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Math Help - Car crash, Seatbetls, impulse

  1. #1
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    Car crash, Seatbetls, impulse

    Also 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 50mph 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 220thís 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
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  2. #2
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    Quote Originally Posted by Dingo View Post
    Also 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 50mph 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 220thís 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
    your acceleration calculation is incorrect ... should be about 316 m/s^2
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  3. #3
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    Quote Originally Posted by skeeter View Post
    your acceleration calculation is incorrect ... should be about 316 m/s^2
    How?
    or how else should i calculate it?
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  4. #4
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    v_f^2 = v_0^2 + 2ad
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  5. #5
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    Quote Originally Posted by skeeter View Post
    v_f^2 = v_0^2 + 2ad
    Where Vf and V0 represent?
    and what forumla is this?
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  6. #6
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    Quote Originally Posted by Dingo View Post
    Where Vf and V0 represent?
    and what forumla is this?
    v_f is final velocity ... 0

    v_0 is initial velocity ... 50 kph

    this is the well-known "no time" kinematics equation.
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  7. #7
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    I get to.... Ive been working on this all night and now swear im brain dead...

    0 = 192.9 + 2*A*0.3

    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...
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  8. #8
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    50 kph = 125/9 m/s

    1 ft = .3048 m

    0 = (125/9)^2 + 2a(.3048)

    a = -(125/9)^2 / [2(.3048)] = -316.439 m/s^2
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