# Homework Help: Newton's laws of motion -- finding the velocity of a Block in a pulley system

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1. Jun 29, 2017

### Vv anand

1. The problem statement, all variables and given/known data
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

2. Relevant equations
Given Velocity downwards at A=2m/s

3. 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

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2. Jun 29, 2017

### haruspex

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

3. Jun 29, 2017

### Vv anand

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

4. Jun 29, 2017

### Vv anand

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

5. Jun 29, 2017

### Vv anand

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

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6. Jun 29, 2017

### 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.

7. Jun 29, 2017

### Staff: Mentor

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

8. Jun 29, 2017

### Vv anand

Is it 3$\delta$

9. Jun 29, 2017

### Staff: Mentor

No. Look at the diagram carefully.

10. Jun 29, 2017

### Vv anand

Oh is it 4 $/delta$

11. Jun 29, 2017

### Vv anand

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

12. Jun 29, 2017

### Staff: Mentor

No. Look carefully. The wire between pulley

13. Jun 29, 2017

### Staff: Mentor

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.

14. Jun 29, 2017

### Vv anand

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

15. Jun 29, 2017

### Vv anand

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

16. Jun 29, 2017

### Vv anand

Wrote that upper comment by mistake...

17. Jun 29, 2017

### Staff: Mentor

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

18. Jun 29, 2017

### Vv anand

Sir vb

19. Jun 29, 2017

### Vv anand

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

20. Jun 29, 2017

### Staff: Mentor

Yes. So?

21. Jun 29, 2017

### Vv anand

But sir the solution is 0.5 m/s

22. Jun 29, 2017

### Staff: Mentor

I guess I don't agree.

23. Jun 29, 2017

### haruspex

I confirm 0.5m/s.

24. Jun 29, 2017

### Merlin3189

When I first looked at this, I got VB=2VA/3, but when OP asked for more info on how, I checked and am now convinced that it is VA/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?

25. Jun 29, 2017

### 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?