### Video Transcript

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. How much energy is stored in the spring? Take ๐ equals 9.8 meters per second squared.

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. And this is going to give us 49 over six. And the units are going to be newtons per meter. And thatโs because we saw that we had 9.8 newtons divided by 1.2 meters. Okay, so now whatโs the second step?

The next step is to find the change in length of the spring. And we can do that using the equation ๐๐ is equal to ๐ multiplied by ๐ฆ, where ๐ฆ is the change in length. So if we rearrange this, we can say that ๐ฆ is gonna be equal to ๐๐ over ๐. So this is gonna be equal to 0.5 multiplied by 9.8 divided by 49 over six. And thatโs because thatโs what we found for ๐ in the first part. And this is gonna give us result of three over five meters.

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. 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. 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. And this is gonna be all squared.

And then, finally, when we calculate this, weโre gonna get the potential energy, so our elastic potential energy. Itโs gonna be 1.47 joules. So therefore, we can say the amount of energy stored in the spring is going to be 1.47 joules.