Newton's laws of motion -- finding the velocity of a Block in a pulley system

[Vv anand]

Homework Statement

Determine the speed with which block B rises in figures if the end of cord at A is pulled down with a speed of 2ms^-1

Homework Equations

Given Velocity downwards at A=2m/s

The Attempt at a Solution

Really stuck... Couldn't even start the question solving...I know all policies and therefore i am not demanding the question to be solved but just a hint on how to start will surely help

 

[haruspex]

a hint on how to start

Create some variable names for the different unknown velocities. See what equations you can write to relate them.

 

[Vv anand]

Create some variable names for the different unknown velocities. See what equations you can write to relate them.

Yes that i hv already done... Will start again.. Thx

 

[Vv anand]

Yea i started again but ended with nothing..I can show u my work if u want

 

[Vv anand]

This is what i did...i m stuck after this!

 

[Merlin3189]

I don't know if it is allowed, but I used distances instead of velocities.
Just took a starting position, moved the block B 1 unit distance and calculated the distance each other bit moved if the string stayed tight.
That gave me a velocity ratio.

 

[Chestermiller]

If mass B moves up $\delta$, how much does the pulley that supports A move down?

 

[Vv anand]

If mass B moves up $\delta$, how much does the pulley that supports A move down?

Is it 3$\delta$

 

[Chestermiller]

Is it 3$\delta$

No. Look at the diagram carefully.

 

[Vv anand]

No. Look at the diagram carefully.

Oh is it 4 $/delta$

 

[Vv anand]

Oh is it 4 $/delta$

Just because of the middle string attached to the mass coming from the upper left pulley

 

[Chestermiller]

Oh is it 4 $/delta$

No. Look carefully. The wire between pulley

 

[Chestermiller]

I get that the pulley supporting A moves down $\delta$ if mass B moves up $\delta$. This focuses on the wire that passes over pulley D.

 

[Vv anand]

I get that the pulley supporting A moves down $\delta$ if mass B moves up $\delta$. This focuses on the wire that passes over pulley D.

Sir I am coming to the solution that since pulley supporting B moves up the pulley supporting a moves down 3$/delta$ as i hv to ke

 

[Vv anand]

Sir I am coming to the solution that since pulley supporting B moves up the pulley supporting a moves down 3$/delta$ as i hv to ke

Yes sir...i got that the $/pulley$ is moving delta downwards

 

[Vv anand]

Yes sir...i got that the $/pulley$ is moving delta downwards

Wrote that upper comment by mistake...

 

[Chestermiller]

So if $v_B$ is the upward velocity of mass B, what is the downward velocity of the pulley that supports A?

 

[Vv anand]

So if $v_B$ is the upward velocity of mass B, what is the downward velocity of the pulley that supports A?

Sir vb

 

[Vv anand]

Sir vb

But this brings me to the solution that vb=2/3.

 

[Chestermiller]

But this brings me to the solution that vb=2/3.

Yes. So?

 

[Vv anand]

But sir the solution is 0.5 m/s

 

[Chestermiller]

But sir the solution is 0.5 m/s

I guess I don't agree.

 

[haruspex]

I guess I don't agree.

I confirm 0.5m/s.

 

[Merlin3189]

When I first looked at this, I got V_B=2V_A/3, but when OP asked for more info on how, I checked and am now convinced that it is V_A/4
When I pull with force T, I find a mechanical advantage of 4:1, by just looking at all the tensions. (assuming massless blocks, light frictionless strings, etc.)

Since you noted the blocks move equally, surely the section from C to E shortens twice as fast as the other two legs?

Perhaps you could expand on your reasoning?

 

[haruspex]

The set-up is sufficiently complicated that it is best to take a very disciplined approach.
There are four distances of interest: AC, CE, CD, DE.
We need four equations to relate them. Some equations will be that one distance is the sum of others, while others will be that a sum of distances is constant.
@Vv anand , what equation relates:
AC, CE, DE?
CD and DE?
AD, AC and CD?
CD, CE and DE?

 

[Vv anand]

When I first looked at this, I got V_B=2V_A/3, but when OP asked for more info on how, I checked and am now convinced that it is V_A/4
When I pull with force T, I find a mechanical advantage of 4:1, by just looking at all the tensions. (assuming massless blocks, light frictionless strings, etc.)

Since you noted the blocks move equally, surely the section from C to E shortens twice as fast as the other two legs?

Perhaps you could expand on your reasoning?

Like this?

 

[haruspex]

Like this?

Yes, that works.

 

[Chestermiller]

@haruspex I'm trying to get an understanding of where I went wrong. Was I correct in assessing that, if $v_A$ is the downward velocity of A and $v_B$ is the upward velocity of B, then the rate of increase in length of the segment of wire between A and the pulley that supports A is $v_A-v_B$?

EDIT: Ooops. That's not correct. I really messed up on this one.

Chet