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Homework Help: Three Blocks Two Pulleys and a Table

  1. Oct 24, 2009 #1
    This was a problem on an exam I had the other day and I want to know if my attempt was correct.

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

    Please look at the attached image. You have a system of two ideal pulleys set up on a table. Block A is hanging from a string on the left side of the table which passes by a pulley connecting it to block B. Block B is resting on the table, and the kinetic coefficient of friction between the surface of the table and the block is 0.557. Block C is hanging from a string on the right side of the table which passes by a pulley and is attached to Block B. Block C is four times as massive as block A, and block B is three times as massive as block A. When the system is released from rest, block C accelerates downward until it reaches the floor, a distance of 105cm.

    Find: The acceleration of block C and the time it takes to reach the ground.

    2. Relevant equations

    y = y0 + v0yt + 1/2 at2
    N = mg

    3. The attempt at a solution

    I started by trying to find the net force acting on block B in order to find the acceleration of the system. In this case,

    Fnet= FC - (FA + FF)


    Fnet= (4mAg) - 1mAg - ([tex]\mu[/tex]3mAg)


    Fnet= 3mAg(1-[tex]\mu[/tex])

    because mB=3mA you can rephrase the above equation

    Fnet= mBg(1-[tex]\mu[/tex])

    so the acceleration of block B would be g(1-[tex]\mu[/tex]), and plugging in the values I got the answer -4.34m/s2 rounded to three figures. This would also be the acceleration of block C.

    Next I needed to find the time it took block C to hit the ground.

    y = y0 + v0yt + 1/2 at2


    y = 1/2 at2
    t = sqrt(2y/a)
    t = sqrt(2*-1.05m/-4.34m/s2)
    t = 0.695s rounded to three figures

    Did I do this problem correctly? And if not, can you please show me the correct way of doing a problem like this? Thanks.

    Attached Files:

  2. jcsd
  3. Oct 25, 2009 #2
    Now that I review my notes, I think I might have gotten this problem incorrect. Was I supposed to take the net force acting on block B and divide by the total mass of A + B + C to find the acceleration of the system?
  4. Oct 25, 2009 #3


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    Homework Helper

    It is better if you first draw the free-body diagram for all bodies, including the forces of tension in the ropes.

  5. Oct 25, 2009 #4
    what have you meant is correct.
    To find the acceleration , you have to divide by total mass as they are all connected by a string, therefore sharing same a
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