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Force and Momentum

  1. Aug 30, 2009 #1


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    Ive been studying basic mechanics lately and have been trying to understand what "force" really is. First off, heres my understanding of momentum: If you take the mass of a moving object and multiply it by its velocity (just a constant velocity) you get momentum. P=mv. I know that force is measured in newtons. N=ma. Heres my problem... BTW, this is not a homework question so please dont badger me about that...

    Scene 1: Lets say a car with a mass of 100 kg (being to scale isn't the point) is traveling east at a constant velocity of 20 m/s. After 100 meters it hits a wall.

    Scene 2: The same modal car is accelerating at a rate of 10 m/s^2. After 100 meters it hits a wall.

    Since the first car wasn't accelerating, does that mean it didn't exert any newtons on the wall? It had momentum but no force so to my understanding the first car was "forceless" so to speak. Now why does the accelerating car exert force (newtons) on the wall if it hits the wall just like the first car?

    I hope my question made sense. Thanks in advance :)
  2. jcsd
  3. Aug 30, 2009 #2
    In the first case though the car had a constant velocity of 20 m/s it is evident that the car must have started from 0 m/s ie at rest. from there it must have ACCELERATED to achieve this speed of 20m/s. So we cannot say that the Acceleration was ZERO.

    In this case there is an initial acceleration equal to the difference in the initial velocity ie at rest = 0 m/s , and the final constant velocity 20 m/s which comes to be (20- 0)/t = 20/t m/s^2 where t is the time interval taken to reach 20m/s form rest.

    So the car will be having this acceleration which shall be used for any calculation in the particular case where the velocity has remained constant for some time but it did have to rise from Zero to this value and this would not be possible without accelerating the car from rest.

    So the car does have aceleration in the complete scenario as a whole. And so does have Force.

    Hope its clear.
  4. Aug 30, 2009 #3


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    But when the car hits the wall, the car is not accelerating. It has a constant velocity of 20 m/s. Are you saying that once something accelerates and then evens out to a constant speed, it keeps its force from when it started accelerating?
  5. Aug 30, 2009 #4


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    The car will apply a force upon crashing into the wall no matter how it achieved it's speed. Force isn't a property of an object by the way. A force is an interaction between 2 objects; with 1 object, there is no force to speak of. Both cars will be decelerated to 0 from the velocity they have upon slamming into the wall. This change in velocity is due to the force of the wall resisting the impact which results in an acceleration and thus, a force.
  6. Aug 30, 2009 #5


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    Welcome to PF!

    Hi Fuz! Welcome to PF! :smile:
    Force = rate of change of momentum.

    Impulse = total change of momentum.

    That's good ol' Newton's second law :tongue2: … F = d(mv)/dt, I = ∆(mv).

    (I know you usually see it written F = ma, but F = d(mv)/dt is the full version :wink:)

    So the car's momentum is reduced by a total amount equal to the impulse on the wall. :smile:

    (To put it another way: the car decelerates when it hits the wall)
  7. Aug 30, 2009 #6


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    Thanks for the reply Tim. Impulse is new to me so I kinda got confused when you started talking about it.
  8. Aug 30, 2009 #7


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    Hi Fuz! :wink:

    Impulse is just a convenient name for the total force over a period of time (usually a very short period, as in a crash or a bat hitting a ball).

    For some details, see http://en.wikipedia.org/wiki/Impulse :smile:
  9. Aug 30, 2009 #8
    I remember learning about force and momentum back in high school, and it was fun, imo!
  10. Aug 30, 2009 #9
    When the car hits the the wall then it is no longer traveling at a constant velocity, therefore it is decelerating and it exerts a force upon the wall;
  11. Aug 30, 2009 #10


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    Oh so if any object hits another object, the first object will always hit the second object with force regardless of its speed? Does this apply to all physical things? Also, if the first object hits the second object with 10 newtons, could you also say the second object exerted 10 newtons on the moving object? Again, there is always force regardless of speed, correct?
  12. Aug 30, 2009 #11


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    No, it's a lot more complicated than that.

    Force (or rather, impulse) does depend on speed, or rather on change in speed … impulse = change of momentum.

    Have you done "collisions" yet"?

    Total momentum (ie, total of both bodies) is always conserved in a collision,

    so the momentum transferred from one body is the same as that transferred to the other body …

    and impulse is change in momentum,

    so the two impulses are equal and opposite. :smile:
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