The mass of Venus is 81.5% that of the earth, and its radius is 9...

Question

The mass of Venus is 81.5% that of the earth, and its radius is 94.9% that of the earth. (b) If a rock weighs 75.0 N on earth, what would it weigh at the surface of Venus?

Accepted Answer

Hey everyone welcome back in this problem. We're told that Uranus is mass is 14.5 times that of Earth. Okay. And that its radius is four times that of Earth. And we want to know what would you weigh on the surface of Uranus if you weighed 800 newtons on Earth's surface. Okay, so we're thinking about weight on a planet. Okay, let's recall that weight. So let's say weight of Uranus on Uranus is equal to mass times the gravitational acceleration. Okay, so mass times the gravitational acceleration of Uranus. This is what we're trying to find. Well we don't know our mass. Okay. We're told the weight on our surface but we don't have the mass and we don't know the gravitational acceleration of Uranus either. Okay, so let's go ahead and try to find these values so that we can plug them into our equation. Let's start with the weight. Okay, We know our weight on Earth. Okay, so we can find The mass using the following formula. Okay, so the weight on Earth is the mass times the gravitational acceleration on Earth. We know that our weight on earth is 800 newtons and we know the gravitational acceleration on Earth is 9. K meters per second squared. This leaves us with a mass m 81.55 kg. Alright, so we have the mass. The only other thing we need is a gravitational acceleration of uranus. So let's consider g u gravitational acceleration of Uranus. Now recall for any planet this can be given as Benji times the mass of the planet divided by the radius of the planet squared. We're not told information about the mass or the radius of uranus directly but we are told it in relation to Earth. Okay so let's go ahead and fill in the information that we know. So we know that the mass is 14.5 times that of earth. Okay, so this is gonna be 14.5 times the mass of the Earth divided by and we're told that its radius is four times that of Earth. So this is gonna be divided by four times R. E. The radius of Earth all squared. All right, simplifying as much as we can here we're gonna get G Times 14.5 many times the mass of the earth divided by 16. The radius of the Earth squared. We can go ahead and pull the constant out in front. Okay? It's just multiplying so we can multiply it out in front. So we have 14.5 divided by 16. All times G M. E over R. E squared. This is a gravitational acceleration of uranus and now this thing on the right hand side this should look familiar. Okay recall what we started with the gravitational acceleration of any planet is G. The mass of that planet over R squared. Okay so that means we can write G. E. Is equal to big G. The mass of the earth over the radius of the Earth squared. Mhm. We know that this is equal to 9. meters per second squared. Okay. The gravitational acceleration due to Earth or on Earth. Okay so we can replace this Gm over R. E squared. In our G. You equation four 9. 14.5 divided by 16 case we have G. U. Is equal to 14.5 divided by 16 times gravitational acceleration due to Earth which is just 9.81. This is going to give us a gravitational acceleration on Uranus of 8.89 m/s squared. Okay. And so even though we didn't have the exact mass and radius of uranus knowing its relationship to earth, we were able to find the gravitational acceleration. Okay. And now getting back to the problem again, we're looking for what our weight would be on the surface of Uranus. And so wait, it's equal to mass times the gravitational acceleration. Okay. We found the mass to be 81.55 kg and we found our G. U. To be 8.89 m per second squared which gives us a weight of 725 newtons. Okay, We get 725 kg meters per second squared which is a unit of newton. And so this is going to correspond with answer D. That's it for this one. Thanks everyone for watching. See you in the next video

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