Understanding Atwood's Machine: Forces, Diagrams, and Gravity Explained

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Discussion Overview

The discussion revolves around Atwood's Machine, focusing on the forces acting on two weights connected by a pulley. Participants explore the mechanics of the system, including the role of gravity, tension in the rope, and the implications of different mass weights on acceleration. The conversation includes technical explanations and conceptual clarifications regarding free body diagrams and Newton's laws.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Some participants question why gravity is not considered to pull both weights in the same direction when analyzing the system, given that the weights are connected.
  • It is noted that the weights have different accelerations, with one weight going up while the other goes down, complicating the treatment of the masses as a single system.
  • Participants discuss how the force of gravity affects the weights differently when they are unequal, leading to acceleration of the heavier weight downward and the lighter weight upward.
  • There is a challenge regarding the relationship between the tension in the rope and the difference in weight between the two masses, with some participants questioning why tension does not equal this difference.
  • Some participants assert that the tension must be equal for each weight due to Newton's Third Law, while others explore the implications of the net force on a massless rope being zero.
  • Concerns are raised about the implications of a non-zero net force, suggesting that it would lead to different accelerations for the weights.

Areas of Agreement / Disagreement

Participants express differing views on the relationship between tension, weight differences, and acceleration. There is no consensus on the implications of these relationships, and the discussion remains unresolved regarding the exact nature of the forces at play.

Contextual Notes

The discussion includes assumptions about the nature of the rope (non-stretchy) and the treatment of the system as a whole versus individual components. The implications of these assumptions on the analysis are not fully resolved.

uestions
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Atwood's Machine, with one pulley and two weights, is analyzed with two free body diagrams. Each diagram depicts the forces applied to each weight. If the weights are connected, why isn't gravity considered to be pulling on both weights in the same direction? (Meaning, why aren't the masses for the weights combined to make one force diagram with one mass? Because the acceleration is not equal to 9.8m/s/s?)
A simpler question may be how does an Atwood Machine work?
 
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uestions said:
If the weights are connected, why isn't gravity considered to be pulling on both weights in the same direction?
The weight of each mass does point in the same direction of course--down!

(Meaning, why aren't the masses for the weights combined to make one force diagram with one mass? Because the acceleration is not equal to 9.8m/s/s?)
The masses have different accelerations. One goes up while the other goes down. It would be more complicated to treat the masses as a single system (but you could do that if you liked).
 
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Gravity is pulling down on each weight in the same direction. However, each weight is pulling on the other via the wire and pulley. When the weights are equal, the force of gravity on each weight is equal, and since they pull on each other with a force equal to that of gravity, there is no net acceleration.

However, when the mass of the weights aren't equal, gravity pulls the heavier weight with more force (hence why it is heavier). This translates to the heavier weight pulling on the lighter weight with more force than vice versa. So the heavier weight falls while the lighter weight is lifted. The greater the difference between the masses of the weights, the faster the weights will accelerate.

Does that make sense?
 
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Drakkith said:
This translates to the heavier weight pulling on the lighter weight with more force than vice versa.
Does that make sense?

Poor choice of words. The force between the weights is the tension on the string which is identical at both ends.
 
Why does the magnitude of the tension not equal the magnitude of the difference in the weight of the weights?
 
uestions said:
Why does the magnitude of the tension not equal the magnitude of the difference in the weight of the weights?
Why should it? What if the weights were the same?
 
uestions said:
Why does the magnitude of the tension not equal the magnitude of the difference in the weight of the weights?


Because the system is not at rest.
 
Why must the tension be equal for each weight? Because of Newton's Third Law?
Does the tension take into account the other weight's (as in object) weight (as in force) pulling on another weight (object)?
 
Last edited:
uestions said:
Why must the tension be equal for each weight?
The net force on a massless rope must be zero.
 
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Doc Al said:
The net force on a massless rope must be zero.


Why must the net force be zero? If it weren't, would that mean one weight would have a different acceleration?
 
  • #11
uestions said:
Why must the net force be zero?
The net force on any massless object must be zero:
∑F = ma = (0)a = 0

(The alternative would be infinite acceleration.)

If it weren't, would that mean one weight would have a different acceleration?
Since the masses are connected via the rope, they are constrained to have the same acceleration. (Assuming a non-stretchy rope.)
 

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