Tension and acceleration problem

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Homework Help Overview

The problem involves analyzing a system of weights connected by pulleys, specifically focusing on the tensions in the ropes and the acceleration of the masses. The weights are given as 200N and 300N, with one pulley being stationary and the other free to move.

Discussion Character

  • Mixed

Approaches and Questions Raised

  • The original poster attempts to apply free body diagrams (FBD) to analyze the forces acting on the masses, noting relationships between the tensions and accelerations. They express confusion regarding discrepancies between their calculations and the book's answer.

Discussion Status

Participants are engaging in clarifying the equations used by the original poster, specifically questioning the signs in the equations related to the forces acting on the masses. Some guidance has been offered regarding potential errors in the setup of the equations.

Contextual Notes

There is a mention of a specific answer from the textbook, which may influence the discussion, as well as the original poster's uncertainty about their calculations compared to that answer.

freshcoast
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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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