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

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In summary, Atwood's Machine involves one pulley and two weights, which are analyzed using two free body diagrams. The masses of the weights are not combined into one force diagram because they have different accelerations - one goes up while the other goes down. However, gravity is still pulling down on each weight in the same direction. The difference in the masses of the weights results in the heavier weight falling while the lighter weight is lifted due to the tension in the rope. The tension in the rope must be equal for each weight in order for the system to be at rest. This is because the net force on a massless rope must be zero. If the net force were not zero, one weight would have a different acceleration.
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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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  • #4
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.
 
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Why does the magnitude of the tension not equal the magnitude of the difference in the weight of the weights?
 
  • #6
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?
 
  • #7
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.
 
  • #8
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)?
 
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uestions said:
Why must the tension be equal for each weight?
The net force on a massless rope must be zero.
 
  • #10
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.)
 

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

1. What is an Atwood's Machine and how does it work?

An Atwood's Machine is a simple device used to demonstrate the principles of mechanical forces and gravity. It consists of two masses connected by a string that passes over a pulley. The two masses are typically unequal, and when one is released, it accelerates towards the ground due to the force of gravity. This creates a tension in the string, causing the other mass to accelerate in the opposite direction.

2. How do you calculate the forces in an Atwood's Machine?

In an Atwood's Machine, there are two main forces at play: the weight of each mass and the tension in the string. The weight of each mass can be calculated using the formula W = mg, where m is the mass and g is the acceleration due to gravity (9.8 m/s^2). The tension in the string can be calculated using Newton's second law, which states that force equals mass times acceleration (F=ma). By setting up and solving equations for each of the forces, you can determine the net force and acceleration of the system.

3. How do you draw a free body diagram for an Atwood's Machine?

To draw a free body diagram for an Atwood's Machine, you first need to identify all the forces acting on each mass. These include the weight of the mass (mg), the tension in the string, and the normal force (if the mass is on a surface). Then, draw a diagram with arrows representing each force, making sure to label them with their corresponding values. Finally, use Newton's second law to set up and solve equations for the net force and acceleration of the system.

4. What is the role of gravity in an Atwood's Machine?

Gravity plays a crucial role in an Atwood's Machine as it is the force that causes the masses to accelerate towards the ground. To understand this, you can think of each mass as experiencing a downward force due to its weight, which creates a tension in the string. The unequal weights of the masses also contribute to the acceleration, with the heavier mass pulling down with a greater force.

5. How does the mass of the pulley affect an Atwood's Machine?

The mass of the pulley in an Atwood's Machine does not significantly affect the overall dynamics of the system. However, a heavier pulley may experience more friction and may cause the system to accelerate at a slightly slower rate. In most cases, the mass of the pulley can be ignored when calculating the forces and acceleration of an Atwood's Machine.

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