Tension and acceleration problem

AI Thread Summary
The discussion revolves around solving a tension and acceleration problem involving two weights of 200N and 300N connected by pulleys. The participant initially set up free body diagrams and applied Newton's second law but encountered discrepancies in their calculations. They noted that the tension for mass 2 is twice that of mass 1 and that the acceleration for mass 2 is half of mass 1. A key point of confusion was identified regarding the sign convention used in the equations, particularly for mass 2's upward movement. After clarification on the sign error in the equations, the participant was able to resolve their misunderstanding.
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1. Problem statement/ given data
The weights of the objects are 200N and 300N. The pulleys are essentially frictionless and massless. Pulley P1 has a stationary axle, but pulley P2 is free to move up and down. Find the tensions FT1 and FT2 and the acceleration of each body.

2. Homework Equations .
F=ma

3. Attempt.
I drew a FBD for each mass with m1 going down with down as the positive and m2 going up with up as the positive direction. I know that in this system the tension for mass 2 is twice the tension of mass 1 and that the acceleration for mass 2 is half of mass 1. I have the answer and the explained solution but I don't know how I'm getting a different answer than they are. Can someone check what I am not seeing here? I know if I find the right acceleration I just have to plug that into find the tensions.

29mq1c1.jpg


The answer in the book is a= 1.78m/s^2
 
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It looks to me that your second equation has a sign error.
 
For mass 2? Since that mass is going up shouldn't the upwards be the positive direction? So it would be T - mg ?
 
Yes, that's right. I should have been clearer. I was referring to the second line of your equations where you wrote for m1: FT1 = m1ay + m1g. Check the signs in this equation.
 
Oh I see it now, got it thanks!
 

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