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Impulse between Bouncy Ball & Wall

Patrick Ford
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Hey guys, let's take a look at this problem here. So, I have a bouncy ball or a rubber ball that's going to strike off of the wall. Let's go ahead and draw that out real quick. So I have this bouncy ball like this. The m is equal to 0.15 And initially it's going with some speed which is 40 m/s to the right, then it strikes the wall like this and then afterwards it's going to rebound and bounce backwards. So then afterward the collision or after the bounce off of the wall, it's going to be going down to the left and because it's going to the left, When I write the final velocity here, it's not gonna be 45 m/s, it's going to be negative 45 m/s. If you have opposite directions and velocities, you're gonna have to pick a direction of positive and stay consistent with that throughout the problem. So, let's take a look at part a and part. We want to calculate the impulse which is J. Delivered to the ball from the collision with the wall. All right, so that's J. Equals And we have an equation for that F times delta T. But this is also equal to the change in momentum, which is M. V. Final minus V. Initial. All right. So we just basically take a look at all the variables which ones we have, which ones we don't. So, we have the force we're told here in the second part, the average force is 410 Newtons during the bounce. That forces also directed to the to the left like this. So this is our force here. So we actually don't have what the change in time is. In fact, that's a that's actually we're going to calculate in part B. So we actually can't use F times delta T. But that's okay because we have mass, we have final velocity and we have initial velocity. So we can calculate the impulse by using that side of the equation. All right, so let's get to it. So J is gonna equal we have the mass which is 0.15. Now, I have to be careful here, so I'm gonna write a little bracket. My final velocity is negative 45 m per second. It is negative 45 minus the initial velocity, which is just 40. So keep track of your minus signs when you actually end up getting here is negative 12.75 kilogram meters per second. That's the answer to part. That's the impulse. Notice how it's negative. And that makes sense because the impulse is actually going to point to the left because it's basically going to cause a change in momentum to the left. Like this. So your impulse should be negative. Let's take a look at part B and part B. Now we want to calculate how long the amount of time that the ball is in contact with the wall. So basically from here to here, the initial to final, the forces acting over a very small adult A. T. In order to create an impulse that acts to the left. And that's what we want to figure out here. So we know that the force the that the Wall exerts on the ball during the balance is going to be 410 But continue to stay system with are consistent with our directions because it points to the left, I'm actually going to write a negative sign here. It's gonna be negative 410 Nunes. So we actually have what our impulse is. We just calculated that in the last part we have this and now we basically want to use the other side of the impulse equation, which is F times delta T. So have times DELTA T. Here. We want to figure out what's this DELTA T. We actually have what the force is so we can go ahead and do that. So you know this is negative 12.75 equals negative 410 times delta T. And all you have to do is just do a division. So basically our delta T. Is going to be, your negatives are going to cancel out together as two of them. This is basically going to be 12.75 divided by 410. And you should get a delta T. Of 0.31 seconds. All right, so it's about 31 milliseconds for the bounce. That's really it. So let me know if you guys have any questions