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(II) You drop a 12 -g ball from a height of 1.5 $\mathrm{m}$ and it only bounces back to a height of 0.75 $\mathrm{m} .$ What was the total impulse on the ball when it hit the floor? (Ignore air resistance).

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$0.11 \mathrm{kg} . \mathrm{m} / \mathrm{s}, upwards$

Physics 101 Mechanics

Chapter 9

Linear Momentum

Motion Along a Straight Line

Kinetic Energy

Potential Energy

Energy Conservation

Moment, Impulse, and Collisions

Cornell University

Hope College

McMaster University

Lectures

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Okay. Sorting chapter nine Problem 47. So says we drop a 12 grand ball from a height 1.5 meters and it bounces up to half that high 0.75 What was the total impulse on the ball and it hit the floor. Okay, well, we know impulses, just the changing momentum. So that's what we're trying to find. So if we call upwards in a positive direction, then the downwards negative direction such the final velocity is positively initial velocity is naked talking about before and after the collision. So sphere out what the speed is when right for the collision. We need the figure out this right when we also need to figure out the speed after. Well, we use our energy conservation for that. So we know that the kinetic energy of the bottom because the potential energy at the top So this just tell this 1/2 in the B squared peoples mg age. Okay, so we rearrange that we see that b of the bottom now is negative because we define this is negative sward of to g h. But Okay, well, similarly, we're gonna have the same thing for the a so we're gonna have one and 1/2 envy after squared equals in G H crime, which is the height after the after the collision like that reaches. So that means this is also gonna be similar. It's not gonna be negative now, because this is going upwards between. Find us positive. So this is to G h prime. Okay, so no, the impulse weaken. Just calculate Delta p So this is inducted be or in times the after minus B before. Okay, so this becomes 10 times to G h crime plus to G h. Cool. So let's just find out what this is. So this becomes them to g times square root of h prime minus square root of each purple sinus. So we have 0.12 kilograms times square root of two times 9.8 years per second. Squared times squared of 0.7 fine. Plus it's wearing of 1 45 Okay, so if we plug that in our calculator, we get a impulse of 0.11 kilogram meters per second. In which direction is this for the change in momentum? It means we have more moment. I'm coming down coming off. So that means that impulse is directed towards Oh, awesome.

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