Calculating Acceleration of Hanging Mass System

[physicos]

Homework Statement

A hanging mass M1 =1 kg is attached by a light string that runs over a frictionless pulley to a mass M2=2 kg that is initially at rest on a frictionles table .
What is the magnitude of the acceleration a of M2 ?

Homework Equations

I used for M1 :
F_g1 + T =M1a (with T tension of string)
and for M2 :
N+F_g2+T=M2a

The Attempt at a Solution

NOW I'm stuck , I can't solve it , any help ??

 

[Doc Al]

and for M2 :
N+F_g2+T=M2a

For M2 you have added forces that are perpendicular to each other. Don't do that! Instead, consider horizontal forces separately. (Assuming the table is horizontal, that's the direction of the acceleration.)

Be careful with signs.

 

[physicos]

What I have written are vectors :
for M1 without vectors :
_m1g+T=-m1a
and for M2 :
N+T-m2g=m2a

I still didn't get your point

 

[Doc Al]

What I have written are vectors :
for M1 without vectors :
_m1g+T=-m1a

Good. (Note that the forces of gravity and tension all act vertically.)

and for M2 :
N+T-m2g=m2a

This combines vertical forces (N, mg) with horizontal forces (T). Don't do that.

 

[physicos]

I thought T was a vertical force too

 

[Rellek]

I thought T was a vertical force too

On mass 1 it is a vertical force. On m2 it is pulling from the side. Remember that since your pulley is massless and frictionless, the tension along the string will be completely constant.

 

[Doc Al]

I thought T was a vertical force too

Not when it acts on M2, which slides along a horizontal table. (A picture would help.)

 

[haruspex]

Not when it acts on M2, which slides along a horizontal table. (A picture would help.)

The OP doesn't actually state the orientation of the string between pulley and M2. Yes, it's probably meant to be horizontal, but in principle could be anything.

 

[physicos]

so what am I supposed to do ? Cause that's all what is available in the problem statement , there is no picture : Should I work with it as a horizontal force ?

 

[haruspex]

so what am I supposed to do ? Cause that's all what is available in the problem statement , there is no picture : Should I work with it as a horizontal force ?

Yes.