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Acceleration of a vehicle

  1. Mar 6, 2016 #1
    1. The problem statement, all variables and given/known data
    Find the Acceleration of a vehicle at 3k rpm and 5k rpm.
    At 3k the engine produces 65hp. At 5k it produces 155hp.
    Car weight is 1000kg. The wheels are 50cm in diameter. The engine is connected to the wheel via 2:1 ratio transmission. Neglect any losses.
    2. Relevant equations
    kW = HP*0.7457 Nm (torque) = (kW*9550)/RPM
    Total Newtons =Nm*(Gear ratio) / Tire Radius in meters
    Acceleration: MA = F ... Total Newtons / Car weight.

    3. The attempt at a solution
    kW = 65*.7457 = 48kW 48*9550/3000 = 154Nm (torque at 3k rpm)
    154Nm*2/.25m = 1232N
    MA= F... F/M = A 1232N / 1000 = 1.232MS^2 but for some reason that doesnt seem right. Others are getting different results so i'm not sure whos wrong.

    The 5k is the same formulas so no point of posting that as well.

    Thanks for reading.
     
    Last edited: Mar 6, 2016
  2. jcsd
  3. Mar 6, 2016 #2

    billy_joule

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    Looks like you forgot to account for the transmission ratio.
     
  4. Mar 6, 2016 #3
    The Transmission ratio is the 2nd number.

    154Nm*2/.25m = 1232N 154Nm * 2 since 1:2 tranny doubles the torque / the leverage of the tire. No?
     
  5. Mar 6, 2016 #4

    billy_joule

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    Ah, I missed that. In that case I'd agree with your answer.

    I guess this could be interpreted (incorrectly IMO) as:
    engine:wheel = 1:2
    Which results in a ridiculous road speed of 942 km/h @ 5000rpm
     
  6. Mar 6, 2016 #5

    haruspex

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    For what it's worth, I get the same answer by a different route.
    3000rpm=50rps, or 25rps at the wheels.
    25π0.5=39m/s (about 140kph)
    F=P/v=48kW/39m/s=approx 1200N.
     
  7. Mar 6, 2016 #6
    Is the Acceleration in M/S2 correct?
     
  8. Mar 6, 2016 #7

    haruspex

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    making my calculation in post #5 a little more accurate, 1230N. 1230N/1000kg=1.23m/s2.
     
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