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A ball with mass $M,$ moving horizontally at 5.00 $\mathrm{m} / \mathrm{s}$ , collides elastically with a block with mass 3 $\mathrm{M}$ that is initially hanging at rest from the ceiling on the end of a 50.0 -m wire. Find the maximum angle through which the block swings after it is hit.

$68.8^{\circ}$

Physics 101 Mechanics

Chapter 8

Momentum, Impulse, and Collisions

Moment, Impulse, and Collisions

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University of Michigan - Ann Arbor

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problem. 8.83. We have a ball with a massive m moving at a speed were given and I was colliding with the block suspended from a wire that has a massive three M given the length of the wire. And now the question we want to know the answer to is what is the maximum angle that the block swings through? First things to a suppose whatever, um, before it, you know what? Well, what's the maximum ankle before it starts coming back down? So block is initially at rest. Let's call it Be this, eh? So equation 8.25 which is for elastic collision, where one thing is addressed speed immediately after the collision. For the resting thing is to m a over and a bus and b times e A. And so this is two to fight it by four em time. Four meters per second and this is two meters per cent Now. The height the goes to when it swings through an angle theater. Why equals l times one minus. Who's that? And you can work out using trigonometry where this comes from. Basically, l minus y is this length that this is L. Why is the height that it goes through? You use the so kowtow to figure out the relationship between these and the So now, knowing what the height is that it goes through. We have the conservation of energy. So 1/2 times three m b b squared. I was going to eat wall three em. I'm g plans the height which the block ascends. Three ends obliging Cancel out for us. So the coastline of the angle is equal to one minus B squared. Fight it by two g, no. And so if you take you evaluate this and take the article no sign of it defined that our angle the 3.7 it means

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