# Homework Help: Pulley with 3 masses

1. Oct 24, 2005

### jamesbob

Three equal masses (m1=m2=m3=m)are hung over a pulley as shown*. Find the acceleration of the system and the values of the
tensions T1 and T2?
I got the tension to be 1/3*g (=3.33ms^-2) this is probably wrong, but im more stuck on the acceleration. Any help would be much appreciated.

*shown is: a pulley system with two masses on the left side and one mass on the right. all masses are equal. T1 is the tension above the upper mass (m2) on the left side. T2 is the tension between the 2 masses on the left side (m1 and m2).

Last edited: Oct 24, 2005
2. Oct 24, 2005

### Astronuc

Staff Emeritus
Assuming I am visualizing this correctly, two masses on the left falling down with gravity, and by virtue of the cable, they are pulling the mass on the right up, which is all subject to the pull of gravity.

Acceleration = F/m

In a static system, T2=mg, since the line between m1 and m2 would suspend the lower weight, m1. However, since the masses are accelerating, T2 < mg.

T1 > mg, since gravity is pulling on m3 and accelerating m3 at the same time.

Remember Tension is just a force.

3. Oct 25, 2005

### jamesbob

Firstly thanks for your help so far. Sorry iv made a mistake in my first message. I got the Acceleration to be 3.3ms^-2 and im stuck on the tension. Does that value for acceleration sound correct? I got it from doing:
a= (m1-m2)/(m1+m2)*g where in this case m1 is actually m1+m2 and m2 is m3.
m1=2m2 so m1-m2=2m2-m2=m2 and m1+m2=2m2+m2=3m2
so a = m2/3m2*g = 1/3*g = 3.33ms^-2 (taking g as 10ms^-2)
How can i get 'values' for the tension if i have no value for the mass? I'm guessing it will come from an equation where the masses cancel, but which equation? I know T=Ma or T-mg=-ma, any of them work?