Newton's Laws of Gravitation

[G-reg]

Homework Statement

Some people believe that the Moon controls their activities. The Moon moves from being directly on the opposite side of Earth from you to be being directly overhead. Assume that the Earth-Moon (center-to-center) distance is 3.82 multiplied by 108 m and Earth's radius is 6.37 multiplied by 106.

(a) By what percent does the Moon's gravitational pull on you increase?


(b) By what percent does your weight (as measured on a scale) decrease?

Homework Equations

F = (GMm)/r^2

The Attempt at a Solution

First I found the force of the gravitational force between me and the moon, then for me and the Earth. Then I set up a proportion and found the percent that the gravitational force between me and the moon is to the gravitational force between me and the Earth.

F(moon) = (6.67e-11 * 7.36e22 * 70.76)/(9.55e7)^2 = 3.81e-2

F(Earth) = (6.67e-11 * 5.98e24 * 70.76)/(9.55e7)^2 = 8.56

F(moon)/F(Earth) = x/100

x = [100 * F(moon)] / F(Earth) = .44

 

[indr0008]

the problem does not actually ask u to find Earth's gravitational pull on you :D

it does not hurt though ;)

 

[G-reg]

So the answer to the first one is just the gravitational force between me and the moon?
I'm still confused lol.

 

[indr0008]

the distance between u and the moon is different for both cases :)

 

[G-reg]

Ok you that makes sense. So the "r" in the equation would be different for each case. But do you think that I'm supposed to use my own mass for the problem?

 

[indr0008]

try it first with what we have so far :)

 

[G-reg]

Ok here we go..

F(moon_opposite side) = (6.67e-11 * 7.36E22 * 70.76) / (3.82e8)^2 = 2.4e-3

F(moon_overhead) = (6.67e-11 * 7.36E22 * 70.76) / (6.37e6)^2 = 8.56

now proportion?

 

[indr0008]

u got the distances wrong :)

 

[G-reg]

oh lol so..let's see..

is the distance for the "moon_opposite side" = 3.88e8?
and the other distance is 3.82e8?

 

[indr0008]

done, give me cookies :D

 

[indr0008]

the other distance is 3.76 e8

 

[G-reg]

haha how'd you get 3.76e8?

 

[indr0008]

try drawing the diagram, u'll see :)

 

[Redbelly98]

oh lol so..let's see..

is the distance for the "moon_opposite side" = 3.88e8?

Yes.

...and the other distance is 3.82e8?

No, that's the distance from the moon to the center of the Earth. You would use that distance if you were located at the center of the Earth, which you aren't in this problem.