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

In summary: 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##?Yes, that works.
  • #1
Vv anand
41
1

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
 

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  • #2
Vv anand said:
a hint on how to start
Create some variable names for the different unknown velocities. See what equations you can write to relate them.
 
  • #3
haruspex said:
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
 
  • #4
Yea i started again but ended with nothing..I can show u my work if u want
 
  • #5
This is what i did...i m stuck after this!
 

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  • #6
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
If mass B moves up ##\delta##, how much does the pulley that supports A move down?
 
  • #8
Chestermiller said:
If mass B moves up ##\delta##, how much does the pulley that supports A move down?
Is it 3##\delta##
 
  • #9
Vv anand said:
Is it 3##\delta##
No. Look at the diagram carefully.
 
  • #10
Chestermiller said:
No. Look at the diagram carefully.
Oh is it 4 ##/delta##
 
  • #11
Vv anand said:
Oh is it 4 ##/delta##
Just because of the middle string attached to the mass coming from the upper left pulley
 
  • #12
Vv anand said:
Oh is it 4 ##/delta##
No. Look carefully. The wire between pulley
 
  • #13
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
Chestermiller said:
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
 
  • #15
Vv anand said:
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
 
  • #16
Vv anand said:
Yes sir...i got that the ##/pulley## is moving delta downwards
Wrote that upper comment by mistake...
 
  • #17
So if ##v_B## is the upward velocity of mass B, what is the downward velocity of the pulley that supports A?
 
  • #18
Chestermiller said:
So if ##v_B## is the upward velocity of mass B, what is the downward velocity of the pulley that supports A?
Sir vb
 
  • #19
Vv anand said:
Sir vb
But this brings me to the solution that vb=2/3.
 
  • #20
Vv anand said:
But this brings me to the solution that vb=2/3.
Yes. So?
 
  • #21
But sir the solution is 0.5 m/s
 
  • #22
Vv anand said:
But sir the solution is 0.5 m/s
I guess I don't agree.
 
  • #23
Chestermiller said:
I guess I don't agree.
I confirm 0.5m/s.
 
  • #24
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?
 
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Likes Vv anand
  • #25
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?
 
  • #26
Merlin3189 said:
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?
Like this?
 

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  • #27
Vv anand said:
Like this?
Yes, that works.
 
  • #28
@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
 
Last edited:

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

1. How do Newton's laws of motion apply to a block in a pulley system?

Newton's laws of motion apply to a block in a pulley system because they describe the relationship between the forces acting on an object and its resulting motion. In this case, the block experiences both gravitational force and tension force from the pulley system, which can be calculated using Newton's laws.

2. What is the formula for finding the velocity of a block in a pulley system?

The formula for finding the velocity of a block in a pulley system is v = (a * t) + v0, where v is the final velocity, a is the acceleration, t is the time, and v0 is the initial velocity. This formula is based on the second law of motion, which states that the acceleration of an object is directly proportional to the net force acting on it.

3. How does the number of pulleys in a system affect the velocity of the block?

The number of pulleys in a system does not affect the velocity of the block, as long as the pulleys are frictionless. This is because according to the third law of motion, for every action, there is an equal and opposite reaction. Therefore, the tension force acting on the block is the same regardless of the number of pulleys, resulting in the same acceleration and velocity.

4. Can Newton's laws of motion be used to calculate the velocity of a block in a pulley system in real-life situations?

Yes, Newton's laws of motion can be used to calculate the velocity of a block in a pulley system in real-life situations. However, it is important to consider factors such as friction and the weight of the pulleys, which may affect the accuracy of the calculations. In some cases, other variables may also need to be taken into account, such as the mass and shape of the block.

5. How can the velocity of a block in a pulley system be measured experimentally?

The velocity of a block in a pulley system can be measured experimentally by using a motion sensor to track the position of the block over time. This data can then be used to calculate the velocity using the formula v = (xf - x0) / t, where xf is the final position, x0 is the initial position, and t is the time. Alternatively, the velocity can also be measured using a ticker-tape timer, where the time between each mark on the tape can be used to calculate the velocity.

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