Solving for Tension & Acceleration in M1 & M2

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SUMMARY

The discussion focuses on calculating the tension in a cord and the acceleration of two masses, m1 (300g) and m2 (200g), under the influence of a force (F=0.4N) with negligible friction. The equations T=m2*a2 and F-2T=m1*a1 are established, with the critical relationship a2 = 2*a1 derived from the constraint of the pulley system. This relationship arises because for every meter m1 moves, m2 moves half that distance, necessitating the acceleration constraint to solve for the system's dynamics.

PREREQUISITES
  • Understanding of Newton's laws of motion
  • Familiarity with basic pulley systems
  • Knowledge of tension in strings and cords
  • Ability to solve linear equations
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  • Study the mechanics of pulley systems in detail
  • Learn about tension forces in connected mass systems
  • Explore the implications of acceleration constraints in physics problems
  • Practice solving problems involving multiple masses and forces
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Physics students, educators, and anyone interested in understanding dynamics involving tension and acceleration in mechanical systems.

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Assume there is negligible friction between the blocks and the table. Compute the tension in the cord and the acceleration of m2 if m1 = 300g, m2 = 200g, and F=0.4N

I figured out that T=m2*a2, F-2T=m1a1.
According to the answer, 2a1=a2. But I don't undestand why.
 

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acceleration constraint

Your force equations are correct, but incomplete. You need to incorporate the constraint imposed by the fact that the masses are connected via a pulley and ropes--that's what will give you the additional equation a2 = 2 a1. To understand where that relationship comes from, answer this question: If m1 moves one meter to the right, how far does m2 move? (If you have trouble visualizing the motion, use a piece of string or a paper strip.)
 

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