Question

An elevator car has a mass of 750 kg, and its three passengers have a combined mass of 135 kg. If the elevator and its passengers ride to the ground floor, 20.7 m below, find the change in gravitational potential energy of the car and its passengers. Show all your work.

Answer 1

The change in gravitational potential energy is -1.80x10⁵ J.

Step-by-step explanation:

The change in gravitational potential energy is given by:

`\Delta E_(p) = E_{p_(f)} - E_{p_(i)}`

`\Delta E_(p) = mgh_(f) - mgh_(i)`

Where:

"i" is for final and "f" for final

m: is the mass

g: is the gravity = 9.81 m/s²

h: is the height

For the car and the passengers we have:

`\Delta E_(p) = m_(T)g(h_(f) - h_(i)) = (750 kg + 135 kg)9.81 m/s^(2)(0 - 20.7 m) = -1.80 \cdot 10^(5) J`

The minus sign is because when the elevator car and the passengers are up they have a bigger gravitational potential energy than when they are in the ground.

Therefore, the change in gravitational potential energy is -1.80x10⁵ J.

I hope it helps you!