Question

Two smooth spheres of radius are placed inside a cylinder of radius R. The mass of each sphere is M Assume that R < 2r < 2R All answers should be in terms of . R.M and What is the force of the bottom sphere on the top sphere? What is the force of the cylinder wall on the top sphere ?

Answer 1

See the diagram :

I have marked the forces on the spheres.

N = contact force between the spheres ( to be calculated)

N1 = contact force between bottom sphere and bottom of cylinder.

N2 = contact force between cylinder wall and bottom sphere.

N3 = contact force between cylinder wall and top sphere (to be calculated).

Mg = force of gravity on both spheres.

= angle between line joining centers and horizontal.

Beside there is triangle to calculate .

Now, balacing the forces on the spheres.

For Bottom sphere :

N1 = N sin + Mg ------ (i)

N2 = N cos ------ (ii)

For Top sphere:

N sin = Mg -----(iii)

N cos = N3 -----(iv)

from equation (iii) :

Ans.

Dividing the equa. (iii) and (iv) :

Ans.