# Moving Pulleys

1. May 14, 2007

### Bucky

1. The problem statement, all variables and given/known data
One end of a light inextensible string is attatched to a 4kg mass on a smooth horizontal table. The string passes over the edge of the table and to it's other end is attatched a light smooth pulley. Over this pulley passes another light inextensible string, with masses of 3kg and 2kg attatched to it's ends. If the system is allowed to move freely, show that the 4kg mass moves with acceleration of 6g/11.

2. Relevant equations

3. The attempt at a solution

I'm having a bit of a problem from the outset getting the equations of motion. I don't think the diagram is correct. I feel like there should be another acceleration representing the movement of the pulley against the 4m mass, but i'm not sure how to represent it (and part of me thinks that it's covered by the tension t1. Any help on setting out the problem would be appreciated.

2. May 14, 2007

### Mindscrape

Are you trying to use a Legrangian, is that what you mean by equations of motion? Yes, the mass on the table will accelerate too.

3. May 15, 2007

### Bucky

but how does that fit into the equations of motion?
from what i can see the tension 'connects' the 4m mass to the pulley system.

here are my equations of motion...i know the're wrong but i don't see how the acceleration of the 4m mass on the table fits in...the questions up till now have just been systems of pulleys with weights/more pulleys on them, we haven't encountered a mass on a table before.

4m mass on table: 4m ? = 4mg - t1
3mg mass : 3ma = t2 - 3mg
4mg mass : 4ma = 4mg - t2

4. May 15, 2007

### variation

Hello,

There are three forces exerted on the 4mg on the table:
4mg, normal force by the table, t1.
The first two forces are balanced off in the vertical direction.
The net force on the 4mg is only the t1 in the horizontal direction.
Therefore, the first one of your equations shlould be
$$t_1=4m\times a_1$$

Do you think the 3m and 4m on the pulley have accelerations of the same magnitude but opposite direction ?

Best Regards