Question

Two cars are lifted to the same elevation in a service station. If one car is twice as massive as the other, how do their potential energies compare? 1. The car which is twice as massive as the other will have twice potential energy. 2. Unable to determine 3. The car which is twice as massive as the other will have one half potential energy than the other car. 4. They have the same potential energies since they are lifted to the same elevation.

Answer 1

1. The car which is twice as massive as the other will have twice potential energy.

Step-by-step explanation:

The potential energy of an object is given by:

`U=mgh`

where

m is the mass of the object

g is the gravitational acceleration

h is the height of the object measured to some reference level

In this problem, we have two cars at same elevation (= same h in the formula) but one car has twice the mass of the second car. Calling m the mass of one car and 2m the mass of the second car, we have:

- Potential energy of the first car:

`U=mgh`

- potential energy of the second car:

`U'=(2m)gh=2mgh=2U`

So, the car which is twice as massive as the other will have twice potential energy.