Model Potential Energy - Middle School Physical Science

1. What happens to stored elastic potential energy when a stretched spring returns to its natural length?

   It decreases to $0$ (relative to natural length). Natural length means no deformation, so no elastic PE stored.

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

   Joule (J). Energy is measured in joules in the International System.

3. What is the definition of gravitational potential energy in a model of Earth and an object?

   Stored energy due to an object's height in a gravitational field. Energy exists because gravity pulls objects toward Earth.

4. What does "stored potential energy" mean in a physical model?

   Energy stored due to position or arrangement. Objects store energy based on their location or configuration.

5. Which position has more gravitational potential energy: 2 kg at 3 m or 2 kg at 1 m?

   2 kg at 3 m. Higher position (3 m vs 1 m) gives more PE when mass is same.

6. Identify the correct comparison: if height doubles, what happens to $U_g$ (same $m$ and $g$)?

   $U_g$ doubles. PE is proportional to height, so doubling $h$ doubles $U_g$.

7. Which arrangement stores more elastic potential energy: a spring stretched 5 cm or not stretched?

   The spring stretched 5 cm. Stretched spring stores elastic PE; unstretched has none.

8. Which change increases $U_g$ at the same height: increasing $m$ or decreasing $m$?

   Increasing $m$. More mass at same height stores more gravitational energy.

9. What is the correct model statement linking position/arrangement change to stored potential energy?

   Changing height or deformation changes the system's stored potential energy. Position or shape changes alter how much energy is stored.

10. Identify the variable that represents position in the formula $PE_g = mgh$.

    $h$ (height above a reference level). Height determines how far the object can fall.

11. Which position has more gravitational potential energy: 4 kg at 2 m or 2 kg at 4 m?

    They are equal. Both have $U_g = 8mg$ (4×2 = 2×4), so PE is the same.

12. Identify the correct statement about gravitational potential energy and reference level.

    $PE_g$ depends on the chosen zero height (reference level). Height $h$ is measured from your chosen zero point.

13. If a spring's $k$ doubles while $x$ stays the same, how does $U_s$ change?

    It doubles. Energy is directly proportional to spring constant $k$.

14. Identify the energy storage type for a compressed spring in a toy: gravitational, elastic, or chemical.

    Elastic potential energy. Compression deforms the spring from its natural length.

15. Identify the correct comparison: if mass triples, what happens to $U_g$ (same $h$ and $g$)?

    $U_g$ triples. PE is proportional to mass, so tripling $m$ triples $U_g$.

16. Which arrangement increases electric potential energy: moving like charges closer or farther apart?

    Moving like charges closer together. Like charges repel, so forcing them together stores energy.

17. State the definition of elastic potential energy in a model of a spring or rubber band.

    Stored energy due to stretching or compressing an elastic object. Deforming elastic materials stores recoverable energy.

18. Identify the variable that represents arrangement change in $PE_e = \frac{1}{2}kx^2$.

    $x$ (displacement from equilibrium length). Displacement from natural length determines stored energy.

19. What happens to gravitational potential energy when height increases (mass constant)?

    It increases. PE is directly proportional to height in the formula $U_g = mgh$.

20. State the formula for gravitational potential energy near Earth's surface.

    $PE_g = mgh$. Mass times gravity times height gives gravitational PE.

21. State the formula for elastic potential energy in an ideal spring using $k$ and $x$.

    $U_s = \frac{1}{2}kx^2$. Energy equals half the spring constant times displacement squared.

22. Identify the correct statement: does a steeper ramp change $U_g$ gained for the same vertical height?

    No; $U_g$ depends on vertical height, not ramp steepness. Only vertical height matters for $U_g$, not path taken.

23. What happens to $PE_g$ if height doubles while mass stays the same?

    $PE_g$ doubles. Direct proportionality: $PE_g = mgh$, so $2h$ gives $2PE_g$.

24. What does the variable $x$ represent in the equation $U_s = \frac{1}{2}kx^2$?

    Displacement from equilibrium length (stretch or compression). Measured from the spring's natural, unstretched position.

25. What is elastic potential energy stored in a spring in terms of $k$ and stretch $x$?

    $U_s = \frac{1}{2}kx^2$. PE is proportional to spring constant and square of displacement.

26. In an energy bar model for a released spring, what should happen to the $U_s$ bar after release?

    The $U_s$ bar should decrease. Released springs convert elastic to kinetic energy.

27. If stretch increases from $x$ to $2x$, by what factor does $U_s$ change?

    It increases by a factor of $4$. Energy depends on $x^2$, so doubling $x$ quadruples energy.

