Gravitational force from mass above you

[Mattyguy]

I tried so much but I still can't figure out this question:

If you're standing on the ground 13 m directly below the center of a spherical water tank containing 5.0×106 kg of water, by what fraction is your weight reduced due to the gravitational attraction of the water?

 

[kasse]

I tried so much but I still can't figure out this question:

If you're standing on the ground 13 m directly below the center of a spherical water tank containing 5.0×106 kg of water, by what fraction is your weight reduced due to the gravitational attraction of the water?

You mean 5.0E6 kg?

F = gMm/r^2 = 2.90E5 m
G = gM(earth)m/R^2 = 1.44E12 m

The rest is piece of cake?

 

[borgwal]

You mean 5.0E6 kg?

F = gMm/r^2 = 2.90E5 m
G = gM(earth)m/R^2 = 1.44E12 m

The rest is piece of cake?

On the right-hand sides of your equations you confused the gravitational constant G with g (acceleration due to gravity on the surface of Earth) here. You should have noticed that your final answers, of force per mass m, are ridiculously large (and have the wrong dimension).

Also, it's probably not a good idea to use G for the name of a force that involves gravity.

On the other hand, for calculating the ratio of two gravitational forces your first mistake doesn't matter.