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A ball of mass 0.5 kilograms hangs in equilibrium from the ceiling by a light elastic spring of natural length 1.2 meters and a modulus of elasticity 9.8 newtons.
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How much energy is stored in the spring?
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Take ๐ equals 9.8 meters per second squared.
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So to find ๐, what weโre gonna do is divide 9.8, which is our modulus elasticity, by 1.2, the natural length of the spring.
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And this is going to give us 49 over six.
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And the units are going to be newtons per meter.
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And thatโs because we saw that we had 9.8 newtons divided by 1.2 meters.
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Okay, so now whatโs the second step?
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The next step is to find the change in length of the spring.
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And we can do that using the equation ๐๐ is equal to ๐ multiplied by ๐ฆ, where ๐ฆ is the change in length.
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So if we rearrange this, we can say that ๐ฆ is gonna be equal to ๐๐ over ๐.
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So this is gonna be equal to 0.5 multiplied by 9.8 divided by 49 over six.
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And thatโs because thatโs what we found for ๐ in the first part.
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And this is gonna give us result of three over five meters.
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So now the final stage is to calculate the potential energy, so the elastic potential energy, cause thatโs gonna tell us how much energy is stored in the spring.
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So the elastic potential energy is gonna be equal to a half multiplied by ๐, which is our spring constant, multiplied by ๐ฆ squared, which is our change in length squared.
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So this is gonna be equal to 0.5 multiplied by 49 over six, which is our ๐, multiplied by three over five, which is our change in length.
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And this is gonna be all squared.
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And then, finally, when we calculate this, weโre gonna get the potential energy, so our elastic potential energy.
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Itโs gonna be 1.47 joules.
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So therefore, we can say the amount of energy stored in the spring is going to be 1.47 joules.