What Is the Acceleration of Mass m1 on a Frictionless Table Connected to m2?

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SUMMARY

The discussion focuses on calculating the acceleration of mass m1 on a frictionless table connected to mass m2 via a string. The key equation used is F=ma, where the net force on m1 is determined by the tension in the string, while the net force on m2 accounts for its weight and the tension forces acting on it. The participant struggles with expressing the relationship between the accelerations of m1 and m2, questioning whether they can be the same. The conclusion is that while m1 and m2 are connected, their accelerations can differ due to the forces acting on each mass.

PREREQUISITES
  • Understanding of Newton's Second Law (F=ma)
  • Knowledge of tension forces in connected systems
  • Familiarity with frictionless surfaces in physics
  • Basic algebra for solving equations
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  • Study the dynamics of connected masses in physics, focusing on tension and acceleration
  • Learn how to derive equations for multiple masses using free-body diagrams
  • Explore the implications of frictionless surfaces on motion and forces
  • Investigate the relationship between acceleration and tension in pulley systems
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Students studying physics, particularly those focusing on mechanics and dynamics, as well as educators seeking to clarify concepts related to connected masses and acceleration.

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Homework Statement



In the figure, find an expression for the acceleration of m1 (assume that the table is frictionless).

314tr0y.png


Homework Equations



F=ma

The Attempt at a Solution



My biggest problem here is that I don't know what variables I am supposed to answer in (my homework is done on a computer system that is picky about everything).

I know that because of acceleration constraints m1 and the string must move at the same acceleration. But must m2 move with the same acceleration?

The net force on m1 is the force of tension to the right. The net force on m2 is the sum of two tension forces upward and the weight downward.

The acceleration of m2 must be:

F = ma

weight - 2 (tension) = ma

(weight - 2 (tension)) / m = a
 
Last edited:
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Is there anything I can add to get help on this? I am racking my brain here but I can't seem to figure out m1's acceleration relative to m2.

Intuition tells me that they can't be the same, but expressing this mathematically isn't coming to me so easily.
 

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