A typical adult human has a mass of about 70 kg. (a) What force d...

Question

A typical adult human has a mass of about 70 kg. (a) What force does a full moon exert on such a human when it is directly overhead with its center 378,000 km away? (b) Compare this force with the force exerted on the human by the earth

Accepted Answer

Welcome back everybody. We are looking at the planet mars. And on the planet mars, there is a little rock sitting on the surface of it now, at midday. This rock is exactly between our star, which I'm just our son. I'm just gonna note by the star and the planet mars. And we are told a couple other things. We're told that the distance between the center of the sun to the rock is about 2. times 10 to the 11 m. We're told that the mass of our rock is kg. We are told that the gravitational acceleration on MArs is 3.72 m per second squared. Now, we are tasked with finding two different things here. Art A is what is the force of the sun acting on the rock and part B. Is that we need to compare this or find a ratio between the force of the sun acting on the rock and the force of mars acting on the rock with this constant C. Multiplied by it. So let's start with part A. What is the force of the sun? Well, we're going to use um kepler's laws here. Right? That state that this force is going to be equal to Newton's gravitational constant times the mass of the sun times the mass of the rock all over the distance between the two. Now we have all of these terms. So let's go ahead and plug in some values. Newton's gravitational constant is given by 6.6, 7 Times 10 to the - Times the mass of the sun, which is 1.99 times 10 to the 30th kilograms times the mass of our rock, which is just 1200. All divided by the distance between them, which is 2.28 times. And to the 11th. And just to specify here, when I say the distance between them, I mean the distance between their centers, this gives us at the force of the sun acting on the rock is 3.0, apologies. 06 Newtons great. Now that we found that we need to find what this factor is so that we can find the ratio between these two. So what is our constant C. Well, the force of mars on the rock is just going to be given by Newton's second law. That states it's the mass of our rock times the gravitational acceleration of mars, which we have both of these things. So let's plug it in. We have 1200 times 3.72, which gives us newtons. Now to go ahead and find see this is just going to be the ratio between these two forces. So we're going to take the force of the sun and divide that by the force of mars acting on the rock. To get our factor or a ratio. So we have 3.6 Newtons divided by 4464 Newtons giving us a constant of 6.85 times 10 to the negative fourth, meaning that the force of the sun acting on the rock is 6.85 times 10 to the negative four times the force of mars acting on the rock. We have now found our two answers to Part A and part B, which corresponds to answer choice B. Thank you all so much for watching Hope. This video helped. We will see you all in the next one.

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