Im not sure if im doing it right,

Question

A 3.00 × 10^2 kg car is pushed from the top of a ramp. The ramp has a vertical height of 5.0 m and horizontal distance of 10.6 m. If the force applied along the incline is 5.00 × 10^2 N, what is the potential energy of the object when it is at the top of the ramp with respect to the bottom of the ramp?

My answer: 1.0x10^4

Answer 1

Regardless of how the car gets to the top, the potential energy of the car with respect to the bottom of the ramp is mgh. However, we don't know the mass of the car. Therefore we have to assume that the force up the ramp was just enough to get it up the ramp at a constant velocity. We also have to assume no work goes into frictional work.

If these two assumptions are correct, then we can calculate W = Fd along the incline and this will equal the potential energy change.

d is the hypotenuse and the horizontal and vertical legs are the sides. Use pythagorean theorem for d.

You could also solve for m from the force balance mgsin(theta) = F where sin(theta) = h/d

and then insert the m in order to calculate mgh to find the potential energy change.

You cannot solve this problem with either method if there is frictional loss or acceleration of the car because the work would partially go into kinetic energy or frictional work. Good luck!