At what distance from the center of the earth does g equal 2.0 m/s^2?

[BluRain]

Hi, I was just wondering how one goes about solving this question:

1. At what distance from the center of the Earth does g equal 2.0 m/s^2?

I know the formula for the gravitational force, but somehow, I don't think I did it correctly (might be a miscalculation).

Any help would be appreciated. Thank you.

 

[mezarashi]

The usual formula for gravitational force is an inverse law equation. The equation for the force INSIDE a mass is however, linear (assuming homogeneity). You need to apply Gauss's law, which basically helps to say that the gravitational field felt at the Guassian surface is proportional to the amount of mass contained within the surface.

 

[cscott]

How come you cannot simply use g = G\frac{m_E}{r^2}?

 

[mezarashi]

How come you cannot simply use g = G\frac{m_E}{r^2}?

In fact you can. You just must be careful to replace m_E by the mass enclosed by the Gaussian surface, because any mass outside this surface will have no net effect (they cancel each other out). So in this case:

m_E' = \frac{V'}{V}m_E

where the apostraphe indicates the effective values when the distance is less than the radius R of the Earth. V is the volume.

 

[BluRain]

Oh, I see. Thank you for the help. (My physics teacher has yet to teach the class about Gauss's law.)