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University of Washington

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Problem 33 Medium Difficulty

(a) Find the magnitude of the gravitational force between a planet with mass $7.50 \times 10^{24} \mathrm{kg}$ and its moon, with mass $2.70 \times 10^{22} \mathrm{kg},$ if the average distance between their centers is $2.80 \times 10^{8} \mathrm{m} .$ (b) What is the acceleration of the moon
towards the planet? (c) What is the acceleration of the planet towards the moon?

Answer

(a) $F_{\mathrm{G}}=1.72 \times^{20} \mathrm{N}$ $\\$
b) $a_{M}=6.37 \times 10^{-3} m /s^{-2}$ $\\$
(c) $a_{\mathrm{P}}=2.29 \times 10^{-5} \mathrm{m}/ \mathrm{s}^{-2}$

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Video Transcript

in this person. We have a planet in the ruin and a massive of the planet. And they were given. And distance between centers are also given. It's also given. So uh that three parts in this question, you want to find a gravitational force between on between dependence between dependent and the moon. And acceleration of the movement toward the planets and the acceleration of kind of toward the moon. Okay. Okay. So as mentioned, so we know that there will be gravitational force. Thank you for today on each other. Okay. And there will be of the same menu to the opposite direction. Okay. And to find that force will be using the formula. Yeah. Um F equals two G and P. Times and sub began divided by our square. Yeah. So just putting their numbers. Okay. And then you get 1.72 times 10-20. Okay, so this is the answer of a just put some. Do you just say that this is a gravitational force then uh to find an acceleration of the moon towards the planet? He'll be using uh Newton's second law. If we say that at net it goes to M. A. So a uh the exaggeration of the moon is equal to uh gee divided by the mass of the moon. You calculate this, he gets 6.38 times 10 to the negative three m. goes against where you know, we do the same thing for the planet. Again, using your second hour to a P. Is equal to the traditional forest divided by the mass of the planet. And you get 2.30 times 10 to the -5. You guys 2nd square. So notice that repetition of false on each other at the same. But they have different accelerations because they have different masses. Okay. And that's all for this question.

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