What Is the Acceleration of a Cart Connected to a Hanging Block on an Incline?

[polishdude20]

Homework Statement

An 18kg cart is connected to a 12kg hanging block at the bottom of the incline (ignore friction)

What is the magnitude of acceleration of the cart?

Homework Equations

F=ma
Fx=Fgsinx
Fy=FgCosx

The Attempt at a Solution

well without the hanging weight i calculatoed the force parallel to the plane to be 101.2 N
and the force perpendicular to the plane is 144.5 N
I tried adding the X force (101.2N) to the downward force of the weight on the pulley (176.4 ) and then dividing by the total masses. But I can never get the right answer its supposed to be 7.3 m/s*2 but I don't know how its obtained.

 

[polishdude20]

can anyone help?

 

[jhae2.718]

Try drawing a free body diagram of each block. What forces act on each?

Then use the fact that $$\Sigma \vec{F} = m\vec{a}$$ to find the net acceleration.

 

[polishdude20]

yes i tried that and i don't know do i add the fg of the hanging block to the Fx of the block on the plane?