Advanced Placement Physics B



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Unit E

Worksheet

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Work done by constant force

1. A teacher decided to rearrange his classroom. One large table, having a mass of 90 kg, needs to be moved 2.5m. If the required net force to move the table is 310 N, how much net work will be done in moving the table?

2. A 15 kg crate is pushed along a floor through a distance of 4.8m. If the applied force was 35N and the coefficient of friction was 0.2, find:

a. The work done by the applied force on the crate.

b. The work done by friction.

c. The net work done on the crate.

3. A child pulls his wagon, full of toys, at an angle of 20( above the horizontal. If he pulls it a distance of 16m and does 110J of work, calculate the force he exerts? (Ignore friction.)

4. A 0.5 kg water balloon is thrown directly upwards into the air. It reaches a maximum height of 10m. Calculate the work done by gravity on the water balloon. (Note the sign of your answer. What does this mean?)

5. A 450 kg piano is hoisted up into the air a distance of 20 meters at constant velocity. How much work is done on the piano by gravity? How much work is done by the hoist on the piano? What was the net work done on the piano?

6. A child pulls her friend on a sled (at a constant speed) 8m up a snowy hill at an incline of 15(. If the friend and sled have a total mass of 35kg and the coefficient of friction is 0.15, calculate the work done on the sled by the applied force (child pulling).

Work done by varying force

7. Given the graph of data for a spring at the right, find:

a. the spring constant

b. the work done to compress the spring 0.6m

c. the work done to compress the spring from 0.2m to 0.6m

8. A 2kg remote control car experiences a varying force as shown by the graph below. Assume the car starts from rest.

a. How much work is done on the car from d=1m to d=6m?

b. How much work total was done on the car?

c. What was the car’s velocity at d = 5m?

d. What was the car’s velocity at d = 7m?

9. A child pushes a toy car across a floor. The force experienced by the toy car is shown on the graph below.

a. How much work was done from 2m to 6m?

b. What was the total work done?

d. If the velocity at d = 6m is 5 m/sec,

what is the mass of the car? (Assume vi = 0)

10. During a physics lab it was noted that a particular spring required a force of 6.3N to compress the spring 17cm. How much work would be done on the spring if the student only compressed it 5cm?

Work and Energy

11. What is the kinetic energy of the Earth as it moves around the Sun? (Orbital radius of the Earth is 1.49 x 1011 m; mEarth = 5.98 x 1024 kg)

12. A 1000-kg hot air balloon rises from 100m to 200m above the ground. What was the change in the balloon’s gravitational potential energy? What was the minimum work required to change its height?

13. A 75-kg skier traveling at 20m/s comes to a stop at the bottom of a hill.

a. How much work was done, in order to stop?

b. If he stops over a distance of 30m, what was the magnitude of the force applied (the stopping force)?

14. During a test run, a 1000 kg roller coaster car reaches a speed of 30m/s.

a. What is the roller coaster’s kinetic energy at 30m/s?

b. How much work was required to attain this speed, if the car started from rest?

c. Calculate the amount of work required by friction to slow the car down to 5 m/s.

15. While an 800 kg car was traveling along a road, a lost puppy wondered out in the car’s path. When the very observant driver saw the puppy he immediately hit the brakes. Before coming to a complete stop, the car traveled 12m and -1.3 x 105 J of work was done on the car by friction. (The puppy was not harmed, of course.)

a. What was the velocity of the car before the brakes were applied?

b. What force did the brakes apply to the car?

16. A 1500kg car accelerates from 10m/s to 20m/s in 3 seconds.

a. How much work was done on the car?

b. How far did the car travel? (think kinematics)

c. What was the average force on the car?

Conservation of Energy

17. A 0.5kg water balloon is thrown straight up into the air. It reaches a maximum height of 10m. What was the balloon’s initial speed? (Similar problem done earlier to find work done by gravity.)

18. In an obstacle course there is a zip line that starts at a height of 15m. What is the maximum speed a rider on the zip line could be traveling upon reaching the bottom of the zip line?

