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

[uestions]

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?

 

[Doc Al]

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).

 

[Drakkith]

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?

 

[dauto]

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.

 

[uestions]

Why does the magnitude of the tension not equal the magnitude of the difference in the weight of the weights?

 

[Doc Al]

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?

 

[oneplusone]

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.

 

[uestions]

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)?

 

[Doc Al]

Why must the tension be equal for each weight?

The net force on a massless rope must be zero.

 

[uestions]

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?

 

[Doc Al]

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.)