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two bodies having masses M1 and m2 (M1>m2) are attached to the ends of a light inextensible stringpassing over a smooth frictionless pulley.when the system is released M1 moves downward and m2 move upwards with acceleration a.T is the tension of the string.

free body diagram of M1 gives that

unbalanced force F = Mg - T

my question is how the unbalanced force became the difference of the weight and tension? please give me an accurate answer

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  • $\begingroup$ What do you think the unbalanced force should be? $\endgroup$ – M. Enns Sep 24 '18 at 15:52
  • $\begingroup$ didn't get what you are saying $\endgroup$ – Archa Sep 24 '18 at 16:18
  • $\begingroup$ You mean, how to solve the system? $\endgroup$ – Matteo Campagnoli Sep 24 '18 at 18:41
  • $\begingroup$ By the way, the system you talk about is called Atwood Machine $\endgroup$ – Matteo Campagnoli Sep 24 '18 at 18:45
  • $\begingroup$ Matteo can you please explain this to me $\endgroup$ – Archa Sep 25 '18 at 14:49
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If I understand your question correctly, the force on M1 has to be M1*g - T because the only forces acting on M1 are its own weight (=M1*g) pulling downward and the tension T pulling upward. The fact that one force is down and the other up explains why the total force is the difference between them.

To actually solve for T and A will involve analyzing both masses, and will produce 2 equations and 2 unknowns.

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  • $\begingroup$ but instead of subtracting why can't we just add the total force?Is this because they are acting in the opposite direction $\endgroup$ – Archa Sep 25 '18 at 14:52
  • $\begingroup$ please answer fast sir $\endgroup$ – Archa Sep 25 '18 at 15:46
  • $\begingroup$ @anilbabu Yes, they are acting in opposite directions, so they need to be subtracted. $\endgroup$ – Stuart Van Horne Sep 25 '18 at 19:29

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