Forces and Potential Energy - Middle School Physical Science

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

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

2. If an object's height decreases from $5\,\text{m}$ to $2\,\text{m}$, does $U_g$ increase or decrease?

   Decrease. Lower height means less gravitational PE since $U_g = mgh$.

3. Identify the energy change when an object is lifted upward at constant speed to a higher height.

   Gravitational potential energy increases. Lifting against gravity stores gravitational energy.

4. What does a force–distance model show about work and stored potential energy?

   The area under the $F$–$x$ graph equals work stored as $U$. Work done equals area under force curve, which becomes stored PE.

5. Which statement best links force and potential energy in a model of interacting objects?

   Potential energy changes when a force acts through a distance. Work done by forces converts to stored potential energy.

6. Identify the energy change when an external force stretches a spring and stores energy in it.

   Elastic potential energy increases. Stretching stores energy in the spring's deformation.

7. What is the definition of magnetic potential energy between magnets?

   Stored energy due to positions of magnetic poles. Like poles repel; work stores energy when forced together.

8. What happens to $U_s$ when spring compression changes from $x$ to $2x$?

   $U_s$ becomes $4$ times larger. Doubling $x$ quadruples energy since $U_s \propto x^2$.

9. For a constant force, what is the work formula that relates to change in potential energy?

   $W = Fd$. Force times distance gives work done.

10. Which option describes the force direction for an object moving downhill as $U_g$ decreases?

    Gravity acts in the direction of motion. Gravity pulls down the slope, same direction as motion.

11. Identify the force that stores elastic potential energy when a spring is stretched.

    The elastic restoring force (spring force). Springs pull back when stretched, storing elastic PE.

12. If a spring has $k=4\,\text{N/m}$ and is stretched $x=0.5\,\text{m}$, what is $U_s$?

    $0.5\,\text{J}$. $U_s = \frac{1}{2}kx^2 = \frac{1}{2} \times 4 \times 0.5^2 = 0.5\,\text{J}$.

13. Which statement matches a model of attractive force between objects and potential energy?

    As objects separate, stored potential energy increases. Pulling magnets apart against attraction stores energy.

14. What happens to potential energy when an external force does positive work against a conservative force?

    Potential energy increases. Work done against a force stores energy as PE.

15. Which interaction stores more electric potential energy: pushing like charges closer or farther apart?

    Pushing like charges closer together. Work against repulsion stores more energy.

16. What does a bar-chart energy model show when only gravity acts and friction is negligible?

    Total mechanical energy stays constant while $U_g$ and $K$ trade off. Energy conservation: PE and KE exchange while total stays fixed.

17. Identify the energy transformation when a stretched rubber band is released and speeds up an object.

    Elastic potential energy converts to kinetic energy. Stored elastic PE transforms to motion energy.

18. What is the definition of gravitational potential energy near Earth's surface?

    Energy stored due to height in a gravitational field. Gravity pulls objects down, storing energy when lifted up.

19. What is the formula for gravitational potential energy near Earth?

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

20. What is elastic potential energy in a stretched or compressed object?

    Stored energy due to deformation of an elastic material. Springs and rubber bands store energy when stretched or compressed.

21. If spring stretch changes from $x$ to $2x$, by what factor does $U_s$ change?

    It increases by a factor of $4$. Displacement is squared in the formula, so doubling $x$ quadruples $U_s$.

22. What is the definition of potential energy in terms of an object's position or arrangement?

    Stored energy due to position or arrangement. Objects gain potential energy when moved against a force.

23. What happens to $U_g$ when height changes from $h$ to $2h$ (same $m$ and $g$)?

    $U_g$ doubles. Direct proportionality: double height = double energy.

24. Calculate $U_g$ for $m = 2\,\text{kg}$, $g = 10\,\text{N/kg}$, $h = 3\,\text{m}$.

    $60\,\text{J}$. $U_g = mgh = 2 \times 10 \times 3 = 60\,\text{J}$.

25. What is the definition of potential energy in terms of energy storage?

    Stored energy due to an object's position or arrangement. Energy is stored when forces act to change position or configuration.

26. Calculate $U_s$ for $k = 100\,\text{N/m}$ and $x = 0.20\,\text{m}$.

    $2\,\text{J}$. $U_s = \frac{1}{2}kx^2 = \frac{1}{2} \times 100 \times 0.04 = 2\,\text{J}$.

27. What is the definition of elastic potential energy?

    Stored energy in stretched or compressed materials. Springs and rubber bands store energy when deformed.

28. What happens to potential energy when a conservative force does positive work on an object?

    Potential energy decreases. Conservative forces release stored PE when doing work.

29. Which statement matches a model of repulsive force between objects and potential energy?

    As objects are pushed closer, stored potential energy increases. Pushing like charges together against repulsion stores energy.

30. What is the work formula for a constant force parallel to the displacement?

    $W = Fd$. Force times distance when both point the same way.

31. Which interaction stores more magnetic potential energy: forcing two north poles closer or farther apart?

    Forcing two north poles closer together. Work against magnetic repulsion stores more energy.

32. State the formula for elastic potential energy of a spring.

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

33. What is the definition of electric potential energy between charged objects?

    Stored energy due to positions of electric charges. Like charges repel; work stores energy when pushed together.

34. Which change increases $U_g$ the most: doubling $m$, doubling $h$, or doubling $g$?

    All increase $U_g$ by a factor of $2$. Each variable appears once in $U_g = mgh$, so doubling any doubles $U_g$.

35. What is the definition of gravitational potential energy near Earth?

    Stored energy due to height in a gravitational field. Objects higher up can fall and release energy.

36. If you lift a $2\,\text{kg}$ object by $3\,\text{m}$ with $g=10\,\text{m/s}^2$, what is $\Delta U_g$?

    $60\,\text{J}$. $U_g = mgh = 2 \times 10 \times 3 = 60\,\text{J}$.

37. Identify the energy transformation when an object falls from rest without air resistance.

    Gravitational potential energy converts to kinetic energy. Height energy transforms to motion energy during free fall.

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