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Block Tension question

  1. Nov 3, 2009 #1
    1. The problem statement, all variables and given/known data
    The coefficient of kinetic friction between the 2.0 kg block in figure and the table is 0.350.

    What is the acceleration of the 2.0 kg block?

    2. Relevant equations
    F=uK*Force Normal

    3. The attempt at a solution
    I tried to take the mass's of both the hanging and used them to calculate a net force on the block in the center and then solved for acceleration that way. Here's my work.

    3kg*9.8=29.4N Right Side Tension
    1kg*9.8=9.8N Left Side Tension
    2kg*9.8=19.6N Force Normal




    and it turns out this is wrong please help me out thank you!

  2. jcsd
  3. Nov 3, 2009 #2
  4. Nov 4, 2009 #3


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    you are assuming that the tension is equal to the weight. That is true only if the system is not accelearting. This one is accelerating, so you must use free body diagrams of each block and apply Newton's 2nd and 3rd law.
    isolate each block and solve 3 equations with 3 unknowns.
  5. Nov 4, 2009 #4


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    I've got the same question.

    I've got these three equations:

    m1*a = T1 - m1*g
    m2*a = T3 - T1 - μ*m2*g
    m3*a = m3*g - T3

    Are those right? Solving for a using the first and second equations a=(g(m3-m1))/(m3+m1) which gives a=4.9 which would be the acceleration of the system if the centre mass wasn't there.

    Using that value in the net force equation Fnet = m3(g-a) - m1(g+a) - μ*m2*g gives Fnet=6.86. Solving Fnet=ma for a gives you a=3.43 which is not right the right answer.

    Can anyone tell me where I went wrong? Thanks!
  6. Nov 4, 2009 #5


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    Looks OK, although the acceleration is likely to be in the other direction.
    looks like you cancelled out T1 and T3, in error, using equations 1 and 3. T1 and T3 are not equal
    This is not true. Correct your method of solving the 3 equations with 3 unknowns.
  7. Nov 4, 2009 #6
    are you by any chance doing mastering physics?
  8. Nov 4, 2009 #7


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    Ahh you're a life saver. Thanks a bundle!

    I sure am. Combine those three equations I posted and you'll get the right answer.
  9. Nov 4, 2009 #8
    ok. and btw who is this? are you going to u of c? physics 211 or 221?. the anser i got was 32 but i dunt think thats right. I used the 1st and 2nd equations to get T1 and T3 and plugged them into the 2nd equation. can u tell me wat i did wrong?
    Last edited: Nov 4, 2009
  10. Nov 4, 2009 #9
    ok now i got 8.2 as in answer. is that right?
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