What is the Correct Approach to Solving a Challenging Pulley Problem?

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SUMMARY

The correct approach to solving a challenging pulley problem involves accurately identifying and separating the forces acting on each mass. Specifically, for mass m2, the net force must be calculated by considering both horizontal and vertical forces independently. A free body diagram should be drawn to label these forces clearly, ensuring that the signs are correct. Additionally, it is crucial to write the sum of the forces according to Newton's laws for each mass, which will result in a system of equations necessary for solving the problem.

PREREQUISITES
  • Understanding of Newton's laws of motion
  • Ability to draw and interpret free body diagrams
  • Knowledge of system of equations
  • Familiarity with tension in pulleys
NEXT STEPS
  • Study how to construct free body diagrams for complex systems
  • Learn to apply Newton's laws to multi-mass pulley problems
  • Explore methods for solving systems of equations in physics
  • Investigate the role of tension in different pulley configurations
USEFUL FOR

Students studying physics, educators teaching mechanics, and anyone looking to improve their problem-solving skills in dynamics involving pulleys and forces.

jalen
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please refer to attachment for question =)
 

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Well for one thing, your net force for m2 is wrong. There are two forces acting in the horizontal direction, and two in the vertical. You've mixed them together. You need to write separate equations for each direction.

Where are your equations for m3?

Draw a free body diagram and label the forces. Be careful with your signs. Write out the sum of the forces according to Newton's law for each mass. This will give you a system of equations to work with to find the information you are being asked to solve for.

See if that helps.
 
In your solution for the acceleration, you treat the different tensions as if they were equal. (You also wrote m2 when you meant m3.)
 

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