Two masses connected via pulley: find acceleration

[pivoxa15]

Homework Statement

Two masses A and B, and of mass 1.6kg and 2.4kg respectively are connected by a light string which passes over a frictionless pulley. Calculate the acceleration of the 1.6kg mass.

Homework Equations

The Attempt at a Solution

To get started I must know whether the two masses both have the same acceleration. Is that true? I know the tension of the system is the same.

Assuming it's true I get a simultaneous equation that looks like
16-T=1.6a
24-T=2.4a

which works out for a=10m/s^2 and T=0 which is a bit fishy. But if a is different for each mass than there are 3 variables but only two equations.

 

[cristo]

The two masses have the same acceleration (they are connected by a string!) The smallest mass will move upwards, so its resultant force will be T-16, hence your first equation should read T-16=1.6a

 

[pivoxa15]

I see. The system should have a predetermined positive, negative direction. It's not the case that upwards is always + and downwards always - in this pulley problem.