Understanding Velocity in a Massless, Frictionless Pulley System

[rajumahtora]

Homework Statement

Find V if the pulley is massless, friction less and
Can take any no of variables but V is be in terms of V_P.Ignore gravity and other forces

2. The attempt at a solution
If Pulley comes down by X, the length of string towards left(the side not fixed) will increase by 2X
Therefore, If in same time pulley comes down by V_P, String will increase at rate of V=2V_P.
.'. the answer is V=2V_P
But, The answer in key states V = V_P(1+cosβ)
Where am I going wrong?

 

[BvU]

If the pulley is hanging in the air, everything will come down very quickly. If it is attached to something fixed, and the lower right represents Earth -- which is generally considered fixed as well -- Any amount of V (what is it, actually?) won't have an effect, no matter what.

Please rewrite 1, 2 and 3. We will try to help, but this requires telepathy or clearsightedness,

 

[BvU]

I see you already have an answer. Now the questions. i.e. the question the problem asks and the question you are asking...

 

[rajumahtora]

I see you already have an answer. Now the questions. i.e. the question the problem asks and the question you are asking...

Plz explain what do you want to say?
Is answer 2V_P correct?

 

[BvU]

What I want to say is: 1. State the problem, list known variables and data. 2. List the relevant equations 3. Show what you've done so far and where you get stuck.

Do all three in such a way that someone else has a good chance to understand.

This soounds rude, but the idea is that the template is really useful to help both the one who is posting and potential helpers.

At the moment I can't help you because I can't understand the problem you want to solve, nor what is withholding you from solving it. I really want to help, make it possible!

 

[rajumahtora]

What I want to say is: 1. State the problem, list known variables and data. 2. List the relevant equations 3. Show what you've done so far and where you get stuck.

Do all three in such a way that someone else has a good chance to understand.

This soounds rude, but the idea is that the template is really useful to help both the one who is posting and potential helpers.

At the moment I can't help you because I can't understand the problem you want to solve, nor what is withholding you from solving it. I really want to help, make it possible!

Modified The quesion.
I hope it will help u to understand my question.
I want to give u 100 thanks at once but forum rules restricts me to only one

 

[haruspex]

The problem is not fully specified. I can justify two answers depending on what is supposed to be constant: the angle of the string or the direction of pull. To get the given answer, it has to be the direction of pull.

If Pulley comes down by X, the length of string towards left(the side not fixed) will increase by 2X

If the pulley comes down by X, by how much is the length of the string between pulley and ground anchor reduced? So the length of the string to the left of the pulley has increased by ...?
That argument tells you how the free end moves relative to the pulley, but to get V you need to add in a component of the velocity of the pulley.
(If taking the constant angle of string interpretation, you would add the velocities as vectors instead.)

 

[rajumahtora]

The problem is not fully specified. I can justify two answers depending on what is supposed to be constant: the angle of the string or the direction of pull. To get the given answer, it has to be the direction of pull.

If the pulley comes down by X, by how much is the length of the string between pulley and ground anchor reduced? So the length of the string to the left of the pulley has increased by ...?
That argument tells you how the free end moves relative to the pulley, but to get V you need to add in a component of the velocity of the pulley.
(If taking the constant angle of string interpretation, you would add the velocities as vectors instead.)

So for const direction of pull, is The answer is V_P(2+cosβ) ?
If not, Plz tell me how to solve
PLZ

 

[haruspex]

So for const direction of pull, is The answer is V_P(2+cosβ) ?

No, the given answer is correct for that case. You didn't answer my first two questions:

If the pulley comes down by X, by how much is the length of the string between pulley and ground anchor reduced? So the length of the string to the left of the pulley has increased by ...?

 

[rajumahtora]

No, the given answer is correct for that case. You didn't answer my first two questions:

1.Decreases by X
2.cant figure out

 

[haruspex]

1.Decreases by X
2.cant figure out

Does the string as a whole change length?