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Hello.
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In this problem on the diagram on the right we have a beat who slides on this wire here and we assume that this motion is frictionless or the frictionless can be ignored.
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So at point a, the bead was 80 centimeters high from the zero level here and its velocity was 200 centimeters per second.
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The question is to determine the velocity of this beat at point b where it's on the zero level or and at point c where it's 50 centimeters high.
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So we will use the conservation of energy here in that problem, and we will start by bart a.
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We know that the total energy at point a is equal to the total energy at point b.
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So from here, this means that the kinetic energy at a plus the potential energy at a is equal to kinetic energy at b plus the potential energy.
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At b.
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Putting in the expressions for kinetic energy, we have half multiplied by the mass, multiplied by va squared, plus potential energy is m multiplied by g, multiplied by h at a.
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And we will do the same on the other level.
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So we have that's equal to.
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Let's just minimize this a little bit here.
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So we have this equal to half mvb squared plus m g hb.
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So from here we can first notice that the ms will cancel on each side...