# Homework Help: Two connected particles resting on a smooth cylinder

1. Jul 7, 2007

### Miss Hannah

1. The problem statement, all variables and given/known data

Two particles P1 of mass m and P2 of mass 2m are joined by a model string of lenght piR/2 and placed symmetrically on the surface of a smooth cylinder (i.e. so resting on top). Initially the position of the particles is symetrical with both OP1 and OP2 inclind at an angle of 45 degrees to the upward vertical. The particles are released from rest. After t seconds theta1 and theta2 are the angles P1 and P2 make with the horizontal.

Derive the equation of motion for P1 and express this equation in component form

2. Relevant equations

3. The attempt at a solution

First i drew a force diagram and attempted to figure out what was going on.
P1 had N going in the +eR direction, T going in the +eTheta direction, and weight going vertically down. P2 had the same but with -eTheta for the Tension. (Am i right in thinking that the tensions will be the same as no pulleys are acting?)

I then use the equation for acceleration of a particle moving in a circle to work towards my eqn of motion.

i end up with an equation involving r'', theta'(squared) and theta''. and I don't know what to do now.

How do I go from here to equation of motion? What does it mean in component form? Can I split the acceleration up into the radial and tangential directions?

2. Jul 8, 2007

### Mindscrape

I am a bit confused about the problem. About what axis are the two particles symmetric? Are the particles constrained to the surface of the cylinder?

What level physics is this? Are you familiar with Legrangian mechanics or Calculus of Variations?

3. Jun 30, 2009

### ombi61

I have a similar problem and I am confused too...
How you are going to calculate the tension?
It should equal on both particles (different sign) do you need to know the lenght of string?
Help!