Understanding Pulley Acceleration: Newton's Third Law and Mass Ratios"

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Homework Help Overview

The discussion revolves around a problem involving a pulley system with two masses, m1 and m2, where m1 is greater than m2. Participants are exploring the implications of Newton's third law in relation to the acceleration of the masses and the forces acting on them.

Discussion Character

  • Conceptual clarification, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • The original poster questions how m1 can exert a leftward force on the rope while m2 accelerates downward, suggesting a potential misunderstanding of the forces involved.
  • Some participants clarify that m2 experiences two forces: its weight downward and the tension in the rope upward, leading to further questions about the net force and acceleration of m2.
  • Others discuss the relationship between the two masses and the equations governing their motion, questioning how they can have the same acceleration despite differing weights.

Discussion Status

Contextual Notes

Participants are working under the assumption that the system is ideal, with no friction or other forces acting on the masses aside from gravity and tension. The original poster's reference to a specific image may also imply additional context that is not fully articulated in the text.

madah12
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Homework Statement



hi in this picture ( http://img26.imageshack.us/img26/8458/53487724.png ) the teacher says that even if m1 is greater than m2 m2 will accelerate down and m1 will accelerate to the right but by Newtons third law shouldn't m1 have a leftward force to the rope which should pull m2 up?

Homework Equations



F(m2 to rope ) = -F(rope to m2)
F(m1 to rope ) = -F(rope to m1)

The Attempt at a Solution

 
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Newton's 3rd law says that the rope pulls m1 to the right, and m1 pulls the rope to the left (and this in turn pulls m2 in an upwards direction*). There is no force on m1 to the left.
* This upwards force on m2 acts against the weight of m2 downwards.
So as far as m2 is concerned, there are 2 forces, its weight downwards, and the tension in the rope upwards.
As far as m1 is concerned, there is a force from the rope pulling to the right.
 


so why does m2 accelerate downwards? since tension is up and weight is down shouldn't Fnet = 0 ?
 


madah12 said:
so why does m2 accelerate downwards? since tension is up and weight is down shouldn't Fnet = 0 ?

It accelerates downwards because
a) its weight mg is greater than T, the tension in the string; and
b) the mass m1 is pulled by a force (T) to the right, and the two masses are connected to the same string.
Think about it; how could m1 accelerate to the right yet m2 not accelerate down?
Because they are connected, both masses must have the same acceleration, a.
The equation for m2 is M2g-T=M2a
The equation for m1 is T=M1a
Given g, m1 and m2 you have 2 unknowns, a and T, and two equations.
Eliminate T and solve for a will give you the common acceleration of both masses.
 

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