19. The Stormrunner at Hershey Park accelerates its riders from 0mph to 72mph in 2 seconds.

a. What is a 70kg rider’s change in kinetic energy during the acceleration?

b. After being accelerated along the horizontal portion of the track, the roller coaster car ascends a hill of height, 45 m. What is the maximum speed the coaster car could be traveling at the top of the hill?

20. A tourist drops a quarter off of the observation deck of the Empire State Building. Neglecting air resistance, how fast will the quarter be traveling after falling 1200m.

21. A 30 kg girl on a swing has a velocity of 5m/s at the lowest point. What will be the greatest height she can reach?

22. A pin ball machine uses a spring to launch the ball along a track and then into the playing area. If the 0.10kg ball needs to have a launch speed of 2m/s and the maximum amount the spring can be compressed 6cm, what must be the minimum spring constant for the spring?

23. A 1 kg snowball is thrown downward with an initial velocity of 2m/s from a height of 45m to the ground.

a. What was the snowball’s change in gravitation potential energy?

b. What was the snowball’s final velocity right before hitting the ground?

24. A 50kg crate is lowered from a moving truck to the ground, 2m below, via a ramp that is 5m long.

a. If the crate starts at the top of the ramp with a speed of 1m/s and reaches the bottom with a speed of 3m/s, how much work was done by friction?

b. What is the magnitude of the friction force?

25. A car traveling along a straight roadway makes an emergency stop. The skid marks left by the car are 33m in length. What was the car’s initial speed before the brakes were applied? Assume the coefficient of friction between the tires and the road is 0.70.

26. A 25 kg boy slides down a hill on a slip-n-side. The kid stops after traveling a distance of 12 m. If the frictional force experience by the boy was 50N, what was his initial velocity at the top of the slide (h=2m)?

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27. Several students go sled riding on a snow day. Although happy to have a day off from school, they are disappointed that they can not go to physics class. So, they do their own physics! They collect some equipment to make measurements and record time. They find that the length of a particular hill is 25m and at an incline of 12(. They also find that Jimmy, of mass 70.0 kg, reaches a maximum speed of 5.9m/s at the bottom of the hill. What is the coefficient of friction between his sled and the snow? Assume he starts from rest at the top of the hill.

Power

28. Calculate the power output of the car engine in Problem 18.

29. Calculate the power output required to hoist the piano of Problem 5 in a time period of 2 minutes.

30. A 60kg student runs up a flight of stairs 3m in height at 0.50hp. Calculate the time it took him to run up the stairs.

31. For a 75-watt light bulb:

a. calculate the energy transformed each second.

b. calculate the energy transformed during an hour.

c. calculate the cost of leaving the bulb on for an hour if the “Power Company” charges 4.624 cents per kilowatt-hour.

d. Calculate the cost of leaving the bulb on for 24 hours using the above rate.

Miscellaneous

32. A stone of mass m is thrown at 30 ft/sec from a cliff 25 feet high. With what speed does the stone strike the ground below the cliff? (Use the energy principle! In the English system of units, g = 32 ft/sec2.) Ans. 50 ft/s

33. A 70-kg boy, starting from rest, slides down a 30o hill that is 50 m long. He arrives at the bottom with a speed of 10 m/sec. How much heat energy has been shared between the surface of the hill and the seat of his pants? (Do not find the acceleration. Use the energy principle.) Ans. 13,650J

34. Masses of 2 kg and 3 kg are hanging at opposite ends of a cord that passes over a frictionless, massless pulley. The system is held stationary, then released. What will be the speed of the masses when the 3 kg mass has fallen 0.5 m below its starting point? (Hint: Use energy.) Ans. 1.4 m/s

35. (See sketch below.) A motorcycle daredevil rider zoomed down a ramp, starting from point A, 12 m above the ground, and took off at an angle from point B, 2 m above the ground. Between A and B the rider and his cycle, of total mass 200 kg, received 250 kJ of energy from the engine and lost 100 kJ to friction, air drag, etc. To what height above ground level did the rider ascend, if his horizontal velocity at C (a local maximum height) was 40 m/sec? Ans. 6.9m

36. A roller coaster car filled with screaming terror-freaks has a total mass of 600 kg and a speed of 10 m/s at the top of a 30-m high frictionless hill. The car plunges down the hill. The track levels out and then the car encounters a 4,000-N retarding force. How far does the car travel while this force brings it to rest? (Extra: How much time does it take the force to stop the car? The ideas in the next unit make this easier.)

