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Multiple Pulleys problem

  1. Oct 24, 2011 #1
    1. The problem statement, all variables and given/known data

    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



    2. Relevant equations

    Fnet = ma ?


    3. 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
     
  2. jcsd
  3. Oct 24, 2011 #2

    PeterO

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    Put a few words in red to draw your attention to them.
     
  4. Oct 24, 2011 #3
    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?
     
  5. Oct 24, 2011 #4

    PeterO

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

    In a short period of time, B will move 3 cm to the right [it is travelling 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.
     
  6. Oct 24, 2011 #5
    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.
     
  7. Oct 24, 2011 #6

    PeterO

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    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 travelling at twice the speed of B - so 60cm/sec.
     
  8. Oct 25, 2011 #7
    I get it now, thanks.
     
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