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Two blocks sliding down an incline

  1. Oct 15, 2013 #1
    1. The problem statement, all variables and given/known data
    The figure shows two packages that start sliding down a 20 degree ramp from a rest a distance d=6.6m along the ramp from the bottom. Package A has a mass of 5.0kg and a coefficient of friction 0.20. Package B has a mass of 10kg and a coefficient of friction of 0.15. How long does it take package A to reach the bottom?

    Illustration shows A closer to the ground on the ramp, with B directly behind (and in contact with) it.


    2. Relevant equations



    3. The attempt at a solution

    I made a free body diagram for each block.

    A
    ---
    m = 5kg
    mu_k = 0.20
    f_k = 9.21 N
    n = 46.04 N
    F_G_x = -16.76 N
    F_G_y = -46.04 N

    B
    ---
    m = 10kg
    mu_k = 0.15
    f_k = 13.82 N
    n = 92.1 N
    F_G_x = -33.52 N
    F_G_y = -92.1 N

    ------
    Third law stuff:
    F_(a on b) = F_(b on a) = simply 'F' below.
    a_a = a_b (acceleration constraint)

    ---
    sum of x for A: -7.55 + F = ma = (5)(a)
    for B: -19.7 + F = ma = (10)(a)

    solve the system of equations:

    a = -2.43 m/s^2

    kinematics:

    t = 2.335

    But -- my answer is wrong. Why?

    Thank you
     
  2. jcsd
  3. Oct 15, 2013 #2
    you have not taken proper sign with F.

    Draw and show, your free body diagram. If you check FBD, it will become clear that the direction of F is different in both the case but you have taken same direction for both mass. Balance forces again to clearly see the mistake.
     
  4. Oct 15, 2013 #3
    I will try it out, thank you
     
  5. Oct 15, 2013 #4
    okay!
     
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