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Two blocks tied to a string with mass and accelerating

  1. Dec 17, 2011 #1
    1. The problem statement, all variables and given/known data
    The figure shows two 2.5 kg blocks connected by a rope that has a mass of 450g. The entire assembly is accelerated upwards at 7.4 m/s^

    What is the tension at the bottom end of the rope, near block B

    What is the tension at the at the top end of the rope, near block A




    2. Relevant equations
    I believe the relevant equation needed is just

    Fnet = m * a

    and Fnet = Sum of all forces


    3. The attempt at a solution
    So I am sure I got the first part correct, I made

    Fnet = Tension - Mb * g
    Mb * a = Tension - Mb * g
    (Mb*a) + (Mb*g) = T
    (2.5*7.4)+(2.5*9.8) = 43
    Tension = 43

    (correct me if I'm wrong for the above)

    Now the second part I actually have no clue how to get started, I can't think up an equation that makes sense and could isolate for T
     

    Attached Files:

    Last edited: Dec 17, 2011
  2. jcsd
  3. Dec 17, 2011 #2

    PeterO

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    Homework Helper

    I don't see any diagram attached?? but assuming it is two masses above each other, with the rope in between..

    You could replace the situation you are presented with with a three mass system and mass-less strings.

    The third mass is one of 450g in between the two 2.5 kg blocks.

    The tension in the lower string would then be the same as the tension near block B that you have calculated [presumably correctly; I have not checked your working/answer].
    The tension in the top string would be same as the tension near block A that you are seeking.
    As I said, I have not checked your work so far, just offering a conceptual way to proceed with your calculations.
     
  4. Dec 17, 2011 #3
    Oh wow, that's a really cool approach to this question... I got the correct answer through your way :D

    But I'm kinda curious to why you could change the question like that and it would work... Could you explain please? THANKS!
     
  5. Dec 17, 2011 #4

    PeterO

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    Homework Helper

    The centre of the rope is only important if you are working out what is happening in the centre of the rope. Since you were calculating what happens at each end of the rope, you can include the rope as "just another 450g body" rather than a long object of some mass.

    I have seen questions like this where they want to know "if the rope is 1m long, what is the tension 30 cm from body A?" or similar.

    Even so you could then consider that 135g of the rope is above that point and 315g below; break in into a 4 body system and find the tension in the middle string, with the masses [from the bottom] 25. kg, 315g, 135g, and 2.5 kg.

    note: 30cm is 30% of the 1m rope; 30% of 450g = 135g etc.
     
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