Pulley problem with frictionless ropes

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Homework Help Overview

The problem involves a pulley system with two masses, m1 and m2, where m1 is 10.0 kg and m2 is 29.5 kg. The setup specifies that the pulley is frictionless and the ropes are massless. The original poster seeks to calculate the acceleration of m2 and the tension in the string.

Discussion Character

  • Exploratory, Problem interpretation, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to use free body diagrams and Newton's laws to set up equations for the forces acting on each mass. Some participants suggest drawing the diagrams clearly and defining variables for tension and weight. Questions arise regarding the direction of acceleration and the need for multiple equations.

Discussion Status

Participants are actively engaging with the problem, offering suggestions for clarifying the setup and emphasizing the importance of direction in the equations. There is recognition of potential errors in the original equations, and the discussion is focused on refining the approach rather than reaching a conclusion.

Contextual Notes

There is a request for a diagram to clarify the pulley layout, indicating that visual representation may be necessary for better understanding. The discussion also highlights the need to consider the direction of acceleration, which is a critical aspect of the problem.

Taz.
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Homework Statement


In the diagram, the pulley is frictionless and the ropes are massless. You are given that m1 = 10.0 kg and m2 = 29.5 kg.

Calculate the acceleration of m2 downwards.

What is the magnitude of the tension in the string?

Homework Equations



sum of F= M*A

The Attempt at a Solution



I tried doing a free body diagram and solving for A but I still can't find the tension...
 
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You should post a picture of the pulley layout to make the problem clear.
 
QLacL.png
 
OK, you have written Newton's Law. Draw a free body diagram of each weight calling the tension in the rope T. You should have two equations. Let's see them.
 
m2:

force of tension going up
force of gravity going down

t1-w=ma

m1: same thing ...
t1-w=ma
 
Let's use some subscripts because the masses/weights are different:

T - w1 = m1 * a

T - w2 = m2 * a

Looking at what you've written, you'll need to define what w1 and w2 are. Also, you have a single variable for acceleration. But the accelerations are in opposite directions so what must be done?
 
So I have w1 and w2 and I have m1 and m2. Whats missing is T and A. Can I just solve for A or T ?
 
Taz. said:
So I have w1 and w2 and I have m1 and m2. Whats missing is T and A. Can I just solve for A or T ?

Yes you can but if you do you'll get an incorrect result. You have an error in one of your equations. Acceleration, like 'g', has a direction associated with it.
 
Signing off for today.
 

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