# Identifying the forces in a difficult circular / non-circular motion hybrid problem.

## Homework Statement

http://img188.imageshack.us/img188/9897/73266226.png [Broken]

The problem is to create an equation to find the acceleration of the cart based upon theta. All that is given is the ball hanging is known as mass m.

## Homework Equations

$$f=ma$$
$$f=\frac{mv^{2}}{r}$$

## The Attempt at a Solution

I am assuming that the car is moving to the right, since the hanging mass is tilted backwards. I am really at a loss of even just identifying all the forces exactly. What confuses me the most is that we are assuming the cart is accelerating forward, but there is no force causing it to move forward.

So far, this is what I have:
m being the mass, c being the cart
$$F_{mx}=Tsin\theta$$

$$F_{my}=Tcos\theta - mg$$

$$F_{cx}=m_{c}a - Tsin\theta$$

$$F_{cy}=-Tcos\theta = 0$$

I know that these are probably wrong, but can someone please tell me why?

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Delphi51
Homework Helper

I'm a little confused by all the subscripts! And can't make thetas here.
Vertical: Tcos(A) - mg = 0
Horizontal: Tsin(A) = ma
If you solve one for T and sub in the other, you'll get something that makes sense.

How do you make a theta?

PS it is accelerating to the right because theta > 0. If it wasn't accelerating, it would hang straight. So no need to think about what is making it accelerate.

Haha, well you make a theta using latex code. For the theta symbol, it would be [ t e x ] \ t h e t a [ \ t e x ] (minus the spaces)

Delphi51
Homework Helper

Thank you greenskyy. I fear that is too awkward for me.
I have seen someone with a whole bunch of symbols (theta, pi, etc.) in his signature. I wonder if that is so he can copy a theta whenever he wants it? Do you know how I can have a signature here?

Nope, I looked around and couldn't find it anywhere in the user control panel =\

What is the net force on the ball-cart system? What quantity is conserved, then?