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# Physics and Energy Help

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By McGraw-Hill Professional
Updated on Sep 5, 2011

## Introduction to Energy

Energy exists in many forms. From time to time, we hear news about an “energy crisis.” Usually newscasters are talking about shortages of the energy available from burning fossil fuels, such as oil and natural gas. You might find a barrel of oil and sit down in front of it. Where is the energy in it? It doesn’t seem to be doing anything; it’s just a big container of dark, thick liquid. However, if you light it on fire (don’t!), the energy it contains becomes vividly apparent. Energy is measured in joules, just as is work. In fact, one definition of energy is “the capacity to do work.”

## Potential Energy

Look again at the situation shown by Fig. 8-4. When the object with mass m is raised through a displacement q , a force F is applied to it. Imagine what would happen if you let go of the rope and the object were allowed to fall.

Fig. 8-4 . Work is done when a force is applied over a specific distance. In this case, the force is applied upward to an object against Earth’s gravity.

Suppose that m = 5 kg. This is about 11 pounds in Earth’s gravitational field. Suppose that the object is hard and solid, such as a brick. If you raise the brick a couple of millimeters, it will strike the floor without much fanfare. If you raise it 2 m, it will crack or dent a linoleum floor, and the brick itself might break apart. If you raise it 4 m, there will certainly be trouble when it hits. The landing of a heavy object can be put to some useful task, such as pounding a stake into the ground. It also can do a lot of damage.

There is something about lifting up an object that gives it the ability to do work. This “something” is potential energy . Potential energy is the same thing as work, in a mechanical sense. If a force vector of magnitude F is applied to an object against Earth’s gravitation and that object is lifted by a displacement vector of magnitude q , then the potential energy E p is given by this formula:

E p = Fq

This is a simplistic view of potential energy. As we just discussed, potential energy can exist in a barrel of oil even if it is not lifted. Potential energy also exists in electrochemical cells, such as the battery in your car. It exists in gasoline, natural gas, and rocket fuel. It is not as easy to quantify in those forms as it is in the mechanical example of Fig. 8-4, but it exists nevertheless.

#### Potential Energy Practice Problem

Problem

Refer again to Fig. 8-4 . If the object has a mass of 5.004 kg and it is lifted 3.000 m, how much potential energy will it attain? Take the value of the magnitude of Earth’s gravitational acceleration as a g = 9.8067 m/s 2 . We can neglect vectors here because everything takes place along a single straight line.

Solution

First, we must determine the force required to lift a 5.004-kg object in Earth’s gravitational field:

F = ma g = (5.004 kg) (9.8067 m/s 2 ) = 49.0727268 N

The potential energy is the product of this force and the displacement:

Ep = Fq = (49.0727268 N) (3.000 m) = 147.2181804 J

We are entitled to go to four significant figures here because the least accurate input data are given to four significant figures. Therefore, E p = 147.2 J.

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