What is the Correct Formula for System Acceleration to Prevent Slippage?

[darksyesider]

General question.

Homework Statement

you are given theta, μ, and both masses. Find the acceleration of the system so the block does not slip.

The Attempt at a Solution

Let m1 be the block, and m2 be the trapezoid car thing.
Let F be the applied force
I used a coord system with the x-axis along the area where the trapezoid touches the block. I came up with:

Fnet = m1 g sin θ - ff

Fnet = m1 g sin θ - u F sin theta - u m1 g cos theta = 0

Substituting for the system gives:

$$a = \frac{ -\mu_k m_1 g \cos\theta + m_1g\sin\theta }{\mu_k sin\theta (m_1+m_2) }$$

Although i think this is incorrect since i did not account for the normal force of the car onto the block. Can someone correct this?

 

[Simon Bridge]

Please show your reasoning. I can see what $\theta$ and $\mu$ are, but which mass is $m_1$ and which $m_2$? What does "ff" mean in your equations?

Since this is homework, we won't correct it for you.
What we can do is help you correct it for yourself.