How to work out this Acceleration

[koyabr]

Homework Statement

I`ve posted relevant picture.No thought for any friction.The ramp`s mass is M,and the cubic slider`s is m.Release the slider(no initial speed),What`s the Acceleration(relative to the earth) of it?

Homework Equations

I`ve been told the answer,as is showed in the picture.But I can`t work out it for myself.

The Attempt at a Solution

I got stuck when I`ve brought in too many parameters,I might have mistaken something.

I`m a new comer and English beginner,hope I`ve described the question clearly.Thanks for viewing.:)

 

[EngineerHead]

Remember Newton's 3rd Law of Motion, for every action there is an equal and opposite reaction, meaning:

Think about this given situation at a stand-still, where the block is on the ramp at the top but nothing moves (because everything is starting from rest). There is no motion, correct?

Gravity then pulls the block down the ramp, which then causes the ramp to move as well (remember, everything started from rest, aka net F=0 initially). If the intial net F=0, then the final net F must equal 0 as well, agreed? With the understanding of the fact that momentum is conserved, you must solve for the net horizontal force on the block (horizontal to the ground surface that the ramp is not, not horizontal to the ramp itself). This must also equal the net horiziontal force on the ramp caused by the block. Setting these two equal should be your method of solving for a.

 

[koyabr]

Thank EngineerHead and I think I`v figured out the process,the most disturbing thing is the resultant force of the block,whose direction & size are not so clear.I tried the vector triangle,and found the sine theorem useful in working out the resultant force`s size.

Astonishing enough,I got a different answer from what`s showed in the picture,perhaps I have to consult the question provider.