# Acceleration of a three mass system

1. Oct 28, 2008

### Vaati

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

The system shown in the diagram is accelerating toward the right (clockwise). Find the acceleration in terms of m1, m2, m3, uk, and g.

Note: There aren't any numbers used in this problem. It's just working with the variables to create an expression equal to the acceleration.

2. Relevant equations

Fg = mg
Ff = ukFn
SumofF= ma

3. The attempt at a solution

I began by creating free body diagrams of each mass, starting with m3.

I used the forumla Fg = mg to get m3g. This is also equal to the tension in the string.

T = m3g

I moved on to creating a free body diagram of mass2.

I used the forumla Fg=mg, where this downward force would be equal to the normal force. I then used the equation Ff = ukFn to get the friction force. Subtracting this friction force from the tension in the string would give me the net force for m2.

T = m3g - m2guk

This force would be equal to the tension in the string pulling m1 which is m3g - m2guk. Because the system is moving clockwise I subtract m1g to get the sum of all the sytem's forces moving in the clockwise direction.

F = m3g - m2guk - m1g

Since I need to find the acceleration of the system, I set the expression m3g - m2guk - m1g equal to m1, because m3g - m2guk - m1g is the force pulling m1 up.

Thus.

(m3g - m2guk - m1g) / (m1) = a

Did I solve this problem correctly or was there some flaw to the logic I used?

Thanks ahead of time. I apologize for the quality of the diagrams.

2. Oct 28, 2008

### tiny-tim

Welcome to PF!

Hi Vaati ! Welcome to PF!

(have a mu: µ )

Sorry … the flaw is that T = m3g is valid only if the acceleration is zero.

But anyway, why work out the tensions when the question doesn't ask for them?

Hint: call the distance moved "x", and use the work-energy theorem.