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Old Dec 2nd 2017, 10:42 AM   #1
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Acceleration of a wedge

Problem
A wedge with mass M rests on a frictionless horizontal tabletop. A block with mass m is placed on the wedge. There is no friction between the block and the wedge. The system is released from rest. Calculate the acceleration of the wedge.

Included diagrams
Acceleration of a wedge-aweaweaweayeree.png

What I Tried
I know that the answer ends up being:

$a_1=\frac{m_2gsinθcosθ}{m_1+m_2sin^2θ}\
$

but the system of equations I come up with does not give me that answer
$\displaystyle (1) -Nsinθ=m_1a_1$
$\displaystyle (2) Ncosθ-m_2g=m_2a_2sinθ$
$\displaystyle (3) Nsinθ=m_2(a_2cosθ+a_1)$

The answer for $\displaystyle a_1$ that I derive from that comes fairly close to the intended answer, but I don't see where I went wrong with my identification of forces. Thanks in advance for any help.

Answer I get from those equations
$a_1=\frac{m_2gsinθcosθ}{2m_1sin^2θ+m_2sin^2θ-m_1}\
$
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