 #1
iceninja3
 6
 4
 Homework Statement:
 A block (mass m) slides on an inclined plane(mass M, angle = 60˚ to the horizontal). Ignoring friction between the surfaces, find the acceleration of the inclined plane when the block is sliding.
 Relevant Equations:

F=ma
Components of force of gravity on inclined plane: mgsinθ, mgcosθ
My attempt:
As I need to find acceleration I believe that I need to use F=ma(and thus draw a free body diagram).
I drew the block's weight components(mgsinθ, mgcosθ) and concluded that the only force acting on the plane in the horizontal direction is the horizontal component of mgcosθ>mgcosθsinθ . I then took the mass of the system since the block and plane move horizontally together(?) to be m+M. This led me to:
a = (mgcosθsinθ)/(m+M)
a = (mg√3/4)/(M+m) which is obviously wrong.
Possible places I went wrong:
1. Is the small mass m maybe not "effectively" m anymore?
2. Perhaps I'm missing some other force components (or misrepresenting the ones I already have)?
Any small hints would be welcome.
Note: The answer is E but I am not sure how to get there.