A car is lifted a vertical distance in a service station and therefore has potential energy relative to the floor. If it were lifted twice as high, how much potential energy would it have?

1. The same

2. One half as much

3. Unable to determine

4. Twice as much

Answer: 4. Twice as much

Explanation:

Potential energy of an object is given by the equation

PE = mgh (where m is the mass, g is the acceleration due to gravity and h is its vertical distance above ground level)

If it were lifted twice its initial height,

PE = mgH (where H is the new height, which is twice the initial vertical distance)

PE = mg (2h)

PE = 2mgh

We can see that the potential energy doubles as the vertical distance is doubled.

4. Twice as much

Explanation:

Potential Energy: This is the energy a body posses b virtue of its position.

It can be expressed mathematically as

Ep₁ = Mgh

Where Ep₁ = potential energy, M = mass, g = acceleration due to gravity, h = height.

From the question, let the mass of the car be (m) = N kg

and let the height be (h) = y m, and g = 9.8 m/s²

Therefore, Ep₁ = 9.8 * N * y

Ep₁ = 9.8Ny ... equation 1

When the car is lifted twice its height,

new height (h₂) = 2y m, mass of the car = N kg, g = 9.8 m/s

therefore the new potential energy of the car Ep₂ = 9.8 * 2y * N

Ep₂ = 19.6Ny ... equation 2

Comparing equation 1 and equation 2 it can be seen that

Ep₂ = twice Ep₁

Therefore, the right option is twice as much.