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? Why does F=ma instead of F=mv ?

  1. Jul 22, 2012 #1
    I know this is probably a complete n00b question, but I have tried all over the www and couldn't find it explained.

    Correct any of these premises if they are wrong, maybe that's my problem, but...

    velocity is current speed and acceleration is change in speed.

    So, if something is moving at a constant speed, it's acceleration is zero.

    So if a car (say 2000kg) is travelling at a constant speed of say 70mph on the motorway, and I like to have a picnic in the center lane, and that car hits me, the force it exerts should be zero because F=2000 x 0 which is zero so no force exerted on me?

    Yet I'm still thinking I'd be in trouble.. So what would cause me trouble if not a force exerted on me..

    I assume my misunderstanding is something very basic and obvious.

  2. jcsd
  3. Jul 22, 2012 #2


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    So far so good.

    Assuming no friction or air resistance, then sure, the car doesn't have a force on it. In reality, it does. Still, you are sitting in the middle of the highway moving at zero velocity. After you are hit, do you think you will still be moving at zero velocity? Certainly not. You would be accelerated to effectively the same speed as the car and over a very short time, meaning a large acceleration and a large force to go with it.
  4. Jul 22, 2012 #3


    Staff: Mentor

    For determining the force exerted on you the important thing is your acceleration. If you are sitting at your highway picnic and no car is hitting you then you are at 0 mph and remain at 0 mph so you are not accelerating and there is no force. When the car hits you go from 0 mph to 70 mph almost instantaneously so you accelerate dramatically due to the very large force acting on you.

    The car, meanwhile, has also accelerated. It has much more mass than you do, say 20 times as much. So while you accelerate by 70 mph the car decelerates by 3 or 4 mph. The force required to do so leaves a big dent in the fender, plus all of the mess from your picnic.
  5. Jul 22, 2012 #4
    Probably the more important question is ... why would someone be having a picnic in the middle of the motorway?
  6. Jul 23, 2012 #5
    If a car hitting you would exert 0 force...then why not? Hence OP's question.
  7. Jul 23, 2012 #6
    It should be

    F = ma


    KE = 1/2mv^2

    For accelerating systems, F=ma, determines the force required to ACCELERATE the body. This is not the energy the body possesses.

    The situation you are describing, constant speed of car, the KE formula does what you want, determines the kinetic energy that the body possesses. i.e. how hard it "hits" something.
  8. Jul 23, 2012 #7
    Correct any of these premises if they are wrong, maybe that's my problem, but...

    So, is this a premise or a conclusion? If it's a premise, where did you get it from, because it certainly looks wrong. If it's a conclusion, you made a non-sequitur logical fallacy, since it does not follow from your previous premises.

    Do you know that 2nd Newton's law should be applied to one body at a time? Your premises are about the car, and it seems to me you are wondering if a force would be exerted on an unlucky object in the middle of the road.
  9. Feb 16, 2014 #8
    I think you should use this relationship; p = mv (which is Momentum).
    p; the affect on you. So to calculate that:
    p = 2000 (kg) x 70 (mph) = 140,000 kg.mi/h
  10. Feb 16, 2014 #9


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    No,Acceleration is change in velocity

    Not necessarily.If the object is changing direction.(Think of centripetal motion.)

    Force=Change in momentum/time taken
    Say you have 50kg and after the car hit you,your velocity increases to 50m/s(Common sense) in 5 seconds
    Force exerted on you=##\frac{mv-mu}{t}=\frac{50*50-50*0}{5}=500N##
    So the car exerted 500N of force on you.

    (That's the net force acting on the car
    Using F=ma,
    The net force on car is 0N yes.But it's moving at constant velocity then how can there be no force?
    Ans:The net force is zero(That does not mean there are no forces)

    Force exerted on you,
    F=50*a(You will surely accelerate,the car won't go through you.)
  11. Feb 16, 2014 #10


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    When the car hits you the car will slow down (slightly) and you will be accelerated (significantly). So the acceleration isn't zero.
  12. Feb 16, 2014 #11


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    Two-year old thread that did not need to be resurrected. Locked.
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