Two cars are raised to the same elevation on service- station lifts. If one car is twice as massive as the other, how do their potential energies compare?

The potential energy of the more massive one is twice that of the other.

Explanation:

Potential energy is given by

PE = mgh

where m = mass of body, g = acceleration of gravity and h = height or elevation.

For the less massive car, let the mass be . Then its PE is

For the massive car, let the mass be .  Its PE is

But

Hence, the potential energy of the more massive one is twice that of the other.

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