The acceleration of a massless pulley in a double Atwood machine

• UnPetitGarcon
In summary, the conversation discusses a physics question about calculating the acceleration of a massless pulley in a double Atwood's machine. The question was previously posted but did not address the doubt of the person. The conversation then explains that it takes no torque or net force to accelerate a massless object, leading to the conclusion that the tension in string A and C are equal. A sketch of the system is also provided for visualization.
UnPetitGarcon
Homework Statement
Calculating the acceleration of pulley B
Relevant Equations
F=ma
So there is a textbook physics question in which it asks us to calculate the acceleration of pulley B(which is massless). This exact question was posted and asked previously in this thread. However, it didn't discuss my doubt. To be exact, the question I have troubles with is (b).
How on Earth is it even possible to accelerate a massless pulley? When setting up equations, we can reach to the conclusion that the tension in String C equals to the two tensions in String A so that there is no acceleration. How come there is acceleration?

UnPetitGarcon said:
Problem Statement: Calculating the acceleration of pulley B
Relevant Equations: F=ma

So there is a textbook physics question in which it asks us to calculate the acceleration of pulley B(which is massless). This exact question was posted and asked previously in this thread. However, it didn't discuss my doubt. To be exact, the question I have troubles with is (b).
How on Earth is it even possible to accelerate a massless pulley? When setting up equations, we can reach to the conclusion that the tension in String C equals to the two tensions in String A so that there is no acceleration. How come there is acceleration?
It's very helpful to include a sketch of the system in question. Here's a snip of the figure in the thread you refer to.

Two issues here:
One is that it takes no torque to accelerate a massless pulley.

Therefore, the tension in string A is the same on both sides o pulley B. Likewise, the tension in string C is the same on both sides o pulley D.

The other issue is that it takes no (zero) net force to accelerate any massless object. So net force on any massless object is zero. This follows from Newton's 2nd Law: ##\vec F _\text{net} = m \vec a##. So that if ##m=0## then ##\vec F _\text{net}## must be zero.

SammyS said:
It's very helpful to include a sketch of the system in question. Here's a snip of the figure in the thread you refer to.
View attachment 247590

Two issues here:
One is that it takes no torque to accelerate a massless pulley.

Therefore, the tension in string A is the same on both sides o pulley B. Likewise, the tension in string C is the same on both sides o pulley D.

The other issue is that it takes no (zero) net force to accelerate any massless object. So net force on any massless object is zero. This follows from Newton's 2nd Law: ##\vec F _\text{net} = m \vec a##. So that if ##m=0## then ##\vec F _\text{net}## must be zero.

1. What is a double Atwood machine?

A double Atwood machine is a simple mechanical system consisting of two masses connected by a string or rope that runs over a massless pulley. This system is used to demonstrate the principles of acceleration and tension in physics.

2. What is the acceleration of a massless pulley in a double Atwood machine?

The acceleration of a massless pulley in a double Atwood machine is zero. This is because a massless pulley does not have any mass to accelerate, so it remains stationary while the masses on either side experience equal and opposite accelerations.

3. How does the acceleration of the masses in a double Atwood machine compare to the acceleration due to gravity?

In a double Atwood machine, the acceleration of each mass is equal to the acceleration due to gravity, which is approximately 9.8 m/s^2 on Earth. This is because the tension in the string is equal to the weight of the masses, and according to Newton's second law of motion, F=ma, the masses will accelerate in the direction of the net force acting on them.

4. What factors affect the acceleration of a double Atwood machine?

The acceleration of a double Atwood machine is affected by the masses of the objects involved and the tension in the string. The masses will accelerate differently if they have different weights, and the acceleration will increase as the tension in the string increases.

5. Can the acceleration of a massless pulley in a double Atwood machine ever be non-zero?

No, the acceleration of a massless pulley in a double Atwood machine will always be zero. This is because a massless pulley does not have any mass to accelerate, so it remains stationary while the masses on either side experience equal and opposite accelerations. This is a fundamental principle in physics known as the Law of Inertia.

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