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 a 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 meters per second to the right. Then it strikes the wall like this, and then afterward, it's going to rebound and bounce backward. So then after 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 going to be 45 meters per second. It's going to be negative 45 meters per second. If you have opposite directions and velocities, you're going to have to pick a direction of positive and stay consistent with that throughout the problem. So let's take a look at part a. In part a, we want to calculate the impulse, which is j, delivered to the ball from the collision with the wall. Alright? 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(vfinal - vinitial). Alright. So we just basically look at all the variables, which ones we have and 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 force is also directed 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 actually what 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 the final velocity, and we have the initial velocity, So we can calculate the impulse by using that side of the equation. Alright. So let's get to it. So j is going to equal. We have the mass, which is 0.15. Now I have to be careful here, so I'm going to write a little bracket. My final velocity is negative 45 meters per second. So this is negative 45 - the initial velocity, which is just 40. So keep track of your minus signs. What you actually end up getting here is negative 12.75 kilogram meters per second. That's the answer to part a. 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. In part b, now we want to calculate how long or the amount of time that the ball is in contact with the wall. So basically, from here to here, the initial to final, the force is acting over a very small delta 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 that the wall exerts on the wall during the bounce is going to be 410, but in you know, to stay consistent with our directions, because it points to the left, I'm actually going to write a negative sign here. It's going to be negative 410 newtons. 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 f 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 we 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 Well your negatives are going to cancel out because there are 2 of them. This is basically going to be 12.75 divided by 410, and you should get a delta t of 0.031 seconds. Alright. So it's about 31 milliseconds for the bounce. That's really it. So let me know if you guys have any questions.
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Intro to Impulse
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