Physics Problems (2) : Work & Power

Question

• How much power is expended to raise a 300 kg roller coaster car to the top of a 35 m hill in 10 seconds?
• How much potential energy does the roller coaster car have at the top of the hill?

 

Show all work for both please.

Answer 1

Power is the rate of doing work. Work is transfer of energy by applying a force in a specific direction/distance or displacement.

Thus:

P = W/t = Fd / t = mgd / t = (300)(9.8)(35) / 10 = 10,290 watts.

 

The Work-Energy theorem states that the work done on a system is equal to the change in energy of the system.

The work done on the roller coaster car in lifting it to the top of the hill will be equal to the change in the gravitational potential energy of the car. Since GPE = mgh and W = Fd = mgd, thus the work done is equal to the gain in gravitational potential energy of the car.

Thus:

GPE = W = mgd = (300)(9.8)(35) = 102900 joules