Pulley problem with frictionless ropes

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SUMMARY

The discussion focuses on solving a physics problem involving a frictionless pulley system with two masses, m1 = 10.0 kg and m2 = 29.5 kg. Participants emphasize the importance of drawing free body diagrams and establishing two equations based on Newton's Laws to find the acceleration of m2 and the tension in the string. Key equations include T - w1 = m1 * a and T - w2 = m2 * a, where w1 and w2 represent the weights of m1 and m2, respectively. The need for careful attention to the direction of acceleration is highlighted to avoid incorrect results.

PREREQUISITES
  • Understanding of Newton's Laws of Motion
  • Ability to draw and interpret free body diagrams
  • Knowledge of weight calculation (w = mg)
  • Familiarity with basic algebra for solving equations
NEXT STEPS
  • Study the application of Newton's Laws in multi-body systems
  • Learn how to effectively draw and analyze free body diagrams
  • Explore the concept of tension in ropes and strings in physics
  • Investigate the effects of directionality in acceleration and forces
USEFUL FOR

Students studying physics, particularly those tackling mechanics problems involving pulleys and forces, as well as educators seeking to enhance their teaching of Newton's Laws.

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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