Question

strategic thinking

1. compare and contrast potential and kinetic energy. how are they similar and different?
2. if a roller coaster is at the top of a hill, what type of energy does it have? what happens to this energy as it goes down the hill? what happens to

Explanation:

Question 1: Compare and contrast potential and kinetic energy. How are they similar and different?

• Similarity: Both potential and kinetic energy are forms of mechanical energy and are measured in joules. They are interconvertible (e.g., in a pendulum, potential energy at the top converts to kinetic at the bottom and vice versa).
• Difference: Potential energy (PE) is stored energy due to position/condition (e.g., gravitational PE = $mgh$, elastic PE = $\frac{1}{2}kx^2$), while kinetic energy (KE) is energy of motion ($KE = \frac{1}{2}mv^2$). PE depends on height/configuration, KE on velocity/mass.

• At the top of the hill, the roller coaster has gravitational potential energy (PE) due to its height ($PE = mgh$). As it moves down, height ($h$) decreases, so PE decreases. This PE converts to kinetic energy (KE) (since velocity increases), following the law of conservation of mechanical energy (ignoring friction: $PE_{initial} + KE_{initial} = PE_{final} + KE_{final}$; initially, $KE_{initial} \approx 0$ if at rest, so $PE$ converts to $KE$).

Answer:

• Similar: Both are mechanical energy, interconvertible, measured in joules.
• Different: PE is stored (position/condition), KE is motion (velocity/mass). PE formulas: $mgh$ (gravitational), $\frac{1}{2}kx^2$ (elastic); KE formula: $\frac{1}{2}mv^2$.

Question 2: If a roller coaster is at the top of a hill, what type of energy does it have? What happens to this energy as it goes down the hill?