How Do You Solve These Challenging Gravitation Problems?

[Glenn K]

Okay, I've looked over all of my formulas numerous times and I just can't figure out what to do for these two:

In terms of Earth radii, how far from the center of the Earth would you have to travel in order to cut your weight from 900N to 300N?

The gravitational force between two electrons 1m apart is 5.42x10^-71N. Find the mass of an electron.

Could anyone help me out here? I'm trying to figure out what to do, but I'm just drawing blanks.

 

[Jameson]

I'm assuming that it claims you have a force of 900N at a normal ground level, which would make the Earth's radius 6.47 * 10^6m. You're going to use the universal law of gravitation and solve for m1 (your mass).

$$900 = \frac{(6.67*10^{-11})(5.98*10^{24})m_1}{6.47*10^6}$$

Force is in Newtons, and everything else is in standard SI units.

Solve for m1. The plug that number into the gravitation equation again with 300N as your force and solve for d.

Jameson

 

[whozum]

In terms of Earth radii, how far from the center of the Earth would you have to travel in order to cut your weight from 900N to 300N?

If your weight is 900N at the surface, find your mass. It's a pretty simple conversion. Then solve the gravitational force equation for the radius and use F = 300N to find your new r.

The mass of two electrons is equal, so the force equation simplifies to

$$F = G\frac{m^2}{r^2}$$

You are given F, G, and R.