28. What happens to $PE_g$ if mass triples while height stays the same?

    $PE_g$ triples. Direct proportionality: $PE_g = mgh$, so $3m$ gives $3PE_g$.

29. Which reference choice makes $PE_g$ equal to $0$ at the floor: floor or tabletop?

    Floor as the reference level. Objects on the floor have zero height above floor level.

30. Which has more elastic potential energy: a spring stretched to $x$ or to $2x$ (same $k$)?

    Stretching to $2x$ (it is $4$ times as much). PE depends on $x^2$, so doubling stretch quadruples energy.

31. Which model best represents increasing $U_g$: raising an object or sliding it sideways at same height?

    Raising the object. Only vertical displacement changes gravitational PE.

32. Identify the energy transfer when an object falls: $U_g$ decreases and what energy usually increases?

    Kinetic energy increases. Falling converts gravitational potential to motion energy.

33. What is gravitational potential energy in terms of mass, gravity, and height?

    $U_g = mgh$. Formula shows PE depends on mass, gravity, and height above reference.

34. What is the definition of gravitational potential energy in an Earth-like gravitational field?

    Energy stored due to an object's position (height) in gravity. Height determines how much work gravity can do on the object.

35. What is the definition of elastic potential energy in a spring-like object?

    Energy stored due to stretching or compressing an elastic object. Deformed elastic materials store recoverable energy.

36. Which has greater $U_g$: a 3 kg book on a 2 m shelf or on a 0.5 m table (same $g$)?

    On the 2 m shelf. Higher shelf (2 m vs 0.5 m) gives more PE for same mass.

37. Which situation stores more elastic potential energy: $x = 0.10\,\text{m}$ or $x = 0.20\,\text{m}$ (same $k$)?

    $x = 0.20\,\text{m}$. Larger displacement stores more energy since $U_s \propto x^2$.

38. What happens to gravitational potential energy when mass increases (height constant)?

    It increases. PE is directly proportional to mass in the formula $U_g = mgh$.

39. Which change increases $U_g$ for the same object: increasing $h$ or decreasing $h$?

    Increasing $h$. Higher position means more stored gravitational energy.

40. Which option increases stored potential energy in a spring: increasing $x$ or decreasing $x$ (same $k$)?

    Increasing $x$. Greater displacement from equilibrium stores more elastic PE.

41. Identify the correct unit for potential energy in the SI system.

    Joule (J). Energy is measured in joules in SI units.

42. Which has more elastic potential energy: a spring compressed by 3 cm or by 6 cm (same $k$)?

    6 cm compression (it is $4$ times as much). PE depends on $x^2$, so doubling compression quadruples energy.

43. What is the relationship between gravitational potential energy and vertical position in a simple model?

    Higher vertical position means greater $U_g$. Objects higher up have more gravitational PE relative to ground.

44. In an energy bar model, what should happen to the $U_g$ bar as height $h$ increases?

    The $U_g$ bar should increase. Bar height represents amount of stored energy.

45. Which arrangement stores more $U_s$: a relaxed spring or the same spring compressed by $x$?

    The spring compressed by $x$. Deformed springs store energy; relaxed springs store none.

46. Identify the energy storage type for a raised book on a shelf: gravitational, elastic, or chemical.

    Gravitational potential energy. Height above ground stores energy due to gravity.

47. Which arrangement decreases electric potential energy: moving opposite charges closer or farther apart?

    Moving opposite charges closer together. Opposite charges attract, releasing energy when approaching.

48. What is the correct model statement for a system: potential energy can change when ______ changes?

    Position or arrangement of objects in the system. PE changes when objects move or rearrange in space.

49. State the formula for gravitational potential energy near Earth (use symbols $m$, $g$, $h$).

    $U_g = mgh$. Mass times gravity times height gives stored energy.

50. What does the variable $k$ represent in the equation $U_s = \frac{1}{2}kx^2$?

    Spring constant (stiffness). Measures force per unit displacement in N/m.

51. What is the key feature of a model that shows stored potential energy changes in a system?

    It tracks energy storage changes as position or arrangement changes. Shows how stored energy varies with configuration.

52. Which arrangement has greater $U_g$: a book on a shelf or the same book on the floor?

    The book on the shelf. Higher position means greater gravitational potential energy.

53. What is the definition of chemical potential energy in a model of atoms in a substance?

    Stored energy in the arrangement of atoms and chemical bonds. Energy stored in molecular bonds and atomic positions.

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