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Physics impulse

  1. Jun 24, 2009 #1

    Ive been trying to get my head around an equation for seatbelts. Hyperphysics has an auto calculator and ive been trying to do it algebraically and still cannot get the same answer.

    Here is what i have done...

    In relation to a car travelling at 50kmph with a driver which weighs 75kg and stops with in 1 foot.
    Car Crash Example

    m = 75 kg, initially travelling at 50kmph = 13.88888889m/s d= 30 cm
    Distance time interval =
    dt = 0.3 m / 13.88888889 m/s = 0.022 s

    During this 220th’s of a second it is decelerated from 13.88888889 m/s to zero, so
    a = dv/dt = 13.88888889 m/s / 0.022 s = 631 m/s^2

    So the impact force is
    F = m x a = 75 kg x 631 m/s^2 = 47348N ....

    But it is completely different answer, i believe my acelleration calculation is wrong BUT cannot seem to find out how
  2. jcsd
  3. Jun 24, 2009 #2


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    Notice that the velocity over the 1 foot is not constant, so the time interval you calculated is incorrect. In fact, you should use the v^2 = v0^2 - 2ax formula to calculate the acceleration (assumed to be constant here), and then the force.

    Hope that gives you the right answer.
  4. Jun 24, 2009 #3
    0 = 192.9 + 2*A*0.3

    so do i...

    0 =192.9 + 2*A*0.3 -2*A*0.3
    - 2*A*0.3 = 192.9
    -2*A*0.3/0.3 = 192.9/0.3
    -2*A = 643

    -2*A/-2*A = 643/-2*A
    0 = 643 / -2*A/A
    0/A = 643 /-2
    A = 643/-2

    A = 643 / -2
    A = 321.5 ms^2 (- Negative due to deceleration... )
  5. Jun 24, 2009 #4
    A/g = 321.5/9.81 = ~33 g's. This deceleration would be pretty rough on anyone. This is why modern cars have collapsible front ends, so perhaps d -> 100 cm and the deceration is reduced to ~10 g's.
  6. Jun 25, 2009 #5


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    Well, even so, it would be for hitting a wall, which would really hurt. Compared to hitting another car, the collision time is a lot shorter.
  7. Jun 25, 2009 #6


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    Dropping dead on the a concrete floor will produce a lot more G's than that, and no drunkard die on me for just that. 33 G is quite reasonable as seatbelts absorb some energy before stopping you. The energy from a 50 Km/h collision should be like a drop from a 9 m height.

    Seatbelts use the fact that you have a certain elasticity in your body, so broken bones or strained muscles are acceptable. Without them you would hit the dashboard which has little elasticity so much of the energy from the impact goes to your vitals (brain etc.)
  8. Jun 25, 2009 #7


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    Yay seatbelts!

    9 m = 3+ stories. Add to that the fact that your centre of mass will travel further than 0.3 m over the deceleration, the deceleration is less than 33 G's. Since a 3 storey fall is likely to break something or another, 33 G's is too much to get through without significant injury.
  9. Jun 26, 2009 #8


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    0.3 m is about right for a seatbelt but dropping on concrete or hitting the dashboard will decelerate you in only a few cm ( 2 - 5 maybe ) that means a 6-15 fold increase in G force experienced, and people still tend to survive 450 G's. There are very few fatal accidents at 50 Km/h that is why it's the European city speed limit.
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