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Kinetic energy and momentum (Conceptual Question)

  1. Feb 21, 2012 #1
    1. The problem statement, all variables and given/known data

    The two toy cars shown in the figure, with masses as given in the figure, are ready to race. Both cars begin from rest. For each question, state whether the correct answer is car A, car B, or whether the two cars have equal values for the parameter in question.

    For the next three parts assume that the cars’ motors supply the same force to each car over the course of a 1.0-meter race.

    Car A mass= 1000g

    Car B mass= 800g

    I know that A) Which car crosses the finish line 1.0 away first?

    => Car B wins because it has less mass and more acceleration therefore more force.

    B) Which car has the larger kinetic energy when it crosses the finish line 1.0 away?

    => Both cars have the same kinetic energy I know that both cars have the same kinetic energy because is a scalar , it does not depend in any other variable than energy. So they both have the same amount of kinetic energy.

    C) Which car has a larger momentum when it crosses the finish line 1.0 away?

    => Car A because car A has a greater mass than car B they both have the same speeds therefore car A it will have more momentum.

    D) Which car has traveled farther after 10^8 ?

    => Car B (I really don't get this one) (or why)

    E) After 10^8 which car has a larger kinetic energy?

    => Car B (I really didn't understand this one nether)

    F) After 10 which car has a larger momentum?

    => Both cars have the same momentum. (I don't know why both have the same momentum when they both have different masses and same velocity.)

    Help? Can someone explain this to me?? please??
     
  2. jcsd
  3. Feb 21, 2012 #2

    PeterO

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    Homework Helper

    Comments above , and generally.

    Work = Force x distance

    Impulse = Force x time

    Work leads to a change in KE on a flat surface
    Impulse leads to a change in momentum.

    Both these cars are subject to the same force, so variations in Work - KE and Impluse - momentum come about due to differeing distances and/or differing times.

    The different masses mean B accelerates at a higher rate - will thus gain a higher speed, and cover a greater distance - in a given time.

    If the "race" lasts only 1 metre, Car B, which has accelerated more quickly will win, because it is travelling faster.

    Force x distance is the same for both cars; so Ke is the same

    Force x time is greater for Car A, since it takes a greater amount of time to get there.

    If the acceleration is carried out for a set amount of time, then the impulse applied to each is the same; so they have the same momentum.

    In that time, B will have covered a greater distance, so the work done on B is greater than the work done on A; so B will have the greater KE. [remember; work = force x distance]
     
  4. Feb 21, 2012 #3
    Thanks! I can see now the meaning. Is just that i did not quite understood the concept of Work and impulse. Work is the change in KE on a flat surface and impulse is the change in momentum. It all seems clear now. Thanks man!
     
  5. Feb 21, 2012 #4

    PeterO

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    Homework Helper

    I mentioned the flat surface as sometimes these things happen on slopes, and part of the work goes to a change in Potential energy as well.
     
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