# Homework Help: Which way does the cylinder roll? Solution posted doesn't make sense.

1. Apr 3, 2013

### ph7ryan

1. The problem statement, all variables and given/known data
A cylinder weighing 30lbs is initially at rest on a horizontal surface. There is a spring attached directly below the center, 2ft away from the center point o, pulling to the right horizontally. There is a string attached to the center and to a mass (around a pulley, frictionless) that can free-fall upon release of the system, with tension to the left direction (horizontally). There is enough friction to oppose slipping in this case.
(I know it says no pictures, but its a little hard to visualize this.)
http://i688.photobucket.com/albums/vv242/ph7ryan/Miniquiz_2_zpsd47d7512.png
Weight of mass = 10lb
weight of cyl= 30lb
k=50ft/lb
delta_x=2ft (stretched)
r1(to spring from center)=2ft

There was a lot to do on this problem but the question that I am confused with is it wants to know in what direction will this travel after release. Apparently it moves to the right, although I don't see how this is possible without slipping.

2. Relevant equations
He gives a hint to use the moment equation, where Mo=Io(alpha). In the posted solution, he also uses the parallel axis theorem, Ip=Io+md^2.

3. The attempt at a solution
I took the moments about point o. The spring force would have a moment of 25lbft ccw, the tension doesn't have a moment, and friction is unknown, but would have to be to the left in order to prevent slipping (causing a cw moment). The resulting direction would be that it would roll to the left.

He took a different approach.

He said, because we don't know friciton, but we can represent T=massofweight*accelofsystem and we know fs (spring force), we can take the moment about point P, the bottom most part of the cyl in contact with the ground with vp=0. Thus the moment of fs is cw, and the moment by T is ccw, but because the spring force is much greater than the tension force, the fs moment outweights the T moment, thus it rolls to the right (cw).

Everyone agrees with me that this doesn't make sense, but no one knows how to argue the case against it. Maybe we are all wrong, but no one has explained it in a way that would let us change our mind.

here is his math in case anyone is interested in how he did it.

http://i688.photobucket.com/albums/vv242/ph7ryan/miniquiz2soln_zpsa245c17e.png

2. Apr 3, 2013

### rcgldr

If the cylinder rolls to the right, what direction does the cylinder end of the spring move, and what is the relationship between the distance the cyliner rolls versus the distance the cylinder end of the spring moves? Do the math for this and the answer should make sense.

3. Apr 4, 2013

### ph7ryan

it would move to the left... meaning it would stretch more, and the weight would move up. the energy would have to come from somewhere for this to not violate thermo law 1.

and I did the math for the ratio traveled, it comes out to like 2:3.