work and potential energy Exam Review PDF

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work and potential energy exam review for junior year, honors physics. Includes practice problems for the conservation of energy....

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Work, Power, & Energy Exam Review 1. A 2.0 kg block is dropped from a height of 40 cm onto a spring with spring constant k= 1960 N/m. Find the maximum distance the spring is compressed.

2. Jason and Brent race up a hill that is 30 m high, as shown avove. Jason takes a path that is 60 m while Brent uses a longer path that is 100 m long. It takes Jason 40 seconds, while Brent runs up his path in a shorter time of 30 seconds. They both start from rest at the same height and stop at the top. Also, they have the same weight. a. Is the work that Jason does going up the hill greater than, less than, or equal to the work that Brent does in going up the hill? Explain. b. Is the power generated by Jason in going up the hill greater than, less than, or equal to the power generated by Brent? Explain.

3. Abbie and Bonita decide to race up a hill that is 30 m high, as shown above. Abbie takes a path that is 60 m long while Bonita uses a path that is 100 m long. It takes Abbie 40 seconds because her route is steep, while Bonita runs up her path in 30 seconds. They both start from rest at the same height and stop at the top. Abbie has a weight of 700 N, and Bonita has a weight of 500 N. a. Is the work that Abbie does going up the hill greater than, less than, or equal to the work that Bonita does in going up the hill? Explain. b. Is the power generated by Abbie in going up the hill greater than, less than, or equal to the power generated by Bonita? Explain.

4. A 56 kg diver dives from the edge of a cliff into the water which is located 4.0 m below. Determine the following: a. Her total energy relative to the water’s surface when she leaves the cliff. b. Her speed half-way down. c. The speed at which she enters the water. 5. A 12.5 kg mass is pulled 8 m across a horizontal surface by a 65 N force applied at 18°. The coefficient of friction is 0.35. If the mass begins from rest, what is its speed after traveling the 8 m?

6. For each set of figures below, balls are traveling in different directions. The balls have the same size and shape, but they have different masses and are traveling at different velocities as shown. For each set, rank the kinetic energy of the balls from greatest to least. a.

b.

7. An amusement park has a slide for which participants are given a cloth sack to sit on. The top of the slide is 6.0 m high. a. Determine the speed attained by a child at the bottom of the slide. b. If the slide has a second hill and the child slows to a speed of 2 m/s when she reaches the top, calculate the height of the second hill. 8. A 200 g ball is released horizontally from a spring with a spring constant of 350 N/m. The spring was compressed 4 cm and the ball travels 30 cm before coming to a stop. a. Solve for the ball’s maximum velocity. b. Solve for the coefficient of friction. 9. Which of the following statements are true about work? Include all that apply. a. A Watt is the standard metric unit of work. b. Superman applies a force on a truck to prevent it from moving down a hill. This is an example of work being done. c. An upward force is applied to a bucket as it is carried 20 m across the yard. This is an example of work being done. d. A force is applied by a chain to a roller coaster car to carry it up the hill of the first drop of the Shockwave ride. This is an example of work being done. e. The force of friction acts upon a softball player as she makes a headfirst dive into third base. This is an example of work being done. f. A force acts upon an object to push the object along a surface at constant speed. By itself, this force must NOT be doing any work upon the object. g. A force acts upon an object at a 90-degree angle to the direction that it is moving. This force is doing negative work upon the object. h. An object is moving to the right. A force acts leftward upon it. This force is doing negative work.

10. Two crazy physics students are trying to get a 1000 kg refrigerator up to the second floor, which is approximately 10 meters high. The first student decides to lay a ramp over the stairs, which have an angle of about 30°, and push the refrigerator up. The second student decides to get a very strong rope, and pull the refrigerator straight upwards. a. Which student will do more work? b. Calculate the amount of work.

11. In the figures above, identical boxes of mass 10 kg are moving at the same initial velocity to the right on a flat surface. The same magnitude force, F, is applied to each box for the distance, d, indicated in the figures. Rank, from greatest to least, the work done on the box by the force while the box moves the indicated distance. 12. A 1500 kg car is coasting down a hill with a 30° incline at an initial speed of 12 m/s. If the coefficient of kinetic friction is 0.2, what is the speed of the car after it has traveled a distance of 50 m along the incline? 13. Several children suspend a rope from an overhead tree limb. A 40 kg child running at 8.0 m/s grabs the rope and swings off the level ground. a. What maximum height does the child reach? b. How fast would a 30 kg child have to run to reach the same height as the 40 kg child? 14. The same 40 kg child from above still running at 8.0 m/s grabs the rope and reaches the same maximum height, but at the lowest point on the way down the child is only traveling at 6.5 m/s. a. If the child keeps swinging, what new height would she reach? b. What percent of her energy was “lost”. 15. A block is pushed with a parallel force so that it moves up a ramp at constant speed, as shown in the image to the right. For each part below, identify if the work done by the specified force while the block moves from point A to point B is positive, negative, or zero. Explain. a. b. c. d. e.

The work done on the block by the hand. The work done on the block by the normal force. The work done on the block by friction. The work done on the block by gravity. The net work done on the block.

16. Shown above are blocks that slide down frictionless inclines. All masses start from rest at the top of the incline. Rank the kinetic energy of the sliding masses the instant they reach the bottom of the incline from greatest to least. 17. A ball with a mass of 1.5 kg is dropped from a height of 20 meters. Analyze the kinetic energy, potential energy, and total energy of the ball for different times during its way down to the ground. Draw the chart below in your notebook. Picture

Height

A.

h = 20 m

20 m

h = 15 m

15 m

h=0m

0m

B.

C.

