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California State Polytechnic University, Pomona

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Problem 63 Easy Difficulty

A steel ball with mass 40.0 $\mathrm{g}$ is dropped from a height of 2.00 $\mathrm{m}$ onto a horizontal steel slab. The ball rebounds to a height of 1.60 $\mathrm{m}$ . (a) Calculate the impulse delivered to the ball during impact. (b) If the ball is in contact with the slab for 2.00 $\mathrm{ms}$ , find
the average force on the ball during impact.

Answer

(a) $J=0.474 \mathrm{kg} \cdot \mathrm{m} / \mathrm{s}$ upward
(b) $F=237 \mathrm{N}$ upward

Discussion

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Video Transcript

{'transcript': "welcome to a new problem This time we have ah ball. It's steel ball So given were given a steel ball and it happens to have the mass ofthe forty kilograms or rather forty grams. So I you know, we'LL say muscle Steele is forty grams. Who can change that right away, too. Kilograms by multiplying that by a thousand kilograms. So we have zero point, um zero. So forty into a thousand. Let's see. What's that going to give us? It's going to give us zero point zero four kilograms. So that's the way the not the way but the Marcel's still ball, you know, it's dropped from the height. Oh, two meters. Okay, so we're going to call these, Uh hey JJ initial. Yes, h initial two point zero zero meters and then it bounces off and goes all the way. Bounces off and gets to a new height. Um, this is the ball. So this is the new height. Final height happens to be one point six zero meters, so that's the final height that it's bouncing. Member acceleration due to gravity G is nine point eight meters per second squared. You can think off going downwards as positive and going up with us. Negative. You can think of it that way on. But, hey, we want to find the impulse. The care off, off the force in positive, delivered by the force member impulses. Just the change in momentum off the final momentum minus the initial momentum. So in that case, we're gonna have to find the final and initial. The last second part is that we're given a time T equals two two zero zero milliseconds. Oh, if you want to change that right away, you could say in seconds, this is over a thousand seconds. And that's going to give us, um, zero point zero zero two seconds. Okay, zero zero two seconds. That's the time it takes to bounce off for moment on and so on. But be want to find what's the What's this average force? Ah, that's responsible. Okay, for that change, what's their average force responsible for that change? S o. The fasting will do we have to compute the initial and final velocity. The initial the last e is just this quote off to G H one and that gives us a radical ah, two times nine point eight meters per second squared times the height displacement which is two point zero zero meters and this becomes a six point three meters per second. That's the initial velocity. The final velocity is the same type of formula radical to G eight final. Ah and so this is two times nine point eight meters per second squared. Then multiply that by the final height, which is one point six meters, that's going to give us final velocity off off five point six meters per second. That velocity is a minus because off our direction and orientation in the next page were set to compute the impulse which happens to be final minus initial the mass. This is the final final velocity. You get a changes a little bit. We have we have to put in the mass were given the most zero point. Oh, if you can recall if I go back, this is the mass right here. It's zero point zero four kilograms, so that's the one we're gonna use. So zero zero point their point zero for kilograms and then the final velocity is negative five point six meters for second, minus six point three meters per second and so this When you plug in those numbers, you get like zero point four eight kilogram, uh, meters off the second. That's, you know, mass and velocity. So the magnitude the mob magnitude off the impulse, the magnitude ofthe the impulse is ah, zero point. You're right. That zero point for eight, uh, killer grub meters per second. You know, that's the magnitude of the impulse. The next thing that happens is we know the time off contact, and that's going to help us determine the average force. So force average it close to the impulse off the time of contact. You really have the impulse, which is your point for eight kilogram meters for second in terms of magnitude and then the time off contact. If you go back to find it's zero point zero zero two seconds. So we'LL plug that zero point zero zero two seconds. Uh, and if you put in those numbers, you get that the in a four forty eight divided by point zero zero two and that becomes twenty four thousand twenty four thousand Newtons, which you could also write us two point full time stand to the three mutants. So like that two point four times ten to the three Newton's hope you enjoy the problem. We had to find the impulse, which is pretty much the change in momentum. Zero point for a kilogram, meters per second. And then we also had to find the force responsible for change for, um, full the average force during the time of impact. So that's two point four times ten to the three mutants. Feel free to ask any questions. You, Khun, send any questions my way and have a wonderful day. Okay, thanks. Bye."}