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

AI Thread Summary
To determine the acceleration of an 18kg cart connected to a 12kg hanging block on an incline, the relevant forces must be analyzed. The force parallel to the incline was calculated as 101.2 N, while the perpendicular force was 144.5 N. The correct approach involves summing the forces acting on both the cart and the hanging block, applying Newton's second law (F=ma) to find the net force. The expected acceleration is 7.3 m/s², but confusion arises regarding the combination of forces from both blocks. A free body diagram is recommended to clarify the forces acting on each block and to accurately calculate the net acceleration.
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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.
 
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can anyone help?
 
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.
 
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?
 

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