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A 2000.0 kg boulder sits on the top of a 50.0 m cliff. As the boulder rolls off, it loses 3.0% of...

Question:

A 2000.0 kg boulder sits on the top of a 50.0 m cliff. As the boulder rolls off, it loses 3.0% of its mechanical energy as heat.

How much heat energy goes the boulder lose?

How much mechanical energy does the boulder have right before hits the ground?

Mechanical Energy:

When the energy of the object is stored within the body due to its motion then the energy is said to be in the form of mechanical energy and it can be of two forms potential energy and the kinetic energy. Potential energy is due to the height of the body and kinetic energy is due to the motion of the body.

Answer and Explanation:

Given

Mass of the boulder is {eq}m=2000\ kg {/eq}

Height of the cliff is {eq}h=50\ m {/eq}

Now for the potential energy of the boulder at that height:

{eq}P.E=mgh\\ P.E=2000\times 9.81\times 50\\ P.E=98100\ J {/eq}

Since 3 % of energy is being lost :

{eq}K.E_f=98100-\frac{3}{100}(98100)\\ K.E_f=95157\ J {/eq}

The heat energy available will be equal to:

{eq}H.E=\frac{3}{100}(98100)\\ H.E=2943\ J {/eq}

Thus, the heat energy will be equal to 2943 J

When the boulder reaches the ground then all the energy after a loss will convert into kinetic energy and the energy that is available at the ground will be in the form of kinetic energy equal to 95157 J


Learn more about this topic:

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Energy Conservation and Energy Efficiency: Examples and Differences

from Geography 101: Human & Cultural Geography

Chapter 13 / Lesson 9
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