Calculating Acceleration of Hanging Mass System

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Homework Help Overview

The problem involves a system of two masses, M1 and M2, connected by a string over a frictionless pulley. The original poster seeks to determine the acceleration of mass M2, which is on a frictionless table, while mass M1 hangs vertically. The setup raises questions about the forces acting on each mass and their respective directions.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants discuss the forces acting on both masses, particularly the tension in the string and how it relates to the direction of acceleration. There is confusion regarding the treatment of forces as vertical or horizontal, especially concerning mass M2.

Discussion Status

There is an ongoing exploration of the correct interpretation of forces acting on the masses. Some participants have provided guidance on separating horizontal and vertical forces, while others are questioning the assumptions made about the orientation of the string and the forces involved.

Contextual Notes

The original poster notes a lack of visual representation in the problem statement, which may contribute to the confusion regarding the orientation of the forces. This absence of information is acknowledged by participants in the discussion.

physicos
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Homework Statement


A hanging mass M1 =1 kg is attached by a light string that runs over a frictionless pulley to a mass M2=2 kg that is initially at rest on a frictionles table .
What is the magnitude of the acceleration a of M2 ?


Homework Equations


I used for M1 :
Fg1 + T =M1a (with T tension of string)
and for M2 :
N+Fg2+T=M2a

The Attempt at a Solution


NOW I'm stuck , I can't solve it , any help ??
 
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physicos said:
and for M2 :
N+Fg2+T=M2a
For M2 you have added forces that are perpendicular to each other. Don't do that! Instead, consider horizontal forces separately. (Assuming the table is horizontal, that's the direction of the acceleration.)

Be careful with signs.
 
What I have written are vectors :
for M1 without vectors :
_m1g+T=-m1a
and for M2 :
N+T-m2g=m2a

I still didn't get your point
 
physicos said:
What I have written are vectors :
for M1 without vectors :
_m1g+T=-m1a
Good. (Note that the forces of gravity and tension all act vertically.)

and for M2 :
N+T-m2g=m2a
This combines vertical forces (N, mg) with horizontal forces (T). Don't do that.
 
I thought T was a vertical force too
 
physicos said:
I thought T was a vertical force too

On mass 1 it is a vertical force. On m2 it is pulling from the side. Remember that since your pulley is massless and frictionless, the tension along the string will be completely constant.
 
physicos said:
I thought T was a vertical force too
Not when it acts on M2, which slides along a horizontal table. (A picture would help.)
 
Doc Al said:
Not when it acts on M2, which slides along a horizontal table. (A picture would help.)
The OP doesn't actually state the orientation of the string between pulley and M2. Yes, it's probably meant to be horizontal, but in principle could be anything.
 
so what am I supposed to do ? Cause that's all what is available in the problem statement , there is no picture : Should I work with it as a horizontal force ?
 
  • #10
physicos said:
so what am I supposed to do ? Cause that's all what is available in the problem statement , there is no picture : Should I work with it as a horizontal force ?
Yes.
 

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