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Deceleration force question

  1. Apr 11, 2010 #1

    First post here.

    I am trying to calculate the force applied to a 150 lb. person riding in a vehicle that decelerates from 12mph to 8 mph in .5 seconds.

    If I am understanding correctly the formula is:

    Initial velocity-Final Velocity/.5

    12-8/.5 = 8

    The to calculate the force,

    m x d = f

    so mass is 150 lbs

    Deceleration is 8

    so force is 1200 Lbs?

    This does not seem correct to me, any help would be appreciated.


  2. jcsd
  3. Apr 11, 2010 #2

    Doc Al

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    You are trying to apply Newton's 2nd law (F = ma), but you are messing up the units.

    Use standard units for velocity: ft/sec, not mph.

    Mass is 150/32 slugs, not 150 lbs.
  4. Apr 11, 2010 #3
    Are you telling me that mass will be 150 LBS divided by 32 slugs?

    This is the part I am not understanding.
  5. Apr 11, 2010 #4
    This is why I always convert to metric before I do these calculations. I try to avoid any equation with the word "slug" in it like the plague.
  6. Apr 11, 2010 #5

    Doc Al

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    No. The mass is measured in slugs. (32 is the acceleration due to gravity in ft/s^2.)

    In the British system of units, mass is measured in slugs. The weight (force) is related to the mass via weight = mg, where g is the acceleration due to gravity. In that system of units, g = 32 ft/s^2 (approximately).
  7. Apr 11, 2010 #6
    Ok so for the first part I would use:
    Initial Velocity= 17.6 ft/s (12mph)
    Final Velocity = 11.7 ft/s (8mph)
    Deceleration time = .5 seconds
    So then

    17.6-11.7= 5.9 ft/s

    5.9ft/s /.5 seconds = 11.8 ft/s

    Is this correct for the first part of the calculation?
  8. Apr 11, 2010 #7

    Doc Al

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    Yes. (But the units for acceleration are ft/s², not ft/s.)
  9. Apr 11, 2010 #8
    So the final result would be 11.8 Ft/s²?

    Al I really appreciate your patience here. This is just something I am beginning to understand.

  10. Apr 11, 2010 #9
    So written correctly it should be:

    17.6 ft/s²-11.7ft/s²= 5.9ft/s²

    and then

    5.9 ft/s² /.5= 11.8 ft/s²

    Is this correct Sir?
  11. Apr 11, 2010 #10

    Doc Al

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    The units for speed would be ft/s, not ft/s².

    5.9 ft/s /.5 s = 11.8 ft/s²
  12. Apr 11, 2010 #11
    Understood so far.

    So my rate of deceleration is 11.8 ft/s²

    So now I move to force.

    Force= mass x deceleration.

    Is this correct Al?

    So my deceleration is 11.8ft/s²

    Where I am lost is in figuring the mass based on slugs. Can you show me how to do this?
  13. Apr 11, 2010 #12

    Doc Al

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    All good.

    Weight = mass X g(acceleration due to gravity)


    mass = Weight/g(acceleration due to gravity)

    Here we measure weight in pounds, g is 32 ft/s², and the mass is in slugs. So:

    mass = [150 lbs]/[32 ft/s²] =
  14. Apr 11, 2010 #13
    mass = [150 lbs]/[32 ft/s²] =4.6875 slugs?
  15. Apr 11, 2010 #14
    So then

    4.6875 slugs x 11.8 ft/s ^2 is a force of 55.31 slugs or 55.31 lbs of force?
  16. Apr 11, 2010 #15

    Doc Al

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    The force will be in pounds, not slugs. (The mass was in slugs.)
  17. Apr 11, 2010 #16
    So the final result is that the force is 55.31 lbs of force?
  18. Apr 11, 2010 #17

    Doc Al

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    Right. That's the average force for the given acceleration.
  19. Apr 11, 2010 #18
    Al could I bother you for just a second to review this for me.

    I am posting this written like this so please look this over for me.

    We can calculate the force created by braking from 12mph to 8 mph in .5 seconds, and its force upon a 150lb human.

    To calculate the deceleration rate we take this formula:

    Initial Velocity - Final Velocity / time = deceleration rate.

    First we convert mph to ft/s:

    12mph is 17.6 ft/s
    8mph is 11.7 ft/s
    Braking time is .5 seconds


    17.6 ft/s - 11.7 ft/s = 5.9 ft/s


    5.9 ft/s / .5 seconds (time) = 11.8ft/s²

    Now we can figure force.

    Force = mass x deceleration

    deceleration as defined above = 11.8 ft/s²

    Mass has to be converted to slugs
    A slug is weight/g (acceleration due to gravity)


    150lbs/32 ft/s²= 4.6875 slugs. This is the mass in slugs based of deceleration due to gravity.


    Mass= 4.6875
    Deceleration = 11.8ft/s²

    11.8ft/s² (deceleration) x 4.6875 (mass)= 55.31 pounds of force.

    If this is correct than you have done a fantastic job for me AL and it is much appreciated. I thank you for your patience.

  20. Apr 11, 2010 #19

    Doc Al

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    Looks good to me!
  21. Apr 11, 2010 #20
    Again Al many thanks!

    In your opinion would this amount of force create a noticeable reaction from the vehicle occupants?
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