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Problem 30 Easy Difficulty

A space traveler weighs 540.0 N on earth. What will the traveler weigh on another planet whose radius is twice that of earth and whose mass is three times that of earth?

Answer

405.0 $\mathrm{N}$

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Video Transcript

we begin this question by can't leading the acceleration of gravity on the surface off these other planet. So remember that the surface gravity off any planet is it goes to Newton's constant times. The mass off the planet divided by the radios, squared off this planet. So for planet earth, we have a gravitational acceleration that is given by G m. E, divided by the radios off the earth squared for the other planet we have the following It is it goes to g times the mass off the other planet divided by the radios off this other planet squared. But the mass off the other planet is because to three times the mass off the earth and at the same time the radios off this other planet is it goes to two times the radios off the earth. So we have two times r e squared here and this gives us g times m e divided by r e squared times three divided by four. And this is nothing else than the surface gravity off the Earth Time Street, divided by four. Therefore, exploration off the gravity on the surface off this other planet is equals to 3/4 Deceleration off gravity on the surface off your now we proceed to couple eating. What is the weight off? That's place traveller on the surface off these other planet. Remember that the weight force is given by the mass times acceleration off gravity The reform The mass off this place traveller on the earth is equals to the mass off the space traveler which is a known times next relation off the gravity on the surface of the earth. At the same time, the weight off the space traveler on the surface off this other planet is equals to the mass off the space traveler times acceleration off gravity on the surface off this other planet. But as we have calculated, the acceleration of gravity on the surface off the other planet is equals to 3/4 explanation of gravity on the surface of the earth. So these is equal to the mass off the astronaut times 3/4 crimes the gravity on the surface off the earth and this is equals 234 times the mass times the gravity from the earth. And this is nothing else than the weight off the space traveler on the Earth before the weight off the space traveler on these other planet is, he goes to 3/4 times the weight off this space traveler on the Earth, which is equals to 540 new terms. So we have 3/4 off, 540 which is equals to 405 new terms. So the weight off the space travel on the surface off these other planet is equals to 405 new towns.

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