# Potential Energy of Oscillating surface

1. May 24, 2012

### catmando

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

A rectangular sheet of thin material is rolled into a portion of a circular cylindrical surface of radius r. It rests under the action of gravity on a fixed cylindrical surface of radius R, symmetrical about the vertical centre line as shown below. If rolled slightly to the left or the right and released, the object will rock from side to side (assume no slipping).

write an expression for the gravitational potential energy of the object at some instant during the oscillation. Use the rest position of the centre of mass as the potential energy datum

ht tp://s11.postimage.org/gdrfgsoep/lol.jpg

b = k*r

2. Relevant equations

PE = mgh

3. The attempt at a solution

h = b - x

x = (R+r) - (R+r)cos(β)
b = kr - a
a = kr cos (β + θ)

h = kr +kr cos (β + θ) -(R+r) + (R+r)cos(β)

therefore potential energy

PE = mg(kr +kr cos (β + θ) -(R+r) + (R+r)cos(β))

2. May 24, 2012

hi catmando!