# Equlibrium and Elasticity

1. Dec 2, 2006

### PremedBeauty

Two identical, uniform, and frictionless spheres, each of mass m, rest in a rigid rectangular container. A line conecting their centers is at 45 degrees to the horizontal. Find the magnitudes of the forces on the spheres from (a) the bottom of the container, (b) the left side of the container, (c) the right side of the container and (d) each another. (Hint: The force of one sphere on the other is directed along the center-center line)
I'm sorry, the image is off alittle (I'm a lefty and this mouse is on the right side) but the two balls are touching the walls, and the w's are supposed to be in the center of the spheres. :uhh:

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2. Dec 2, 2006

### Staff: Mentor

You stated the problem, but where's your attempted solution? Show what you've done and point out where you got stuck.

Hint: Since the spheres are frictionless, what must be true about the contact forces acting on them?

3. Dec 2, 2006

### PremedBeauty

solution

solution:
The contact force exerted by the lower sphere on the upper is along that is 45o and the forces exerted by the walla and floors are normal.

Equilibrium force on the top sphere leads to

Fwall = F cos 45 and F sin 45 = m g

According to newtons third law the equilibrium of forces on the bottom sphere leads to

F'wall = F cos 45 and F'floor = F sin 45 +mg

a)magnitudes of the forces on the spheres from the bottom of the container

F'floor = mg +mg = 2mg
b)magnitudes of the forces on the spheres from the left side of the container

F'wall = mg
c))magnitudes of the forces on the spheres from the right side of the container

F'wall = mg
d) magnitudes of the forces on the spheres from each other

F = mg / sin 45 = mg * √2

Is that correct?

4. Dec 2, 2006

### Staff: Mentor

Looks good to me!

5. Dec 2, 2006

### PremedBeauty

Thank you. I was wondering if it's correct when I did it.

Last edited: Dec 3, 2006