Mechanical Potential Energy.

Labs written for the CARA Space Explorers, Fall 1993

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This is meant to be handed out to the students.*

So how can we get a number for the amount of energy that you put into a spring? How hard it is to compress or stretch is measured by a number called the spring constant. The spring constant is different for every spring and depends on what the spring is made out of, how tightly it's coiled, things like that. We symbolize the spring constant by a letter k. The units of k are g/s. If I compress a spring by an amount I'll call x, the energy contained in a spring is given by the formula:

MPE = (1/2) k x

Here x is the difference between the length the spring normally is, and the length it is when it is compressed. If I stretch, rather than compress, a spring by an amount x, the energy is still given by the amount above. Notice that the amount of energy contained in the spring is the same whether I stretch or compress the spring; if I compress the spring by 5 centimeters, it has the same energy as if I had stretched the spring by 5 centimeters. If I stretch the spring 5 cm, it wants to compress back to its original position; if I compress the spring 5 cm, it wants just as badly to stretch back to its original position.

We can convert mechanical potential energy to kinetic energy by compressing a spring with a mass on the end of it, then letting it go. If we point the mass towards the ceiling, then the kinetic energy will be converted to gravitational potential energy when it is as high as it will go. Then, the gravitational potential energy will be converted to kinetic energy as it falls to the floor. When it hits the floor, the energy is converted to heat and noise. Remember that the gravitational potential energy of something is given by:

GPE = m g h

where g = 980 cm/s, m is the mass of the object, and h is its height. Today we are going to work with the conversion of energy between gravitational potential energy and mechanical potential energy.

What is the length of your spring before you compress it? (UNITS!)

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What is the length of your compressed spring? (UNITS!)

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So what is the difference between the relaxed and the compressed length? (UNITS!)

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What is the total mass of the things you are going to launch? (UNITS!)

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Go ahead and launch your system, trying not to hit anyone, and warning people you might hit before you let it go.

How high did the mass fly? (UNITS!)

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We know that the energy contained in the spring basically all goes into gravitational potential energy, so we can write this equation:

mgh = (1/2) k x

Rearrange this equation so that there is a "k = " on one side and a combination of letters on the other side. This is called "solving for k." Do it here:

Check with one of us to make sure you have it right, then stick in all the information you have to solve for the k of your spring. Remember g = 980 cm/s.

What is the k of your spring? (UNITS!)

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Now, pick a different mass. What is this new mass? (UNITS!)

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If you repeat the experiment with this new mass, how high will the mass rise? (UNITS!)

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Do it. Were you right (within experimental error)?

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If there is time, pick a new mass, and try again.

2. If a spring has 1,000,000 ergs contained in it when it is stretched 40 cm, what is the spring constant of the spring? (UNITS!)

3. Is there more energy stored in a spring when you hang a heavy weight on it or a light one?

4. How much energy is contained in a compressed spring right before it makes a 50 gram mass jump 50 cm? (UNITS!)

5. If a mass of 5 g is put on a spring launcher (with a k of 400,000 g/s2) that gets compressed 1 cm, how high will the mass jump?

**Important Disclaimers and
Caveats**

Go back to the Chicago Fall 1993 Energy home page.