The acceleration of a massless pulley in a double Atwood machine

[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).
https://www.physicsforums.com/threads/double-atwoods-machine.882491/
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?

 

[SammyS]

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).
https://www.physicsforums.com/threads/double-atwoods-machine.882491/
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.

 

[UnPetitGarcon]

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.

Thanks for reply! Got it!