Two Spheres Attracted by Gravitational Force

[maximoanimo]

Homework Statement

Two spheres have equal radius R = 14m and mass m = 1420kg. Their centers are separated a distance 4R. The spheres are released from rest. What will be their speed when they collide? Answer in m/s.

Homework Equations

U(g) = -G*m1*m2/R

The Attempt at a Solution

We know from the conservation of energy that U(i) + K(i) = U(f) + K(f). Since the spheres are initially at rest, K(i) = 0. Initially, the two spheres are 4R apart. Upon collision, they must be 2R apart (the sum of their radii when they are touching). Knowing this information, we can plug in:

-Gm^2/4R = -Gm^2/2R + mv^2/2
-Gm^2/4R = -2Gm^2/4R + 2Rmv^2/4R
Gm^2 = 2Rmv^2
v^2 = Gm^2/2Rm = Gm/2R

Plugging in the values given, I found v = 5.8172e-5 m/s. However, it says this solution is incorrect. Can someone help me find the flaw in my solution?

Thanks so much,
Steven

 

[Cider]

Remember that each of the spheres are going to have a value kinetic energy, so you'll have to take that into account when balancing the initial and final energies. Fix that and the rest should follow in a similar manner as in your derivation.

 

[Redbelly98]

Ah, it took me a while to see what was wrong with the derivation in Post #1. Cider is correct; there are two spheres of course.