How Do You Solve a Frictionless Pulley System Problem?

[Yosty22]

Homework Statement

A light rope is attached to a block with mass 4.00 kg that rests on a frictionless, horizontal surface. The horizontal rope passes over a frictionless, massless pulley, and a block with mass m is suspended from the other end. When the blocks are released, the tension in the rope is 10.0N.
a.What is the acceleration of either block?
c.Find the mass m of the hanging block.

Homework Equations

ƩF=ma

The Attempt at a Solution

My attempt at solving the problem is attached. Can someone tell me where I went wrong?
(It got cut off at the bottom, it just says that my answer of 0.813kg is wrong, but I don't know why. THE CORRECT ANSWER IS: m=1.37kg

 

[Yosty22]

Sorry, My attempt at the solution is now attached.

 

[haruspex]

You've been inconsistent in your choice of directions. Which way is the mass m accelerating?

 

[Mentalist]

Recheck your free body diagram. Where are the blocks accelerating? Specifically, on what axis as I am seeing two different axis here and that is not correct.

EDIT: Sorry, didn't see haruspex's post when I responded, I did the same problem.

 

[Nickie]

)

Hello, thank you for presenting your solution attempt. I can see that you have correctly set up the equation ƩF=ma and identified the tension in the rope as the only force acting on the blocks. However, it seems that you have made a mistake in your calculation for the acceleration. Instead of dividing the tension by the mass of the block attached to the rope, you should be dividing by the total mass of the system (4.00kg + m). This will give you an acceleration of 2.5 m/s^2.

Next, to find the mass m of the hanging block, you can use the same equation ƩF=ma and substitute in the known values for the tension and acceleration. This will give you the equation 10.0N = (4.00kg + m)(2.5m/s^2). Solving for m will give you the correct answer of 1.37kg.

Overall, your approach was correct, but you just made a small error in your calculation. Keep up the good work!