Question

mr. r is an engineer. he is investigating potential energy with two identical magnetic roller coaster cars on different sides of a center magnet that cannot move. to test his ideas, he will move one car one space. which movement will result in the largest increase in potential energy?
moving car 2 one space away from the center magnet.
moving car 1 one space toward the center magnet.
moving car 2 one space toward the center magnet.
all of these movements will result in the same change in potential energy because they each move a roller coaster car the same distance.

Explanation:

Magnetic potential energy depends on the distance between magnets and their interaction (repulsion or attraction). The center magnet and the cars likely have like - poles (so repulsion, as it's a magnetic roller coaster setup). Moving a car against the magnetic force (increasing the "stored" energy) will increase potential energy.

• For "Moving Car 2 one space away from the center magnet": If the center and Car 2 repel, moving away would be with the force (decreasing potential energy, as less work against the force).
• For "Moving Car 1 one space toward the center magnet": If Car 1 and center repel, moving toward is against the repulsion force. We are doing work against the magnetic force, so potential energy increases.
• For "Moving Car 2 one space toward the center magnet": If repelling, moving toward is against the force? Wait, no—wait, the cars are on different sides. Wait, maybe Car 1 and center repel (so Car 1 is on one side, center magnet, Car 2 on the other. If the center magnet repels both cars (like - poles), then:
• Moving Car 1 toward the center: against the repulsion (work done, PE increases).
• Moving Car 2 toward the center: also against repulsion? But wait, the initial positions: Car 1 is farther from the center? Wait, the diagram (even though we can't see it fully) — but the key is that magnetic potential energy from repulsion: the closer two repelling magnets are, the higher the potential energy (like compressing a spring). So moving a car toward the repelling center magnet (against the force) increases PE. But wait, the options: let's re - evaluate. Wait, maybe Car 1 is on a side where moving toward the center is against repulsion, and Car 2 moving toward is also? No, the correct logic: when you move a magnet against a repulsive force (toward another repelling magnet), you increase potential energy (like pushing two north poles together). When you move it with the force (away), you decrease it. So "Moving Car 1 one space toward the center magnet" — if Car 1 and center repel, moving toward is against the force, so PE increases. Wait, but maybe the answer is "Moving Car 1 one space toward the center magnet" or "Moving Car 2 one space toward..." Wait, no—wait, the question is which movement gives the largest increase. Wait, maybe the cars are on opposite sides, and the center magnet repels both. So Car 1 is on the left, center in the middle, Car 2 on the right. If we move Car 1 (left car) toward the center (against repulsion), we do work, PE increases. Moving Car 2 toward the center (right car) toward center: also against repulsion. But maybe Car 1 is initially farther? No, the options: let's check the options again. Wait, the correct answer is "Moving Car 1 one space toward the center magnet" because moving toward a repelling magnet (against the force) increases potential energy, while moving away (with the force) decreases it, and the "all same" is wrong because direction (with/against force) matters, not just distance moved.

Answer:

B. Moving Car 1 one space toward the center magnet