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Problem 26 Easy Difficulty

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 $\mathrm{m} / \mathrm{s} .$ What is the mass of this canister?

Answer

$m_{e}=81.8 \mathrm{kg}$

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Video Transcript

in this question, a matter naught with a mass off 78.4 kg is standing still and a large gas canister off unknown mass is moving in her direction with velocity off 3.5 m per second as soon as the astronaut can, it gives a push to the canister such that the velocity of the canister after that push is 1.2 m per second but still in the same direction. And now the velocity off the astronaut is 2.4 m per second. Then we have to determine what is the mass off the gas canister. For that, we have to use the law off momentum conservation. So the net momentum before is equal to the net moment after so all you have to do is the following right is down the net mo mentum before. Is he a cause to the net momentum? After what is the net momentum before? Before we have on Lee the canister moving and it's moving to the left? Let's say that everything that is moving to the left is moving to the negative direction in my reference frame. So in the beginning, you Onley have the momentum of the canister, which is given by minus the mass off the canister times its velocity off 3.5 m per second. That minus sign is because it's moving to the left and my reference friend points to the right. Then we have the momentum after so after what we have is the following. Both the canister and the astronauts are moving and both are moving to the left. So we have to contributions of the momentum. One coming from astronaut with a mass off 78.4 kg and a velocity off 2.4 m per second. Again minus sign because it she's meeting to the left and then we have the contribution from the canister which is minus the mass of the canister. Times 1.2. Now all we have to do solve this equation for the mass of the canister. We can do that as follows, so send this term to the other side. Then we have minus the mass of the canister times 3.5, plus the mass of the canister times 1.2 is equals to minus 78.4 times 2.4. Now you can subtract these two terms to get the following minus the mass off the canister. Times 2.3 is equal to minus 78.4 times 2.4. Therefore, the mass of the canister is given by minus 78.4 times 2.4 divided by minus 2.3 on these results in a mass off approximately 81.8 kg. And this is an answer to this question.