Barron's 2nd Edition DT Q24

24) This problem prompts us to find the acceleration of mass m. This is also the same as the net acceleration. We can start by drawing a representation of all the forces in the diagram.

Where m is mass, F[t] is tension force, and W is weight

For pulleys, rather than taking all the forces in the x-plane or y-plane, we instead take the forces acting along the direction of the string. Additionally, since the tension force acts on the same string, but in different directions. they will be the same magnitude and can cancel out of our equation. We can write an expression of the net force. I will include the tension force just to show that it will cancel out.

Where W is weight and F[t] is tension force

Now we can further expand all the terms and find our net force.

Where W is weight and F[t] is tension force

Additionally, we can expand the net force term, which will then allow us to solve for the acceleration.

Answer: C