Work, Energy, Power
Work
1. Trying to break down a door, a man pushes futilely against it with a large force. Is work being done? Explain using the work formula
A) You pull a wagon along the floor with the handle at an angle of 45 degrees with the floor. If you travel a distance of 5.0 m, do you do work on the wagon? Assume constant speed.
B) Suppose you change the angle to 30 degrees and pull the wagon 5.0 m. Do you do more/less/the same amount of work? Assume constant speed again. Explain.
1. When you lift a mass in the gravitational field, do you do work? Does the gravitational force do work? What is the net work done on the mass/
2. Gravity: a) When a mass is in free fall, is work being done on it? What force does work?
B) Does the gravitational force do any work on an orbiting satellite?
Energy
3. Can kinetic energy be negative? Explain.
4. How is force related to the change in energy of a mass?
5. If a sprinter triples his speed, by how much does his energy change?
6. If positive work is done on an object and its potential energy remains constant, the object must ________________. If negative work is done on an object and its potential energy remains constant, the object must ____________________.
7. To double the kinetic energy at the bottom of a roller coaster, the height of the hill must be ___________________, this will result in _______________ the velocity.
8. To double the velocity at the bottom of a roller oaster, the height of the hill must be ______________.
9. To double the height of a ball that is thrown straight up, the kinetic energy must be __________, this means increasing the velocity by ________________
10. If energy is conserved, why doesn’t a dropped pendulum or a dropped bouncy ball ever swing or bounce back up to the same height from which they were dropped?
11.
Consider the track above. Assuming the marble starts at ‘1’ from rest, label the locations having
- Most PE
- Most KE
Assume no friction for this question.
12. Does considering friction change your answers to # 13? Why is the first hill the highest hill of a traditional roller coaster?
13. If a bouncy ball or pendulum is thrown downward they can swing or bounce back up to or even past the starting height. Explain in terms of energy and work.
14. In a baseball game, two pop-ups are hit in succession. The second rises twice as high as the first. Compare the speeds of the balls when they leave the bat.
Problems
15. A 75.0 kg skier skis down a 15 degree hill that has a vertical rise of 25 m.
How much work does gravity do on the skier? 1.8 x 104 J
16. A grocery cart of mass 18 kg is pushed at a constant speed along the aisle at an angle of 20 with the horizontal. The applied force is 12 N over the 15 m aisle. How much work is done on the cart by the applied force? (W = 170 J )
17. Power:
The 75.0 kg skier from problem 1 hikes up the 25 m hill in 50 s. What is the power generated? P = 370 W
18. A force is applied to a 0.4kg ball, increasing its velocity from zero to 30 m/s over a distance of 0.9 m. What is the Work done on the ball? What magnitude of force was applied? W = 180 J, F = 200 N
19. A 900-kg car speeds up from 22.0 m/s to 44.0 m/s. What is the car’s change in kinetic energy? What is the net work done on the car? (Both = 6.53 x 107 J)
20. A train of mass 2.50 x 104 kg is powered across a level track with a force of 5.0 x 105 N over a distance of 509 m.
a) Calculate the work done on and the change in KE of the train 2.55 x 108 J
b) If the initial velocity of the train was zero, what is the final velocity? Vf = 143 m/s
21. A cart of mass 15.0 kg receives a constant force of 10.0N, which causes it to reduce its velocity from 7.5 m/s to 3.2 m/s. What distance did the cart travel during the application of this force? (35 m)
22. A weightlifter raises a 180-kg barbell to a height of 1.95 m. What is the change in PE?
ΔPE = 3.44 x 103 J
The weightlifter lowers the barbell onto a rack that is 1.0 m off the ground. What is this change in PE (calculated from the highest location?) ΔPE = - 1.68 x 103 J
23. A 7.30-kg bowling ball is lifted from the storage rack, (h1 = 0.6 m) to your shoulder (h2 = 1.3m)
What is the change in the PE of the ball? How much work was done on the ball by you? How much work was done by gravity? What is the net work done on the ball?
24. If an object of mass 2.0 kg falls from a 0.35 m table, what is its change in PE? How much work do you do when you put the mass back on the table?
25. If you run up a 5.0 m flight of stairs, how much work do you do? (mass (kg) = weight (lbs)/2.2). If you do this in 0.9 s, what power do you generate?
26. A bike and rider have a total mass of 65.0 kg. Initially, the (bike+ rider) is travelling 5 m/s at the top of a 10.0 m hill. The rider coasts down the hill.
a) Assuming no frictional losses of energy, what will the velocity of the bike+rider be at the bottom of the hill? (Vf = 14.9 m/s)
b) If the rider continues to coast and the road immediately slopes up, how high will the bike coast up the next hill before stopping? (h = 15 m)
27. A roller coaster has a starting drop of 100. m from the top to the bottom where the track curves out.
a)Assuming that the coaster is at rest before the drop, and neglecting friction, what is the expected speed at the bottom? (vf = 44 m/s)
b) If the coaster actually loses 5% of its energy to friction on the first drop, what is its actual speed at the bottom? (vf = 43 m/s)
c) What is the maximum 2nd hill height this coaster could have? ( h = 95 m)
28. A child, mass is 30 kg, is on a playground swing that is 0.30 m above the ground. She is pushed by another child who releases the swing (from rest) from 1.0 m above the ground.
a) How fast is the child moving at the lowest part of the swing? (v = 3.7 m/s)
b) If the child is actually moving at 3.0 m/s at the lowest point, how much energy has been lost to dissipative forces? (Wnc = 71 J)
29. A skier starts from rest at the top of a 45 m hill. He skis down a 30 degree incline into a valley, then up a 40 m hill. Ignore friction.
a) What is the skier’s speed at the bottom of the hill? (V = 30 m/s)
b) What is the skier’s speed at the top of the 40 m hill? (v = 9.9 m/s)
30. Two rocks of the same mass are thrown from a 12 m ledge. Rock A is thrown up at 4.0 m/s, while rock B is thrown down at 4.0 m/s.
a) Calculate and compare the impact speeds of rock A and rock B.
b) Would this finding change if the rocks’ had different masses?
31. A child on a sled, mass of 35-kg, is starts from rest and slides down a snowy, 20-m hill.
a) Ignoring friction, what is the expected speed of the sled at the bottom of the hill? (v= 20 m/s)
b) If the actual speed is 8 m/s, how much work was done by friction?
(Wnc = 5740 J)
32. Shooting from a height of 2.15 m, a basketball forward shoots a 0.6 kg basketball with a speed of 4.2 m/s straight up toward the 3.05 m hoop. Will the ball have enough energy to clear the hoop?
33. Desperado, a roller coaster in Nevada, has a vertical drop of 68.6 m. The coaster is designed so the speed at the bottom of the drop is 35.6 m/s. Assuming zero starting speed at the top of the drop, what percentage of the initial energy is dissipated by friction? (6%)
Supplemental problems
Work, KE, PE gravitational
Pg. 262 # 1,2 pg. 278 # 52-54, 56, 58, 60, 61, 64-66
pg. 306 #34, 36, 39, 44
Pg. 287 # 1-3, pg. 307 # 54,55, 57, 59-61
Conservation of ME
Pg. 297 # 15, 17, 18
Pg. 308-309 # 74, 76,77, 81
pg 311 # 2, 7
Non-conservative work
Pg. 301 # 27, pg. 309 # 82, 85 pg. 311 # 4
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