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$\bullet$ An astronaut in space cannot use a scale or balance to weigh objects because there is no gravity. But she does have devices to measure distance and time accurately. She knows her own mass is $78.4 \mathrm{kg},$ but she is unsure of the mass of a large gas canister in the airless rocket. When this canister is approaching her at $3.50 \mathrm{m} / \mathrm{s},$ she pushes against it, which slows it down to 1.20 $\mathrm{m} / \mathrm{s}$ (but does not reverse it) and gives her a speed of 2.40 $\mathrm{m} / \mathrm{s}$ . (a) What is the mass of this canister? (b) How much kinetic energy is "lost" in this collision, and what happens to that energy?

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in this problem. We have a national with massive 78.4 kilograms and a canister flying at the astronaut, Um, with a speed of 3.5 meters per second, the canister the yesterday pushed it against the canister, and then the canister slowed to 1.20 meters per second. And the astronaut, which is initially at rest, um, picks up speeds to go at 2.4 meters per second as she pushes against the canister, um, so were asked to find, um what is the mess of the canister? Um, so this is just a simple conservation of momentum problem. So the initial momentum will be equal to the final momentum, and the initial momentum is all carried by the canister. So the mess of the canister times the initial, um, speed of the canister is going to be equal to the mass of the astronaut times. The initial the final speed of the astronaut rather plus the mass of the canister times the, um, final speed of the chemist. Er, the only thing we don't know here is the mass of the canister. So we're going Teoh, move. Subject this term from both sides and, ah, factor out the massive a canister. So the mass of the canister times the initials B of the canister minus its final speed is going to be equal to the mass of the national at times the final speed of the astronauts. Then we just divide by, um, this term in brackets to get the mass of the canister all on its own. So the mass of the canister is equal to mess with the astronaut times final speed of the astronaut over the initial speed of the canister minus the final speed of the canister. Um, this is substituting in Constance 78.4 kilograms times three points. Though the final speed of castor is, um, 2.40 meters per second, we divide that by, um, the initial speed of the canister, Um or sorry, that was the final speed of the astronaut. We divide by the initial speed of the canister, which is 3.50 meters per second, minus the final speed, which is 1.20 meters per second. Plugging this into a calculator, we find that the mass of the canister is 81.8 kilograms in the second part of the question, we're as to say how much kinetic energy is lost in this collision. So the initial kinetic energy is, um, 1/2 times the mass of the canister times the initial, um, speed of the canister squared, which is plugging this into a calculator with the mass being 81.8 kilograms is we just found out this is 501 Jules. Um, now, the final kinetic energy is includes both the mass of the canister times, the final speed of canister as well as, um, the mass of the astronaut times. The final speed of the astronaut squared. I'm this a squared to I think I forgot to say that and plugging those constants in and putting that into a calculator, we find that the final kinetic energy is just 285 jewels. So the difference in kinetic energy is then to, um is unequal to 285 jewels minus 501 jewels which is equal to negative 216 jewels. That energy is going to be dissipated into other forms like sound and heat. Just as the collision does make sound and, um, does sort of rattle things around a bit. Um, so that's where that energy goes.

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$\bullet$ On a very muddy football field, a $110-…

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Watch More Solved Questions in Chapter 8

Video Transcript

Hugh D. Young

College Physics

Christina Krawiec

Farnaz Mohseni

Zachary Mitchell

Meghan Miholics

This textbook answer is only visible when subscribed! Please subscribe to view the answer

College Physics

Christina Krawiec

Farnaz Mohseni

Zachary Mitchell

Meghan Miholics

Hugh D. YoungCollege Physics

Christina Krawiec

Farnaz Mohseni

Zachary Mitchell

Meghan Miholics

Hugh D. Young

College Physics