Chantelle W.

asked • 06/01/16# Fill in the Blank: Potential Energy

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.

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## 2 Answers By Expert Tutors

Robert D. answered • 06/01/16

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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/s**

^{2})**= 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/s**

^{2})(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.

Arturo O. answered • 06/01/16

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Experienced Physics Teacher for Physics Tutoring

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Robert D.

hof the incline? With the heighth, you can calculate thePEof the sphere at the top of the incline, which ismgh.ThePEof the sphere halfway down the incline would bemg(h/2).06/01/16