Potential Energy - AP Physics C Mechanics

1. Calculate the gravitational potential energy for a 12 kg object at 8 m height. (Use $g = 9.8 \text{ m/s}^2$)

   940.8 J. $U = mgh = (12)(9.8)(8) = 940.8$ J.

2. What is the potential energy change for raising a 10 kg mass by 2 meters? (Use $g = 9.8 \text{ m/s}^2$)

   196 J. $\Delta U = mg\Delta h = (10)(9.8)(2) = 196$ J.

3. What is the potential energy for a 15 kg object at 12 m height? (Use $g = 9.8 \text{ m/s}^2$)

   1764 J. $U = mgh = (15)(9.8)(12) = 1764$ J.

4. What type of potential energy is associated with an object's position in a gravitational field?

   Gravitational potential energy. Energy due to position in Earth's gravity field.

5. Identify the variable $h$ in the gravitational potential energy formula $U = mgh$.

   Height. Vertical distance above reference point.

6. State the formula for gravitational potential energy.

   $U = mgh$. Mass times gravitational acceleration times height.

7. State the relationship between potential energy and height.

   Directly proportional. PE increases linearly with height in formula.

8. Calculate the gravitational potential energy for a 50 kg object at 10 m height. (Use $g = 9.8 \text{ m/s}^2$)

   4900 J. $U = mgh = (50)(9.8)(10) = 4900$ J.

9. What is the unit of potential energy in the SI system?

   Joule (J). Standard unit for all forms of energy in physics.

10. Identify the variable $x$ in the elastic potential energy formula $U = \frac{1}{2} kx^2$.

    Displacement. Distance from equilibrium position.

11. What is the potential energy for a 10 kg object at 6 m height? (Use $g = 9.8 \text{ m/s}^2$)

    588 J. $U = mgh = (10)(9.8)(6) = 588$ J.

12. What is the potential energy of a 3 kg object at a height of 4 m? (Use $g = 9.8 \text{ m/s}^2$)

    117.6 J. $U = mgh = (3)(9.8)(4) = 117.6$ J.

13. What type of potential energy is stored in a compressed gas?

    Elastic potential energy. Compression stores elastic energy like a spring.

14. What happens to potential energy as an object falls freely under gravity?

    Decreases. Height decreases, so gravitational PE decreases.

15. State the effect on potential energy when an object is lowered.

    Decreases. Lower height means less gravitational PE.

16. What does the variable $k$ represent in the formula $U = \frac{1}{2} kx^2$?

    Spring constant. Measure of spring's stiffness or resistance to deformation.

17. State the effect of gravity on potential energy when moving uphill.

    Increases potential energy. Moving up increases height and gravitational PE.

18. At what point in its motion does a pendulum have maximum potential energy?

    At the highest point. Maximum height means maximum gravitational PE.

19. Determine the gravitational potential energy change for a 7 kg object lifted 10 m. (Use $g = 9.8 \text{ m/s}^2$)

    686 J. $\Delta U = mg\Delta h = (7)(9.8)(10) = 686$ J.

20. If the spring constant $k$ is doubled, how does elastic potential energy change?

    Doubles. PE is directly proportional to spring constant $k$.

21. Which factor does not affect gravitational potential energy: mass, height, or velocity?

    Velocity. PE depends only on position, not motion.

22. What is the gravitational potential energy for a 1 kg object at 9 m height? (Use $g = 9.8 \text{ m/s}^2$)

    88.2 J. $U = mgh = (1)(9.8)(9) = 88.2$ J.

23. What is the potential energy of a 6 kg mass at 7 m height? (Use $g = 9.8 \text{ m/s}^2$)

    411.6 J. $U = mgh = (6)(9.8)(7) = 411.6$ J.

24. How is potential energy affected when an object's mass is increased?

    Increases. PE is directly proportional to mass.

25. How does doubling the displacement $x$ affect elastic potential energy?

    Quadruples. PE depends on $x^2$, so doubling $x$ gives $4x^2$.

26. Which type of energy transformation occurs when a ball is dropped from a height?

    Potential to kinetic. Height decreases, so PE converts to KE.

27. Find the potential energy for a 4 kg object at 15 m height. (Use $g = 9.8 \text{ m/s}^2$)

    588 J. $U = mgh = (4)(9.8)(15) = 588$ J.

28. What is the potential energy of a 2 kg object at a height of 5 meters? (Use $g = 9.8 \text{ m/s}^2$)

    98 J. $U = mgh = (2)(9.8)(5) = 98$ J.

29. Calculate the potential energy for a 20 kg object at 5 m height. (Use $g = 9.8 \text{ m/s}^2$)

    980 J. $U = mgh = (20)(9.8)(5) = 980$ J.

30. What happens to the potential energy of an object as it is lifted higher?

    Increases. Greater height means greater gravitational PE.

31. State the formula for elastic potential energy.

    $U = \frac{1}{2} kx^2$. Energy stored in deformed elastic objects.

32. Calculate the change in potential energy for a 5 kg object moved 3 m vertically. (Use $g = 9.8 \text{ m/s}^2$)

    147 J. $\Delta U = mg\Delta h = (5)(9.8)(3) = 147$ J.

33. What type of potential energy is present in a raised weight?

    Gravitational potential energy. Elevated mass has energy due to gravity.

34. What is the effect on gravitational potential energy if mass is halved?

    Halved. PE is directly proportional to mass.

35. Identify the potential energy form of a compressed spring.

    Elastic potential energy. Compression stores energy in elastic deformation.

36. Calculate the elastic potential energy for a spring with $k = 200 \text{ N/m}$ and $x = 0.3 \text{ m}$.

    9 J. $U = \frac{1}{2}kx^2 = \frac{1}{2}(200)(0.3)^2 = 9$ J.

37. Identify the energy transformation in a stretched rubber band.

    Potential to kinetic. Stored elastic energy converts to kinetic energy.

38. Identify the energy conversion when compressing a spring.

    Kinetic to potential. Work done compressing stores energy in spring.

39. What type of energy is stored when a spring is compressed?

    Elastic potential energy. Deformation stores energy that can be released.

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