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Homework Help: Tractive effort using D'alemberts principles

  1. Jun 13, 2013 #1
    Hello this is my last questions i have to finish the year, the problem i'm having is finding the correct way to work it out. I've looked at others but there their problem has differences and what units to use.

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

    A vehicle of mass 750kg accelerates up an incline of 1 in 10 (sine) increasing its speed from 20 kmh^-1 to 60 kmh^-1 in a time of 8.5 second; if the frictional resistance to motion is 0.5kN. making use of D'alembert's principles; Determine:

    1. the tractive effort between the driving wheels and the road surface.
    2. the work done during the period of acceleration
    3. the average power developed
    4. use energy method to confirm your answers in 2.

    2. Relevant equations

    1. tractive effort = change in ke + change in pe
    pe= mgh
    ke= 1/2MV
    initial ke = mass/2 x v(intial time)^2
    final ke = mass/2 x v(end time)^2
    time taken = change in velocity/acceleration
    work done = fs
    power = work done/time taken

    3. The attempt at a solution

    1. tractive effort

    initial Ke = 750kg/2 x (no initial time so i used 1) = 375
    final Ke = 750kg/2 x 8.5^2 = 27093.75
    change in Ke = 27093 - 375 = 26718

    Pe = 750 x 9.81 x 40sin( i'm not sure how to get height

    2. work done = f x (20kmh - 60kmh) = f x 40kmh
    acceleration = v^2(final time) - (time taken)8.5^2/2s
    f = 750kg x acceleration

    3. power = work/8.5s

    Thank you very much for any help in advanced.
    Last edited: Jun 13, 2013
  2. jcsd
  3. Jun 13, 2013 #2


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    Science Advisor
    Homework Helper
    Gold Member

    Ouch, you are making all sorts of errors. Are you familiar with D'Alembert's Principle? If not, at least use Newton's laws, although the problem asks otherwise; anyway, your only attempt was (incorrectly) using energy methods.

    Tractive effort is the tires driving force that acts uphill (gravity and friction act downhill). You have shown it as an energy change, which is wrong.
    Check your equation for Kinetic Energy!
    Convert km/hr to m/s for consistency in units.
    You have different equations for work done.

    Check your change in energy equation .

    It is also unclear whether the problem is looking for net average power or just the average power delivered by the engine. I'm guessing net work (total work) done.

    You've got to start again from scratch on this one. There are lots of concepts you are missing or not applying correctly.
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