Solving Physics Problem: 2 Spheres, Gravitational Attraction

[megalloa]

Physics Problem please help!

Homework Statement

An experiment is performed in deep space with two uniform spheres, one with mass 21.0 kg and the other with mass 100.0 kg. They have equal radii, = 0.40m . The spheres are released from rest with their centers a distance 39.0m apart. They accelerate toward each other because of their mutual gravitational attraction. You can ignore all gravitational forces other than that between the two spheres.

1. When their centers are a distance 25.0m apart, find the speed of the 21.0kg sphere.
2. Find the speed of the sphere with mass 100.0kg .
3. Find the magnitude of the relative velocity with which one sphere is approaching to the other.
4. How far from the initial position of the center of the 21.0kg sphere do the surfaces of the two spheres collide?

Homework Equations

F_g = Gm1m2/r^2
Conservation of linear momentum(?)
K = 1/2mv^2
U = -Gm1m2/r

The Attempt at a Solution

I am very lost. All i can think of is that the linear momentum of collision is conserved, and that the only forces acting in this system is the F_g, and because F_g on each object toward one another is equal, the net Force of the system is zero?(thats why linear momentum is conserved?)
I have no idea how and what equations i should utilize to solve these problems.
please help and offer some guidance as to how i should proceed!
thanks1!

 

[Quinzio]

Conservation of linear momentum is verifies because the two forces act in opposite direction, so they cancel out.
But you really don't need to think about momentum.
Find the force Fg, then each sphere accelerates according to its mass. That's all.

 

[megalloa]

I see. But the only way I can think of solving for v or distance, using the acceleration, would be to introduce the time variable(?)? but I don't see a way I can solve for specific times..? or am i just approaching the problem in a wrong way?

 

[Bhumble]

The force isn't constant so maybe it will be easier to solve this problem taking the approach that E = K + U. Assuming that the objects are initially at rest you know that K = 0. Then just solve for U and K at the various positions and use these to solve for your various velocities.

 

[megalloa]

Bhumble: I've tried your method and set up the following equation for the sphere of smaller mass:
.5v(i)^2 - (100G/39) = .5v(f)^2 - (100G/25)
v(i) is v initial of smaller sphere and I used 0 for this value and solved for vf.
the mass of small sphere can be factored out and calcels in the equation, and the 100 is the mass of the larger sphere and G is the constant G = 6.65*10^-11
the answer i get is 1 because G is such a small number, but it is the wrong answer.
any other suggestions?

 

[SammyS]

You ignored the Kinetic Energy of the 100kg sphere.