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In this video, we're going to be looking at an example using the conservation of mechanical energy and the work energy theorem.
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Okay.
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And what we have is a spring.
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All right.
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It has a spring constant k of 1 ,500 newtons per meter.
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Right.
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Attached to this spring is going to be a block of a mass m equals two kilograms.
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We're going to stretch this mass and spring by a distance.
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Of delta x equals three centimeters or 0 .03 meters.
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Okay, we're then going to let it go.
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And we want to find the velocity at equilibrium if the surface between the block and the floor is frictionless, and if it has a coefficient of kinetic friction of uk equals 0 .3.
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Okay.
01:06
Okay.
01:06
So what the conservation of energy says is that mechanical energy is conserved.
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So mechanical energy is kinetic energy plus potential energy.
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So from that theorem, we get initial kinetic energy plus initial potential energy.
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Equals a final kinetic energy plus final potential energy.
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Okay, so let's look at the frictionless case first.
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Right.
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So we'll look at our, the point.
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Where the spring is stretched by three centimeters, right? and we're at rest there.
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We're going to be releasing the block from rest.
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So my initial kinetic energy is zero.
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And my mechanical energy is just my initial potential energy, which is one half k delta x squared.
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Right, and that equals my final kinetic energy plus my final potential energy.
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We know that we're looking for the velocity at equilibrium, at equilibrium, my delta x value is going to be zero.
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So my energy is going to be entirely kinetic, and that's going to be equal to one -half m v squared...