Anderson Video - Stretched Spring and Energy

Professor Anderson
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>> Let's say we have a spring and we want to stretch it out and put some amount of energy in that spring. And let's say we're given some K value for the spring. And let's say it's a pretty heavy duty spring, maybe 500 newtons per meter. And it's rest length is here, and now we're going to stretch it out to some distance X. And we want to see how much energy is in there. And let's say that we want a specific amount of energy. Let's say that the energy in the spring we want to be 100 joules okay. Let's see what that X needs to be in order to accomplish that. Okay that's not too bad right. We know what the energy in a spring is. You can integrate Hooke's Law to calculate that. Or you can just remember that it's 1/2 KX squared where X is the stretch distance right. Starting from the rest length stretching out from that point. We can solve this for X right, multiply by 2 divide by K take the square root. I get 2 energy in the spring U sub S divided by K and then that whole thing I have to square root. And now I have all those numbers. So we've got 2 times U sub S which we said was 100. We're going to divide by K which we said was 500. This becomes the square root of 2 over 5, square root of 2 over 5 is what? Well 2 over 5 is 0.4 and that's got to be pretty close to what? I don't know let's run it and try it okay. 2 divided by 5 we said was 0.4 we're going to take the square root and we get 0.63. Remember this is SI units so this is meters, and so that stretched distance is going to be 63 centimeters okay. Which is pretty far stretch, but 100 joules is a decent amount of energy in that spring. Alright hopefully that's clear, cheers.
>> Let's say we have a spring and we want to stretch it out and put some amount of energy in that spring. And let's say we're given some K value for the spring. And let's say it's a pretty heavy duty spring, maybe 500 newtons per meter. And it's rest length is here, and now we're going to stretch it out to some distance X. And we want to see how much energy is in there. And let's say that we want a specific amount of energy. Let's say that the energy in the spring we want to be 100 joules okay. Let's see what that X needs to be in order to accomplish that. Okay that's not too bad right. We know what the energy in a spring is. You can integrate Hooke's Law to calculate that. Or you can just remember that it's 1/2 KX squared where X is the stretch distance right. Starting from the rest length stretching out from that point. We can solve this for X right, multiply by 2 divide by K take the square root. I get 2 energy in the spring U sub S divided by K and then that whole thing I have to square root. And now I have all those numbers. So we've got 2 times U sub S which we said was 100. We're going to divide by K which we said was 500. This becomes the square root of 2 over 5, square root of 2 over 5 is what? Well 2 over 5 is 0.4 and that's got to be pretty close to what? I don't know let's run it and try it okay. 2 divided by 5 we said was 0.4 we're going to take the square root and we get 0.63. Remember this is SI units so this is meters, and so that stretched distance is going to be 63 centimeters okay. Which is pretty far stretch, but 100 joules is a decent amount of energy in that spring. Alright hopefully that's clear, cheers.