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Homework Help: A car is moving by gravity force

  1. Sep 29, 2012 #1


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    1. The problem statement, all variables and given/known data

    In t=0 a car is free from it's chain and can fall freely through a inclined plane (10 degrees)
    rear wheels weight 500 lb each one and have an diameter of eight feet. Front wheel weights 800 lb and have a radius of 2 feet. The body of vehicle weights 9000 lb. Assume that wheels can drift. Obtain a expression for velocity in function of time.

    2. Relevant equations

    Summation of forces = ma
    We have inerce forces and gravity force. gravity force exerted on vehicle equals to Mgsin10

    3. The attempt at a solution
    inertia force formula is Ia, then I should add the forces.

    5.591471 ft/s^2+Ialpha/M=a
    alpha is angular acceleration.
    A condition for simultaneous rotation and translation movement is v=wr
    dw/dt= 1/r(dv/dt)
    5.591471M+I(1/r) dv/dt=Mdv/dt
    and Inertia applies for each rotating element
    5.6M+(I1/r1+I2/r2) dv/dt=Mdv/dt

    Moment of inertia for a wheel=mr^2/2.
    M is the total mass in the system.
    5.6M+(mr^2/2+md^2)/4+ (m1r1^2/2+md2^2)/2))dv/dt=Mdv/dt
    5.6M+( (8m+md^2)/4+(2m1+md2^2)/2)dv/dt=Mdv/dt
    5.6M+( (8000+1000d^2)/4+(1600+800d2^2)/2)dv/dt=Mdv/dt

    D are distances from the axis, they are unknown.
    I only should put the expression from dv/dt and integrate for get a expression for v in function of t.

    I don't know if my solution is right/
    In which step I am wrong?
  2. jcsd
  3. Sep 29, 2012 #2


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    Well, after a few hours I have noticed my mistake.
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