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A bus, a pendulum and acceleration

  1. Feb 27, 2009 #1
    1. The problem statement, all variables and given/known data

    A bus is descending a uniform 20 degree slope. It brakes with constant deceleration. A pendulum moves 10 degrees away from the vertical to the downward side. Find the acceleration of the bus.

    .............|
    ............/|
    ........ ../.|
    ........./10|
    ......../....|......./
    ......O.....|..../
    .............|/
    .........../.|
    ......../....|
    ...../.......|
    ../....20...|vertical
    /_______ |___________horizontal_____





    2. Relevant equations

    F=ma

    3. The attempt at a solution


    I can deduce the x-component of the acceleration:

    ax = g tan 10 = 1.73ms^-2

    The expected answer is 2.0ms^-2. I can't see how to relate the twenty degree slope to the x component of the acceleration to calculate the total acceleration.

    Any help or advice gratefully received...
     
  2. jcsd
  3. Feb 27, 2009 #2

    Doc Al

    User Avatar

    Staff: Mentor

    Careful: The acceleration is not horizontal.

    Do this: Analyze force components parallel and perpendicular to the incline surface.
     
  4. Feb 28, 2009 #3
    Thanks - point taken - I reworked the expressions for Fy and Fx in terms of string tension:

    sumFy = FTcos 10 - mg cos 20

    sumFx=FT sin10 - mg sin 20

    m x ax = mg cos 20. tan 10 -mg sin 20

    ax =g(cos20.tan10 -sin 20)

    N.B. ax is x acceleration with xy co-ordinates of the slope!

    Sadly the result is still 1.72ms^-2

    Perhaps there is an error with FT cos10 and FT sin 10 in the two sum of forces expressions... and perhaps elsewhere...

    Help, advice gratefully received...
     
  5. Feb 28, 2009 #4

    Doc Al

    User Avatar

    Staff: Mentor

    What angle does the string make with respect to the slope?
     
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