Energy and block

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Energy and block

Mechanical advantage Video transcript Welcome back. So let's do a potential energy problem with a compressed spring. So let's make this an interesting problem. Let's say I have a loop-d-loop. A loop-d-loop made out of ice.

Energy and block

And I made it out of ice so that we don't have friction. Let me draw my loop-d-loop. There's the loop, there's the d-loop.

And let's say this loop-d-loop has a radius of 1 meter.

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Let's say this is-- this right here-- is 1 meter. So of course the loop-d-loop is 2 meters high. And let's say I have a spring here-- it's a compressed spring. Let's say this is the wall. This is my spring, it's compressed, so it's all tight like that. Energy and block let's say its spring constant, k, is, I don't know, Attached to that compressed spring-- so I have a block of ice, because I need ice on ice, so Energy and block have no friction.

This is my block of ice, shining. And let's say the block of ice is, I don't know, 4 kilograms. And we also know that we are on Earth, and that's important, because this problem might have been different if we were on another planet.

And my question to you is how much do we have to compress the spring-- so, let's say that the spring's natural state was here, right, if we didn't push on it. And now it's here. So what is this distance? How much do I have to compress this spring, in order for when I let go of the spring, the block goes with enough speed and enough energy, that it's able to complete the loop-d-loop, and reach safely to the other end?

So, how do we do this problem? Well, in order-- any loop-d-loop problem, the hard part is completing the high point of the loop-d-loop, right? The hard part is making sure you have enough velocity at this point, so that you don't fall down.

Your velocity has to offset the downward acceleraton, in which case-- and here, is going to be the centripetal acceleration, right?

So that's one thing to think about. And you might say, wow this is complicated, I have a spring here, it's going to accelerate the block. And then the block's going to get here, and then it's going to decelerate, decelerate.

This is probably where it's going to be at its slowest, then it's going to accelerate back here. It's a super complicated problem. And in physics, whenever you have a super complicated problem, it's probably because you are approaching it in a super complicated way, but there might be a simple way to do it.

And that's using energy-- potential and kinetic energy. And what we learned when we learned about potential and kinetic energy, is that the total energy in the system doesn't change. It just gets converted from one form to another.

So it goes from potential energy to kinetic energy, or to heat. And we assume that there's no heat, because there's no friction.

So let's do this problem. So what we want to know is, how much do I have to compress this spring? So what I'm essentially saying is, how much potential energy do I have to start off with-- with this compressed spring-- in order to make it up here?

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