem 81

plane if it climbs to a cruising altitude of 2420 m and maintains

a constant speed of 96.5 m/s? (b) What cruising speed would 82. In the Atwood’s machine of Problem 36, the mass in, re-

the plane need at this altitude if its increase in kinetic energy is mains at rest once it hits the floor, but the mass m, continues

to be equal to its increase in potential energy?

moving upward. How much higher does mi go after my has

76. IP At the local playground a child on a swing has a speed of

landed? Give your answer for the case h = 1.2 m, mÃ„Â± = 3.7 kg,

and m2 = 4.1 kg

2.02 m/s when the swing is at its lowest point. (a) To what max-

imum vertical height does the child rise, assuming he sits still 83. An 8.70-kg block slides with an initial speed of 1.56 m/s up

and “coastsÃ¢â‚¬Â? Ignore air resistance. (b) How do your results a ramp inclined at an angle of 28.4Ã‚Â° with the horizontal. The co-

change if the initial speed of the child is halved?

efficient of kinetic friction between the block and the ramp is

77. The water slide shown in Figure 8-26 ends at a height of

0.62. Use energy conservation to find the distance the block

slides before coming to rest.

1.50 m above the pool. If the person starts from rest at point A

and lands in the water at point B, what is the height h of the 84… Repeat the previous problem for the case of an 8.70-kg block

water slide? (Assume the water slide is frictionless.)

sliding down the ramp, with an initial speed of 1.56 m/s.

78… If the height of the water slide in Figure 8Ã¢â‚¬â€œ26 is h = 3.2 m, 85. Jeff of the Jungle swings on a 7.6-m vine that initially makes

and the person’s initial speed at point A is 0.54 m/s, what is the an angle of 37Ã‚Â° with the vertical. If Jeff starts at rest and has a

w

701

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86. A 1.9 kg block slides down a frictionless ramp, as shown in

Figure 8-28. The top of the ramp is 1.5 m above the ground; the

bottom of the ramp is 0.25 m above the ground. The block

leaves the ramp moving horizontally, and lands a horizontal

distance d away. Find the distance d.

93. … An ice cube is placed on top of an overturned spherical

bowl of radius r, as indicated in Figure 8-30. If the ice cube slides

downward from rest at the top of the bowl, at what angle # does

it separate from the bowl? In other words, at what angle does

the normal force between the ice cube and the bowl go to zero?

1.5 m

0.25 m

FIGURE 8-28 Problems 86 and 87

FIGURE 8-30 Problem 93

94. … IP The two blocks shown in Figure 8-31 are moving with an

initial speed v. (a) If the system is frictionless, find the distance

d the blocks travel before coming to rest. (Let U = 0 correspond

to the initial position of block 2.) (b) Is the work done on block

2 by the rope positive, negative, or zero? Explain. (c) Calculate

the work done on block 2 by the rope.

bly.com

87. . Suppose the ramp in Figure 8-28 is not frictionless. Find the

distance d for the case in which friction on the ramp does -9.7J

of work on the block before it becomes airborne.

88. BIO Compressing the Ground A running track at Harvard

University uses a surface with a force constant of 2.5 X 10 N/m

This surface is compressed slightly every time a runner’s foot

lands on it. The force exerted by the foot, according to the

Saucony shoe company, has a magnitude of 2700 N for a typical

runner. Treating the track’s surface as an ideal spring, find (a) the

amount of compression caused by a foot hitting the track and

(b) the energy stored briefly in the track every time a foot lands.

89… BIO A Flea’s Jump The resilin in the upper leg (coxa) of a

flea has a force constant of about 26 N/m, and when the flea

cocks its jumping legs, the resilin in each leg is stretched by ap-

proximately 0.10 mm. Given that the flea has a mass of 0.50 mg

and that two legs are used in a jump, estimate the maximum

height a flea can attain by using the energy stored in the resilin

(Assume the resilin to be an ideal spring.)

90. IP A trapeze artist of mass m swings on a rope of length L.

sics.

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