Help with this pulley question please

[Asad Raza]

Homework Statement

Two objects of equal masses A and B are connected to a system of pulleys as shown in the figure uploaded. The pulleys are assumed to be smooth. Calculate the acceleration of A.

Homework Equations

F=ma

The Attempt at a Solution

Mg-T=ma
I can't figure out the second equation for b becaus I think it is attached to the pulley and will remain stationary. However, in the proposed solution, there's an equation for the movement of b too. How is that possible?[/B]

 

[phinds]

Well, yeah, B does not move relative to the pulley but what is the pulley doing?

 

[Asad Raza]

Pulley is just moving and b is an additional load on the second pulley.
Also, B doesn't move relative to the observer too.

 

[phinds]

Pulley is just moving and b is an additional load on the second pulley.
Also, B doesn't move relative to the observer too.

You might want to rethink that

 

[Asad Raza]

There can be two scenarios which aren't specified in the question.
1) B is loosely held at the centre so that B stays ALMOST stationary to the observer.
2) B is tightly attached to the pulley and it rotates in a circle.

 

[phinds]

There can be two scenarios which aren't specified in the question.
1) B is loosely held at the centre so that B stays ALMOST stationary to the observer.
2) B is tightly attached to the pulley and it rotates in a circle.

You and I seem to be working on entirely different problems. I read this as a very simple, straightforward, standard pulley problem. I have no idea what you are talking about.

 

[Asymptotic]

Homework Equations

F=ma

Listing all of the relevant equations helps you to develop a clear understanding of the problem.

Mass A and B are equal.
In what direction (up or down) will mass A travel? What about the travel direction of mass B?
Why?

3. The Attempt at a Solution
Mg-T=ma

Hint: Annotate your drawing with known and unknown variables, directions of travel, etc.
Use more precise and unambiguous naming, for instance, ma_A and ma_B for the accelerations of mass A and B.

In a larger sense, become acquainted with George Polya's four principles, and as a wise man once said, "Learn it, Know it, Live it".

 

[haruspex]

There can be two scenarios which aren't specified in the question.
1) B is loosely held at the centre so that B stays ALMOST stationary to the observer.
2) B is tightly attached to the pulley and it rotates in a circle.

You seem to be misinterpreting the diagram. The pulley above B rests on the string. It is firmly attached to the mass B, but not to anything else. That pulley and its mass are free to move up and down as a unit.

 

[Chestermiller]

If mass A moves upward, the part of the string supporting mass A gets shorter. If the total length of string is constant, what happens to the length of the part of the string supporting mass B? (a) its length doesn't change (b) its length gets shorter or (c) its length gets longer.

 

[ehild]

There can be two scenarios which aren't specified in the question.
1) B is loosely held at the centre so that B stays ALMOST stationary to the observer.
2) B is tightly attached to the pulley and it rotates in a circle.

The mass B is attached to the axis(represented by the black dot) of the hanging pulley.It moves together with the axis up or down.
The pulley rotates about the axis.
The length of the string is constant. If A moves downward, the left piece of the string gets longer, so the right pieces should get shorter, raising the pulley and mass B.

 

[Kaura]

Try drawing a free body diagram, taking into account the forces of gravity and tension.