Solving Atwood's Machine: Find Forces & Acceleration

In summary, the conversation discusses the use of a machine to understand forces, specifically an Atwood machine with a massless pulley and string. The conversation covers calculating the acceleration and tension in the string, as well as finding the force exerted on the pulley's hanger and testing the results. The speaker is unsure about their approach and seeks clarification or assistance.
  • #1
jungleismassiv
11
0
The machine shown in the figure below can be used to give you a good feel
for forces. Assuming a massless, frictionless pulley and a massless string,
calculate the magnitude of the acceleration on both bodies and the tension in
the string T.

http://img110.exs.cx/my.php?loc=img110&image=d9kq.jpg

Find the force exerted by the Atwood's machine on the hanger which the
pulley is attached to while the blocks accelerate. Neglect the mass of the
pulley.

The pulley in Atwood machine above is given an upward acceleration a. Find
the acceleration of each mass and the tension in the string that connects
them. How can you test your result

No idea with these questions. Any help would be appreciated. Thanks :smile:
 
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  • #2
No idea is not good enough for help.
Try to explain what you think MIGHT work, but why you are uncertain about it.
 
  • #3


Solving Atwood's Machine involves applying the principles of Newton's laws of motion. In this machine, there are two masses connected by a string that passes over a frictionless and massless pulley. The first step in solving this problem is to draw a free body diagram for each mass, showing all the forces acting on them. In this case, there are two forces acting on each mass - the weight (mg) and the tension in the string (T).

Now, using Newton's second law (F=ma), we can write an equation for each mass:

For the first mass (m1):
T - m1g = m1a

For the second mass (m2):
m2g - T = m2a

Since the pulley is massless, we can assume that the tension in the string (T) is the same on both sides. We can also assume that the acceleration of the two masses is the same, as they are connected by a string. Therefore, we can combine the two equations and solve for the acceleration (a):

T - m1g = m1a
m2g - T = m2a

Adding the two equations, we get:
m2g - m1g = (m1+m2)a

Solving for a, we get:
a = (m2g - m1g)/(m1+m2)

This is the acceleration of both masses. To find the tension in the string (T), we can substitute this value of acceleration in any of the two equations we wrote earlier. For example, using the first equation:
T - m1g = m1a
T - m1g = m1[(m2g - m1g)/(m1+m2)]
T = (m1m2g)/(m1+m2)

Therefore, the tension in the string is:
T = (m1m2g)/(m1+m2)

To test our result, we can perform a simple experiment using this Atwood's machine. We can vary the masses and measure the acceleration and tension in the string using a force sensor. We can then compare our calculated values with the measured values to see if they match. If there is a significant difference, we can check for any errors in our calculations and make necessary adjustments. This way, we can verify the accuracy of our solution.
 

1. What is Atwood's Machine?

Atwood's Machine is a simple physics experiment that consists of a pulley, a string, and two masses connected on either side of the pulley. It is used to demonstrate the principles of classical mechanics, such as Newton's laws of motion and the concept of acceleration.

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

To find the forces in Atwood's Machine, you need to use the equation F = ma, where F is the force, m is the mass, and a is the acceleration. You will also need to take into account the forces of gravity and tension in the string. By setting up and solving equations for each mass, you can determine the forces acting on them.

3. What is the acceleration in Atwood's Machine?

The acceleration in Atwood's Machine is determined by the difference in mass between the two masses and the force of gravity. The heavier mass will experience a larger force of gravity, causing it to accelerate towards the ground. The lighter mass will experience a smaller force, causing it to accelerate in the opposite direction. The net acceleration of the system can be calculated using the equation a = (m1-m2)g/(m1+m2), where m1 and m2 are the masses and g is the acceleration due to gravity.

4. Can you change the acceleration in Atwood's Machine?

Yes, you can change the acceleration in Atwood's Machine by adjusting the masses or the length of the string. Increasing the difference in mass or decreasing the length of the string will result in a larger acceleration, while decreasing the difference in mass or increasing the length of the string will result in a smaller acceleration.

5. How can Atwood's Machine be used in real-world applications?

Atwood's Machine can be used to model and understand many real-world situations, such as elevators, cranes, and weightlifting. It can also be used to study the effects of friction and air resistance on a moving object. By understanding the principles of Atwood's Machine, scientists and engineers are able to design and optimize various mechanical systems.

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