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Problem 7 .72, we have a small rock with mass of 0 .12 kilograms.
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It's fastened to a massless string with length 0 .8 meters to form a pendulum.
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And so the pendulum is swing, so it makes a maximum angle of 45 degrees with the vertical.
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We have air resistance is negligible.
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First, whereas what is the speed of rock when a string passes through the vertical position.
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So here i'm going to define our potential energy to gravity to be zero at the best.
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Base.
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So that means that we have just gravitational potential at the top here, and it's going to turn into all kinetic energy at the base here.
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So we have gravitational potential equal to k2.
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I'll write down this as 0 .1, and this is 0 .2.
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So then we find out what those are.
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So we have mg times some height.
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I'll write as y, and that's going to be equal to one half mass velocity squared.
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I'll immediately cancel out the mass.
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But what we need to find is y in order to find what our speed is at the bottom.
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Okay, so we need a little geometry here.
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So the pendulum forms a triangle between our length when it's at 45 degree angle and width of vertical.
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And it's going to be a right triangle.
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So i need to find what this is.
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This is y.
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So i know that this whole length is l, but in order to find what this length is, what i can then do is say l minus this length is going to be y.
01:48
So i want to find this length, i know that the hypopt moves is l.
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I have an angle.
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So find what the adjacent angle is.
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So that's l cosine of 45.
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Degrees.
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So then y equals our full length, l minus this partial length, l cosine 45 degrees.
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Okay, so then i can substitute that in for why.
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So i have a g times l.
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I'm going to immediately just pull that out...