163 Your Turn Solutions
1. A horizontal force of 850 N is needed to push a car across a lot 35 meters wide.
a. Determine the amount of work needed to push the car across the lot.
W= Fd= 850 N * 35m=30,000 J
b. If it rained and the force needed to push the car across the lot doubled, by what factor would the work needed to push the car across the 35 meter lot change.
W=2F * d = 2W
2. Based upon your answer to 1(b), state the relationship between work and force?
F is directly related to W
3. A forklift raises a 580 kg box a vertical distance of 1.2 meters.
a. Determine the work done by the forklift.
W=mgd=580 * 9.8 * 1.2 = 6820J
b. Determine the work done by gravity.
W=mgd cos180 = -6820J
4. Superman keeps a bus from rolling down a hill with a force of 1,000,000 N. Determine the amount of work he does to keep the bus from rolling.
No work is done since there is no displacement.
5. Mr. Schmidgall held his wife in his arms to carry her across the threshold. His wife had a mass of 48 kg and he carried her a horizontal distance of 5 m. How much work did Mr. Schmidgall do?
Since the force component and dislacement components are perpendicular to each other, there is no work done.
6. A rope is used to pull a metal box 15 meters across the floor with a force of 630 N. The rope is held at an angle of 46o with respect to the floor. Determine the amount of work needed to pull the box the 15 meters.
W=630N * 15m * cos 46 = 6600J
7. A body builder lifts 135 lb (2.21 lbs = 10 N) barbell a vertical distance of 1.6 meters. If the barbell is lifted in 1.5 seconds, determine
a. The amount of work done as she lifts the barbell.
W=135 lb * 4.45 N/lb * 1.6m = 960J
b. The amount of power developed by her as she lifts the barbell.
8. If the barbell in challenge 7 were lifted the 1.6 meters in 1.0 seconds how would the work needed to lift it change? How would the power change? Explain.
The work needed would remain the same however the power would increase with less time.
9. A 580 N box is lifted a distance of 20 meters straight up with a rope and pulley system. The job is done in 10 seconds. What is the power developed in watts, kilowatts, and horsepower?
10. An electric motor develops 65 kW of power as it lifts a loaded elevator a distance of 17.5 meters in 35 seconds. How much force does the motor exert.
11. A 550 kg roller coaster sits at rest at a height of 36 meters. Neglect friction and air resistance for the following.
a. Determine the PE of the roller coaster at the height of 36 m.
b. Determine the TME of the roller coaster at the height of 36 m.
c. Determine the TME of the roller coaster at the height of 18 m.
d. Determine the PE of the roller coaster at the height of 18 m.
e. Determine the KE of the roller coaster at the height of 18 m.
f. Determine the TME of the coaster at the height of 0 m.
g. Determine the KE of the coaster at the height of 0 m.
12. The Giant Drop at Great America raises its passengers to a height of 68 meters holds them at rest and lets them drop to a height of 38 meters. Three riders (180 kg total - 60 kg each) and the car 500 kg have a combined mass of 680 kg.
a. Determine the PE of the three riders and car at the height of 68 m.
b. Determine the TME of the three riders and car at the height of 68 m.
c. Determine the TME of the three riders and car at the height of 38 m.
d. Determine the KE of the three riders and car at the height of 38 m.
e. Determine the speed of the three riders and car at the height of 38 m.
13. A 38 kg girl is placed in a swing. With what velocity would she need to be pushed to push her 1.0 meters above her starting height.
14. A 15 kg cart is placed upon a frictionless inclined plane 0.70 meters above the table top.
a. Determine the PE of the cart at the height of 0.70 meters.
b. Determine the speed of the cart has it reaches the table top.
c. If a 150 kg cart were placed upon the incline at the same height, determine the speed with which it would reach the table top.
15. A bowling ball is placed on a wire, lifted 0.80 meters above its lowest position and released.
a. Determine the speed of the bowling ball at its lowest position. Neglect any frictional effects.
b. Determine the height to which the bowling ball swings as it returns to its release position.
