How to find the the acceleration of the block M?

[avistein]

1.Homework Statement
Find the acceleration of the block of mass M in the situation shown.All surfaces are frictionless

2.The attempt at a solution
2Mg-2T=2Ma
T=Mg-Ma
and T-mgsin30=ma

But a is canceled .what to do?

 

[jordanhuh]

T=Mg-Ma

Mg-Ma-Mgsin30=Ma

2Ma = 1/2 Mg
a= 1/4 g

Not cancelled?

 

[avistein]

Sorry, but answer given is g/3.

 

[voko]

Acceleration of which block is denoted by $a$? Are the accelerations the same for both blocks?

 

[avistein]

Acceleration of which block is denoted by $a$? Are the accelerations the same for both blocks?

Oh,sorry.the acceleration of block 2M is a ,so acceleration of M is 2a.

 

[voko]

Do you get the answer with that correction?

 

[avistein]

Do you get the answer with that correction?

Yes sir,after Bvu's help,it is solved.

 

[BvU]

Don't understand. In the expression T-Mgsin30=Ma a is clearly the acceleration of block M, which is what is asked for. So keep it and change the acceleration of the other block to a/2, like:

(2M)g - 2T= (2M) (a/2). Bingo!