Question

fill in the blank. 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 ______________.

Answer 1

The gravitational potential energy of the sphere would be reduced to
`(1/2)` of the initial value.

Step-by-step explanation:

Near the surface of the Earth, the gravitational field is approximately uniform. The gravitational field strength is approximately
`g \approx 9.81\; {\rm N \cdot kg^(-1)}`.

In a uniform gravitational field, the gravitational potential energy (GPE) of an object relative to the ground is proportional to height. For example, if an object of mass
`m` is at a height
`h` above the ground, the GPE of this object would be
`m\, g\, h` relative to the ground.

In this example, the height of the sphere is reduced to
`(1/2)` of its initial value. As a result, the GPE of this sphere relative to the ground would also be reduced to
`(1/2)\!` of the initial value.