Ans. 51.6 m, 3.93 s

37. A simple pendulum of length 2.6 m is swinging with a maximum speed of 0.5 m/s. What is the maximum angle that the string makes with the vertical? Ans. 5.7º

38. A simple pendulum is raised to 2.00 m above the floor and released from rest. It swings down to the vertical position, where it is 1.30 m above the floor, and where a razor blade cuts the string with negligible force. How far horizontally does the pendulum bob travel before hitting the floor? Ans. 1.91m

39. A projectile is launched at 10 m/s and an angle above the horizontal of 60 degrees. Use conservation of mechanical energy to predict the maximum height the projectile reaches. (If you really want to use kinematics, then do so only to check your result obtained by using energy.) Ans. 3.83m

Conceptual Review:

You should be able to:

A. Define the following terms: work, energy, kinetic energy, gravitational potential energy, power, and non-conservative force.

a. Work –

b. Energy –

c. Kinetic Energy –

d. Gravitational Potential Energy –

e. Power –

f. Non-conservative force –

B. Identify the SI units for work, energy, power, and spring constant.

a. Work units:

b. Energy units:

c. Power units:

C. Write the equation for work in terms of force and displacement.

D. State the conditions that must be met regarding force and displacement in order to calculate the work done by that force.

E. Determine the amount of work done by a force given the force information in graphical form.

Example: How much work is done in the first 6m? How much work is done from 0m to 7m? (ANS: 90Nm, 85Nm)

F. Identify whether positive or negative work is done for a given scenario. Give an example for a force doing negative work and for a force doing positive work.

G. Explain the Work – Energy Principle and write it in equation form.

H. Explain the law of Conservation of Energy and write it in equation form.

I. Select the appropriate equation(s), relating to work and energy, based on given information to calculate unknown quantities.

Example: To set a roller coaster into motion some coasters are pulled up the first hill by a chain mechanism. The Millennium Force at Cedar Point has a lift hill of 310 feet (94.5m) at a 45( angle. Given the mass of a train to be 19 tons (17200kg) calculate the following:

a. The gravitational potential energy at the top of the hill. (ANS:1.59x107J)

b. The minimum work done by the chain on the roller coaster during its ascent. (ANS:1.59x107J)

c. The minimum force to pull the train up the incline at constant velocity. (ANS: 1.19x105N)

Example 3: The picture below shows part of the track for a roller coaster. Ignoring friction, find the coaster’s speed at B and C. (vB = 22m/s, vC = 14m/s)

J. List examples of forces that may be non-conservative (or dissipative).

K. Apply the concept of conservation of mechanical energy while accounting for non-conservative forces.

Example: A car traveling at 35m/s (78mph) panic brakes and skids to a stop. If the coefficient of friction is 0.7, how far does the car travel while coming to a stop? (ANS: 89m)

L. Write the equation for power in terms of work and time or energy and time.

M. Apply the power equation to a given scenario to calculate unknown quantities.

Example: If a light bulb is rated at 60Watts, how much energy is being transformed each second? Hour? (ANS: 60 joules each second, 216000J each hour)

Example: Zoom-Zoom: Mazda advertises its Mazda3 sedan with a 2.3L engine is capable of 156hp. What is the minimum time needed to go from 0 to 60mph? Assume a curb weight of 2950lbs (1340kg). (ANS: 4.1 seconds)

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0.2

0.4

0.6

90

60

30

Fapplied(N)

x (m)

F(N)

d(m)

1

2

3

4

5

6

7

5

10

-5

F(N)

d(m)

8

4

2

4

5

6

7

8

-2

h

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F(N)

D(m)

1

2

3

4

5

6

7

10

20

-10

25m

15m

vi=0

B

C

A

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