# Pendulum and cart harmonic motion

1. Nov 5, 2008

### Frillth

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

A simple pendulum of mass m = .28 kg and length L = .65 m is attached to a cart of mass M = 1.0 kg. The mass of the pendulum support is negligible. The cart can roll rreely on a horizontal surface. At t = 0, the pendulum bob is released from rest when the string makes an angle of 10 degrees with the vertical. assume that the resulting motion of the cart relative to the ground is simple harmonic motion. Determine the amplitude of the motion of the cart.

2. Relevant equations

Not sure.

3. The attempt at a solution

I'm not sure how to solve this, but I had a completely unscientific intuitive guess that the distance pendulum travels * pendulum's mass = distance cart travels * cart's mass:

Horizontal distance between bob at 10 degrees and vertical = .65*sin10

.65*sin10 * .28 = 1*x
x = .032 m

Is this at all close to correct? If not, could somebody please point me in the right direction?

2. Nov 5, 2008

### physics girl phd

You seem to be attempting a conservation of energy approach, which might work, but I'm disturbed about a number of things:

Note: for both energy-like terms... you're using distance times mass. Is that right?

First: For the potential energy of the pendulum you are missing a factor that's pretty important. You have height of the pendulum times that pendulum's mass -- but there's something missing to make it ENERGY. In this case the factor you're missing is known.... what is it? hint: It' energy related to height it's gravitational potential energy!) I also suggest you ALWAYS carry the units with your math to be sure your result has units that you want.

Second: Your equation for work done on the cart would also be wrong. Again, your units are off and you're missing a factor.... but in this case... do you know that factor? Even more important... is that factor constant over time? Note: Based on the motion of the cart, I don't think it can be! Note: this unknown might make it possibly very difficult to find the distance based on your approach.

Also note: You haven't considered all ways the energy is transferred... you might want to think about kinetic energy of the pendulum and cart.
What is the pendulum doing when the cart is at maximum displacement?
What are the pendulum and cart doing when the pendulum is at it's lowest point?
etc.

I was thinking about the possibility of a conservation of momentum approach. Have you thought of that? I think it's much more promising. You could probably do something cool with the resulting velocity equation of motion...

3. Nov 5, 2008

### nasu

If the cart can move freely along the horizontal direction then the center of mass of the system is at rest along this direction.
I think that this is what you were trying to do, right?. (distance*mass...)