Find the acceleration : block slides on a wedge

[pcpssam]

sry for typo..it should be acceleration

Homework Statement

A block m slides down from a frictionless inclined surface (theta = 45) of a wedge, mass m, which is on a horizontal plane with coefficient of friction u. Prove that the wedge moves to the right with acceleration equal to g(1-3u)/(3-u) .

im stuck on this question for a whole week..but still can't get the answer
not sure if it is a question related to relative motion?
please help!

Homework Equations

The Attempt at a Solution

 

[Ibix]

As always, draw a force diagram.

If what you want is the acceleration of the wedge, you need to know the net force on the wedge. If you can't figure it out, post your working, and a photo of your diagram if possible.

 

[pcpssam]

cant get the relation of these three accelerations..

 

[Ibix]

You have three equations in four unknowns - you just need one more. You just need to enforce that the block stays on the wedge and doesn't go flying off - kinematic equations may help.

One minor point - your a_y has the same sign as g, but you have defined +y to be up the page. It doesn't affect your maths here, but it can do in general.