GPE

Kinetic Energy

Total Energy

Velocity

18. Which of the following statements are true about kinetic energy? Include all that apply. a. b. c. d. e. f. g. h. i. j. k.

If an object is at rest, then it does not have any kinetic energy. The kinetic energy of an object is dependent upon the mass and the speed of an object. Faster moving objects always have a greater kinetic energy. More massive objects always have a greater kinetic energy. An object has a kinetic energy of 40 J. If its mass were twice as much, then its kinetic energy would be 80 J. An object has a kinetic energy of 40 J. If its speed were twice as much, then its kinetic energy would be 80 J. Object A has a mass of 1 kg and a speed of 2 m/s. Object B has a mass of 2 kg and a speed of 1 m/s. Objects A and B have the same kinetic energy. An object can never have a negative kinetic energy. A falling object always gains kinetic energy as it falls. A 1-kg object is accelerated from rest to a speed of 2.0 m/s. This object gains 4.0 Joules of kinetic energy. If work is done on an object, then the object will either gain or lose kinetic energy.

19. A roller coaster begins from a height of 32 m. a. Calculate the roller coaster’s speed at its lowest point. b. Calculate the roller coasters speed when it is half way off the ground. 20. Which of the following statements are true about potential energy? Include all that apply. a. Moving objects cannot have potential energy. b. Both gravitational and elastic potential energy are dependent upon the mass of an object. c. If the mass of an elevated object is doubled, then its gravitational potential energy will be doubled as well. d. Gravitational potential energy is lost as objects free-fall to the ground. e. The unit of measurement for potential energy is the Joule. f. A 1-kg mass at a height of 1 meter has a potential energy of 1 Joule. 21. A certain spring has a spring constant of 150 N/m. a. What force would be required to compress the spring by 50 cm? b. When compressed by that distance, what amount of energy would be stored? c. If the spring is then used to propel a 58 gram tennis ball vertically, what would be the ball’s maximum height? 22. A 70 kg rodeo rider is riding a bucking bronco when he is thrown off. At the instant he leaves the horse he is located 2.6 m above the ground and is moving straight up at 4.0 m/s. a. What maximum height above the ground does the rider reach? b. At what speed will the rider hit the ground?

23. Cars that are moving along horizontal roads are going to be stopped by plowing into barrel barriers, as seen above. All of the cars are the same size and shape, but they are carrying loads with different masses. All of the cars are going to be stopped in the same distance. Rank the magnitude of the forces that will be needed to stop the cars in the same distance from greatest to least. 24. Which of the following statements are true about mechanical energy? Include all that apply. a. The total amount of mechanical energy of an object is the sum of its potential energy and the kinetic energy. b. Heat is a form of mechanical energy. c. In the absence of friction, mechanical energy of an object is always conserved. d. When conservative forces do work, energy is transformed from kinetic to potential (or vice versa), but the total mechanical energy is conserved. e. When a friction force does work on an object, the total mechanical energy of that object is changed. 25. Use the picture below to answer the following questions. C

B A

a. Calculate the velocity at point B if the object is 1.75 m off the ground. (x = 83 cm) b. Calculate the height at point C. 26. A 10 N force, parallel to an incline's surface, is applied to push a 20 kg crate 14 m up the 15° incline at a constant velocity. a. How much work is done by the force? b. How much total work is done? c. If this takes 25 seconds, what is the power output?

27. A student applies a force to a cart to pull it up an inclined plane at constant speed during a physics lab. A force of 20.8 N is applied parallel to the incline to lift a 3.00-kg loaded cart to a height of 0.450 m along an incline which is 0.636-m long. Determine the work done upon the cart and the subsequent potential energy change of the cart.

28. The situations above show before and after “snapshots” of a car’s velocity. All cars have the same mass. Rank, from greatest to least, the work done on the cars to create these changes in velocity for the same distance traveled. 29. A very long, frictionless, inclined plane has an angle of 15° measured from the horizontal, and is 100 meters long. A person starts a 10 kg ball rolling down from the top of the hill, by giving it an initial velocity of 5 m/s. What is the ball’s velocity at the bottom of the hill? 30. Rank these four objects in increasing order of kinetic energy, beginning with the smallest. Object A m = 5.0 kg v = 4.0 m/s h = 2.0 m

Object B m = 10.0 kg v = 2.0 m/s h = 3.00 m

Object C m = 1.0 kg v = 5.0 m/s h = 5.0 m

Object D m = 5.0 kg v = 2.0 m/s h = 4.0 m

31. Rank these four objects in increasing order of potential energy, beginning with the smallest. Object A m = 5.0 kg v = 4.0 m/s h = 2.0 m

Object B m = 10.0 kg v = 2.0 m/s h = 3.00 m

Object C m = 1.0 kg v = 5.0 m/s h = 5.0 m

Object D m = 5.0 kg v = 2.0 m/s h = 4.0 m

32. Describe the following situations as positive, negative, or zero work. a. A cable is attached to a bucket and the force of tension is used to pull the bucket out of a well. b. Rusty Nales uses a hammer to exert an applied force upon a stubborn nail to drive it into the wall. c. Near the end of the Shockwave ride, a braking system exerts an applied force upon the coaster car to bring it to a stop. d. The force of friction acts upon a baseball player as he slides into third base. e. A busy spider hangs motionless from a silk thread, supported by the tension in the thread. f. In baseball, the catcher exerts an abrupt applied force upon the ball to stop it in the catcher's mitt. g. In a physics lab, an applied force is exerted parallel to a plane inclined at 30-degrees in order to displace a cart up the incline. h. A pendulum bob swings from its highest position to its lowest position under the influence of the force of gravity....