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In the roller coaster calculation, the mass of the coaster cancels out of the final speed equation. What general fact about falling bodies does this illustrate?
AHeavier objects always fall faster when friction is negligible
BAll objects fall at the same rate when friction is negligible, regardless of mass
CMass only cancels for roller coasters, not for other falling objects
DThe final speed depends on the object's weight but not on gravity
Answer & Solution
Correct answer: B. All objects fall at the same rate when friction is negligible, regardless of mass
1. Setting mgh equal to one half m v squared and cancelling the mass m on both sides leaves v depending only on g and h.
2. Because mass drops out entirely, this shows that all objects fall at the same rate when friction is negligible, regardless of how much they weigh.
3. This is not a special coincidence limited to roller coasters, since the same mass cancellation happens for any object falling or sliding down under gravity alone.
4. Heavier objects do not fall faster under these conditions, and the final speed still depends on gravity through g, even though it does not depend on weight.
_Source: OpenStax College Physics (CC BY 4.0), Ch 7 "Work, Energy, and Energy Resources", section 7.3 Gravitational Potential Energy_
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