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Tension Problem Set

  1. Nov 1, 2015 #1
    1. The problem statement, all variables and given/known data
    Find the Acceleration of the system and the tensions in the three ropes.

    *If you can't see the picture there's a triangle (ABC), a train of four objects and three pulleys (one exactly at each corner). Side AC (hypotenuse) at the bottom, side AB to the left and side AC to the right.
    Angle A=37
    Angle B=53
    Angle C=90
    There is only kinetic friction between A and B of 0.125.

    mass A= 10kg (hangs straight off the pulley at Angle A)
    mass B= 5kg (on AB)
    mass C= 10kg (on BC)
    mass D= 20kg (hanging off the pulley at Angle C)

    Up is positive

    2. Relevant equations


    3. The attempt at a solution
    I got an acceleration of 28.96m/s/s but I'm fairly sure it's wrong lol. I used these equations using scalar values:

    m1: Fnet= T1 - Fg
    10a= T1 - (10)(10)
    T1= 10a+ 100

    m2: Fnet= T2 -T1 - Fres - Fg//
    5a= T2 - T1 - (0.125)(50cos37) - 50sin37
    T2= T1 + 5a + 35.08

    m3: Fnet= T3 + Fg// - T2
    10a= T3 + 100sin53 - T2
    T3= T2 + 10a -79.86

    m4: Fnet= Fg - T3
    20a= 200 - T3
    T3= 200-20a

    After finding these four equations I just started at the last equation and kept substituting from there. IMG_0094[1].JPG IMG_0094[1].JPG
     
  2. jcsd
  3. Nov 1, 2015 #2

    TSny

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    Your equations look correct. But as you noted, your final answer for the acceleration can't be correct. ( It's greater than free fall acceleration.) I guess you will need to check your algebra. It's easy to slip up on a sign or something.
     
  4. Nov 1, 2015 #3
    Is this how you would approach and solve this question?
     
  5. Nov 1, 2015 #4

    TSny

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    Yes. But what would happen if you added all the red equations below:
     
  6. Nov 1, 2015 #5
    Yeah I tried it again and I got 7.66m/s/s. I probably messed up in my substitutions somewhere along the way.
     
  7. Nov 1, 2015 #6

    TSny

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    Darn. That's not what I get. Of course I could be making an error in solving the equations. (But I did check my work.)
     
  8. Nov 1, 2015 #7
    Lol idk, I'll try the question with vectors instead of vectors maybe.
     
  9. Nov 1, 2015 #8

    TSny

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    I still like my suggestion in post #4.:smile:
     
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