Pytels Dynamics 12.35: A cart carrying a small package

[Alexanddros81]

Homework Statement

The cart carrying the small 9-N package A is moving up the incline with constant acceleration α. If the package stays at rest relative to the cart in the position θ=45deg, determine the value of α. Neglect friction.

Homework Equations

The Attempt at a Solution

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Are my equations correct?

Also how do I continue finding α? Does the $θ=\frac {s} {r}$ comes into play?

 

[haruspex]

Are my equations correct?

Hard to tell if you do not define your variables.
What forces act on the mass? (I assume you are to ignore friction.) What are the magnitudes and directions of those forces? What is the magnitude and direction of the resultant force?

 

[Alexanddros81]

Here is a body diagram.

and here is my solution:

Can you check this and tell me if it is correct

 

[haruspex]

Here is a body diagram.

View attachment 207915

and here is my solution:

View attachment 207916

Can you check this and tell me if it is correct

I didn't check the precision of the numbers, but it looks right.