Fill in the Blank: Potential Energy

Question

A 0.50-kg sphere at the top of an incline has a potential energy of 8.0 joules relative to the base of the incline. Rolling halfway down the incline will cause the sphere's potential energy to be ______________.

 

Fill in the blank and explain why please.

Answer 1

Let's express the potential energy of the sphere at the top of the incline.

 

The PE of the sphere at the top is the product of the mass of the sphere m, the acceleration due to gravity g, and the height of the incline h_top.

 

PE_top = mgh_top

 

 

We can solve for h_top

 

 

h_top = PE_top / mg

 

       = 8 J / (0.5kg)(9.81m/s²)

 

       = 1.63 m

 

The height of the incline h_top is 1.63m.

 

The PE of the sphere halfway down the incline is such that the sphere is at a height h_top/2

 

 

PE_1/2 = mg(h_top/2)

 

          = (0.5kg)(9.81m/s²)(1.63m/2)

 

          = 3.99 J

 

          ≈ 4 J

 

 

It makes sense that the sphere's gravitational potential energy would be half its original value when the sphere is halfway down the incline.

 

I hope this helped.

Answer 2

Since it went half way down, its potential energy due to gravity will fall by one half, so the potential energy will be 8/2 J = 4 J at that point.