What is the Velocity of Point P in a Multiple Pulleys System?

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Homework Help Overview

The problem involves a system of multiple pulleys and the velocities of blocks A and B, as well as point P. The original poster presents a scenario where block B moves to the right at a constant velocity of 30 cm/s and poses questions regarding the speeds of block A and point P based on this information.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants discuss the relationship between the velocities of blocks A and B, and point P, questioning how the movement of block B affects the other components in the system. Some participants explore the implications of constant velocity and acceleration, while others consider the geometry of the pulley system and the movement of the string.

Discussion Status

There is an ongoing exploration of the velocities involved, with some participants suggesting that point P moves at a different speed than block B. Confusion arises regarding the correct interpretation of the problem, with various interpretations of how the movement of block B influences point P's velocity being discussed.

Contextual Notes

Participants note the lack of information regarding the masses of the blocks and the specific mechanics of the pulley system, which may affect their reasoning. The problem is framed within the context of homework constraints, focusing on speed rather than forces or work.

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Homework Statement



The block B moves to the right with a constant velocity of 30 cm/s. Given this, which of the following is correct:

1. Speed of block A is 15 cm/s
2. Speed of point P is 60 cm/s
3. Speed of point P is 30 cm/s
4. Speed of block A is 40 cm/s



Homework Equations



Fnet = ma ?


The Attempt at a Solution



I don't know where to start. May be I will have to take each block separately, but I do not know the mass of either A or B nor the velocity of B.

http://www.pictureshack.us/images/346Q.png
 
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Quantum Mind said:

Homework Statement



The block B moves to the right with a constant velocity of 30 cm/s. Given this, which of the following is correct:

1. Speed of block A is 15 cm/s
2. Speed of point P is 60 cm/s
3. Speed of point P is 30 cm/s
4. Speed of block A is 40 cm/s



Homework Equations



Fnet = ma ?


The Attempt at a Solution



I don't know where to start. May be I will have to take each block separately, but I do not know the mass of either A or B nor the velocity of B.

346Q.png

Put a few words in red to draw your attention to them.
 
The velocity of A is uniform and in the same direction, 30 cm/s to the right and therefore the acceleration is zero. Since acceleration is constant throughout the system, B should also move with uniform velocity (a = 0).

F = W = ma. Since a is zero, does this mean no work is done? How do I find the velocity of the block A or the point P?
 
Quantum Mind said:
The velocity of A is uniform and in the same direction, 30 cm/s to the right and therefore the acceleration is zero. Since acceleration is constant throughout the system, B should also move with uniform velocity (a = 0).

F = W = ma. Since a is zero, does this mean no work is done? How do I find the velocity of the block A or the point P?

This problem has nothing to do with Force, Work, Acceleration, mass or friction. It is all about speed -thus the distance traveled each unit of time.

In a short period of time, B will move 3 cm to the right [it is traveling at 30 cm/sec]
What happens to the length of the top string while that happens?
Where does that extra string come from or go to?
How far will P and A move in that same time then?

Given the options, you can hope that P moves either 6 or 3 cm, Or A moves 1.5 cm or 4 cm.
More importantly, only one of those had better happen or there is more than one correct answer.
 
I think the point P should also move with the same velocity as block B as the string at the top increases in length. I thought the answer would be choice (3), i.e. 30 cm/s, but apparently this is wrong and the answer is given as (2), i.e. 60 cm/s. This has me confused.
 
Quantum Mind said:
I think the point P should also move with the same velocity as block B as the string at the top increases in length. I thought the answer would be choice (3), i.e. 30 cm/s, but apparently this is wrong and the answer is given as (2), i.e. 60 cm/s. This has me confused.

If you put a reference point on the top string - call it Q - and consider the 3 cm move I suggested then ...

Q will be 3 cm further from the top pulley [Q is tied to the wall and the pulley is tied to B, which has moved 3 cm to the right].

That means the top string is 3 cm longer that it was.

That can only happen if 3 cm of string passes around the top pulley.

That will mean P moves 3 cm closer to the pulley; a pulley that has moved 3 cm.

Thus point P must have moved a total of 6 cm; meaning P is traveling at twice the speed of B - so 60cm/sec.
 
I get it now, thanks.
 

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