Accel of 2 Masses & 3 Pulleys: F=Ma Solution

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The discussion focuses on determining the acceleration relationship between two masses connected by pulleys, specifically that the acceleration of mass M1 is twice that of mass M2. This conclusion is derived from the principle that the total length of the string remains constant, which influences how the movements of the masses relate to each other. Participants clarify that the relationship is not based on the forces acting on the masses but rather on the geometry of the string system. One user requests a free body diagram, but it is suggested that this should be addressed in a separate thread. The key takeaway is the understanding of how string length constraints dictate the acceleration ratios in the pulley system.
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Homework Statement



Find the acceleration of the masses
PAAcdkT.jpg


Homework Equations


##F=Ma##

The Attempt at a Solution


We know that the system is moving so for ##M_1## we have ##M_1gsin\theta## on the other hand on ##M_2## we have ##M_1gsin\theta-M_2gsin\theta##

How can I conclude that the acceleration of ##M_2## is twice of ##M_1##?[/B]
 
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Gbox said:
How can I conclude that the acceleration of M2 is twice of M1?
I assume you meant the other way around.
It follows from the assumption that the string length does not change.
 
haruspex said:
I assume you meant the other way around.
It follows from the assumption that the string length does not change.

Sorry ##M_1## is twice the acceleration as ##M_2##.

Yes the string length does not change
 
Gbox said:
Sorry ##M_1## is twice the acceleration as ##M_2##.

Yes the string length does not change
Do you see how it follows from that?
 
haruspex said:
Do you see how it follows from that?
No I can't understand the forces map
 
Gbox said:
No I can't understand the forces map
It's not to do with the forces. Consider the lengths of the three sections of strings. They add up to a constant, and two are always the same as each other. That allows you to express two in terms of the third. Then see how they relate to the two accelerations.
 
haruspex said:
It's not to do with the forces. Consider the lengths of the three sections of strings. They add up to a constant, and two are always the same as each other. That allows you to express two in terms of the third. Then see how they relate to the two accelerations.
Can you show me the free body diagram of the forces acting in the system
 
Crystal037 said:
Can you show me the free body diagram of the forces acting in the system
This thread was about the algebraic relationship between the two accelerations, which has nothing to do with the forces. It follows entirely from the constancy of the total string length.
If you want to discuss the free body diagrams for this problem, post it as a new thread with your own attempt.
 

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