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Tension between 3 blocks of equal mass

  1. Jul 15, 2012 #1
    1. The problem statement, all variables and given/known data

    The problem, verbatum from my textbook...

    Three identical blocks are pulled, as shown, on a horizontal frictionless surface. If tension in the rope held by the hand is 30N, what is the tension in the other ropes?

    The three blocks are tied together by string and a hand is pulling them all with a force of 30 Newtons.

    2. Relevant equations

    Here is where I am having some serious difficulty in understanding the answer to this problem. I know at least one variable in this situation, F, which in the hand is 30 Newtons. A classmate submitted his homework as well all check each others, and his solution was 10N in block 1 and 2, and 20N in block 2 and 3. Now I have a hard time understanding how he came up with these numbers. And frankly a Google search yielded the same thing.

    Allow me to explain a little further on why I do not understand the numbers they came up with. And for the record I would call my classmate if at all possible but it is Sunday evening and is unreachable at this time. In any case, I think they used F=ma as the equation to solve for their given solutions. However, that depends on some variables that have not been given and are assumed. The first of which is a, which they are assuming is gravtiy, and in our textbook we round up from 9.81m/s^2 to 10m/s^2. This is not given in the problem. And in fact, they might be accelerating at another rate, or, not accelerating at all in be in dynamic equilibrium. So I don't understand that portion.

    The second variable is that they used 3(mass)*acceleration @ 10m/s^2. How on Earth did they figure this to be the case? It appears to me that the problem is relying on us to assume things, which I find to be very wrong, and if that's the case everyone's number could be different for all the blocks.

    Please help!

    3. The attempt at a solution

    I think I mentioned my attempts in the previous section, but again, I have tried to use F=ma however I do not have a number to put with a or m in this instance. I am very lost and really do not even know where to begin, let alone solve the problem.

    Also, I ask that you do not solve the problem for me. I want to figure it out on my own as I find be given the solutions a serious waste of effort and time on my part. I am just asking for guidance and help, not the solution. Thank you very much.
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Jul 15, 2012 #2

    PhanthomJay

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    This problem has nothing to do with gravity, and is independent of the mass M (although you can assume a value for M if you wish, but making assumptions sometimes leads to errors). Try looking at the whole system of 3 blocks to solve for the acceleration as a function of M, using Newton's 2nd law. Then draw free body diagrams of the blocks to solve for the unknown tensions, again using Newton 2; the acceleration of each block is the same as the acceleration of the system of blocks.

    Welcome to PF!:cool:
     
    Last edited: Jul 15, 2012
  4. Jul 15, 2012 #3
    Thanks for the speedy reply, I appreciate it.

    I do not understand how to solve as a function of m though. This is Physics 101, however I know what you mean by function so I will try my best at your recommendtion. However, given the problem, I think I can assign any value to the blocks for mass, and than determain what a will be and therefor solve the problem. However, as you said, making assumptions can lead to errors and I would hate to get this problem wrong with how tricky and time consuming it has been for me. I really want to nail this problem and get it right. That little moment seeing it correct on the homework is really quite nice. lol.

    In any case thank you for your advice I do appreciate it. And if you might be able to expand upon it, as in, make it easier to understand, but please don't solve it, I would also be appreciative of that. :-)

    *EDIT*

    Also, when you as a function of m, the functions we do/did in math were just f(x)=x+2 or whatever for the output. If you meant something different, please elaborate.
     
    Last edited: Jul 15, 2012
  5. Jul 15, 2012 #4

    PhanthomJay

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    To solve for the acceleration as a function of M, what i mean is suppose F=Ma and F is 30. Since F = ma, then a = F/M, or a = 30/M. You can assume M =1 or M= 1000 or M = any number, but don't assume if you are not comfortable making assumptions like this.
     
  6. Jul 17, 2012 #5
    1. U must consider the system of 3 masses as a whole.
    2. Think carefully about the acceleration of the three masses.

    If u need more help, ill tell u more about the key points of the problem.
     
    Last edited: Jul 17, 2012
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