16. A weight lifter raises a 180 kg barbell to a height of 2 meters. Determine the increase in the barbell's potential energy.
17. A person weighing 630 N climbs a ladder to a height of 5.0 meters.
a. Determine the work done by the person.
b. Determine the increase in the gravitational potential energy of the person.
18. A rifle can shoot a 4.2 gram bullet at a speed of 1000 m/s.
a. Determine the KE of the bullet.
b. Determine the amount of work done on the bullet if it starts from rest.
c. If the length of the rifle's barrel is 0.75 meters long (this is the distance through which the rifle's force acts), what is the average force on the bullet from the rifle?
19. In the movie Comet, a comet with a mass of 8 x 1011 kg hit the Earth at a speed of 25,000 m/s . Determine the comet's KE as it impacted the Earth.
20. Explain which of the following choices best describes where the comet's KE (from challenge 19) ended up.
a. The comet's KE was lost and no energy remains.
b. The comet's KE has ended up in the form of thermal energy.
c. The comet's KE is still present. It gave the Earth all of its KE.
d. a-c are all part of the answer.
(b) Most of the kinetic energy of the comet turned into thermal energy. Upon impact, much of the ground and comet was heated (fused), while much of the remaining particles of the comet (as well as parts of the earth) became projectiles gaining gravitational potential energy and eventually falling back to earth. While making contact with the earth, the particles and the ground were again heated as the kinetic energy of the particles was removed.
21. Can the KE of a baseball ever have a negative value? Explain.
Kinetic energy cannot be negative as energy is not a vector quantity; direction does not matter.
22. Becky Lovetaski (Susie's younger sister) skis on the bunny hill and starts at a height of 45 meters. Becky skis down a 30o incline to the bottom of a hill and continues up a 40 m hill. Both the hill heights are measured from the bottom of the hill.
a. Determine Becky's speed at the bottom of the 45 meter hill.
b. Determine Becky's speed at the top of the 40 meter hill.
23. A bicycle rider approaches a hill with a speed of 8.5 m/s. the total mass of the bike and rider is 85 kg.
a. Determine the KE of the bike and rider.
b. The rider coasts up to a frictionless hill. At what height will the bike and rider come to a stop?
24. Tarzan (m=85 kg) swings from a tree on the end of a 20 m vine. His feet touch the ground 4.0 m below their original height. How fast is Tarzan moving when he reaches the ground?
25. Lets say Tarzan had just fell out of the tree and fallen straight down 4.0 meters. Determine his speed now and compare its value to the answer for challenge 19. Explain why the two answers compare the way they do.
In both cases, gravitational potential energy changes into kinetic energy over a vertical displacement of 4 m.
26. Does the Work-Energy Theorem apply when a speeding car puts on its brakes and comes to a stop? Explain.
TMEinitial + Wext = TMEfinal As a car moves, it has kinetic energy. As brakes are applied, the road exerts an external force on the car, doing negative work which causes the car to lose its kinetic energy. The amount of work done must be the same value as the amount of kinetic energy that the car had initially. As a result, the car has no mechanical energy once it comes to rest.
27. Two pendulums are swinging side by side. At the bottom of the swing, the speed of one pendulum bob is four times the speed of the other. Compare the heights from which the two bobs began swinging.
28. A 1500 kg car moves along level ground at a speed of 23 m/s. The driver takes her foot off the accelerator and 850 Newtons of friction act on the car over a displacement of 110 m. Determine the speed of the car after the 110 m displacement.
29. A 420 kg glider glides along at a speed of 65 m/s. If it experiences a wind resistance of 190 N through a displacement of 350 meters of horizontal flying, determine the speed of the glider.
30. The 420 kg glider from above now experiences the same wind resistance, but this time dives at an angle of 30 degrees and drops a vertical from a 350 m altitude to a 325 m altitude.
a. Determine the displacement through which the glider flew.
b. Determine the TME of the glider at the 350 m altitude.
c. Determine the non-conservative work done on the glider by the wind resistance.
d. Determine the speed of the glider after the 25 meter drop.
Last Updated: October 8, 1997