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Incline angle for accelerating cart and Tensions in strings for a suspended mass

  1. Sep 18, 2016 #1
    1. The problem statement, all variables and given/known data
    Hi all, I have solved these problems just wanted to see if it's all ok

    problem 1:
    a trolley starts at the lowest point of a diagonal plane with a 20m/s speed. Its acceleration is 4m/s^2 going downhill, the trolley goes up then slows until it reaches 0 speed and then goes down the plane with the same acceleration
    a. what is the slopes incline? Its is known that the trolley moves without friction?

    problem 2:
    A weight that has m = 12Kg is pendent in rest on a string attached to two other strings and creating an identical β = 60° with the ceiling, calculate the tension of all strings

    2. Relevant equations


    3. The attempt at a solution

    solution 1:

    upload_2016-9-18_20-38-33.png


    V0 = 20m/s

    a = -4m/s2

    g = 10m/s2

    m1g • sinα = m1a

    N = m1g • cosα

    -m1g • sinα = m1a

    Sinα = a/-g

    Sinα = -4m/s2/-10m/s2

    α = 23.58°


    solution 2:

    upload_2016-9-18_20-39-23.png


    T1 = mg

    m = 12Kg

    mg = T1 = 120N

    T1 = T2cos30° + T3cos30°

    T1 = cos30° • (T2 + T3)

    120N = cos30° • (T2 + T3)

    T2 + T3 = 120/cos30° = 138.56

    T2sin30° = T3sin30°

    T2 + T3 = 138.56

    2T = 138.56

    T2 = T3 = 69.3

    TY!
     
  2. jcsd
  3. Sep 18, 2016 #2

    kuruman

    User Avatar
    Homework Helper
    Gold Member

    Both solutions look OK.
     
  4. Sep 18, 2016 #3
    Ty very much!
     
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