Question

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?

Answer 1

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

Step-by-step 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
`m_1`. Then its PE is

`PE_1 = m_1gh`

For the massive car, let the mass be
`m_2`. Its PE is

`PE_2 = m_2gh`

But
`m_2 =2m_1`

`\therefore PE_2 = 2m_1gh = 2(m_1gh) = 2PE_1`

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