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F=ma and momentum question

  1. Jun 6, 2012 #1
    1. The problem statement, all variables and given/known data

    Use the concepts of momentum and Newton’s second law to explain why a motorcycle can accelerate at a greater rate than a large truck.



    2. Relevant equations



    3. The attempt at a solution

    The motorcycle will accelerate at a greater rate because the truck has a greater mass (greater resistance to a change in speed.) This increased rate of acceleration is mathematically proven by the formula a= F/m, which states acceleration is inversely proportional to the mass. In terms of momentum, a mass that experiences a change in velocity (acceleration) has undergone a change in momentum (impulse). As the mass of the motorcycle is smaller, it will take less force and time to move it, thus increasing it's rate of acceleration.

    Is that a sufficient answer?
     
  2. jcsd
  3. Jun 7, 2012 #2

    Andrew Mason

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    You are correct that a = F/m and that the mass of the truck is much greater than the motorcycle. But it also has a bigger engine that can provide a much greater force to the wheels than the small motorcycle engine. So I think you have to deal with the relative engine power.

    You could, for example, find out how engine power or torque compares between a motorcycle and a truck and then compare the relative masses.

    AM
     
  4. Jun 7, 2012 #3
    Meanwhile, I don't get what "momentum" has to do with it. Unless that's just an odd kind of reference to F=ma.

    I agree you need to compare the power/weight ratios. Of course engine "power" is really torque multiplying through gears with losses out to the wheels, and the wheels might have more or less traction, but that's probably out of scope of the problem.

    http://www.sportrider.com/weights_measurements/146_motorcycle_weights_measurements/viewall.html
    will tell you that a sport bike weighs about 500 lbs (a Satanic 666 for a K1200GT) so let's say 700 lbs with a rider. Maybe 70 ft-lbs of torque. That means a ratio of 10 lbs per ft-lb.

    A big semi engine might pump out 1000 ft-lb of torque, swamping the bike. BUT that is hauling around 25,000 to 100,000 pounds. That means a ratio of 25 to 100 lbs per ft-lb. That is very very roughly and vaguely why the motorcycle is faster than the truck.
     
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