# Deceleration force question

1. Apr 11, 2010

### wirenut67

Greetings,

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

So
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.

Thanks!

Mike

2. Apr 11, 2010

### Staff: Mentor

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.

3. Apr 11, 2010

### wirenut67

Are you telling me that mass will be 150 LBS divided by 32 slugs?

This is the part I am not understanding.

4. Apr 11, 2010

### Lsos

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.

5. Apr 11, 2010

### Staff: Mentor

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).

6. Apr 11, 2010

### wirenut67

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?

7. Apr 11, 2010

### Staff: Mentor

Yes. (But the units for acceleration are ft/s², not ft/s.)

8. Apr 11, 2010

### wirenut67

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.

Mike

9. Apr 11, 2010

### wirenut67

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?

10. Apr 11, 2010

### Staff: Mentor

Yes.

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

5.9 ft/s /.5 s = 11.8 ft/s²

11. Apr 11, 2010

### wirenut67

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?

12. Apr 11, 2010

### Staff: Mentor

All good.

Weight = mass X g(acceleration due to gravity)

so:

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] =

13. Apr 11, 2010

### wirenut67

mass = [150 lbs]/[32 ft/s²] =4.6875 slugs?

14. Apr 11, 2010

### wirenut67

So then

4.6875 slugs x 11.8 ft/s ^2 is a force of 55.31 slugs or 55.31 lbs of force?

15. Apr 11, 2010

### Staff: Mentor

The force will be in pounds, not slugs. (The mass was in slugs.)

16. Apr 11, 2010

### wirenut67

So the final result is that the force is 55.31 lbs of force?

17. Apr 11, 2010

### Staff: Mentor

Right. That's the average force for the given acceleration.

18. Apr 11, 2010

### wirenut67

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

So

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

then

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)

So

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

So

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.

Mike

19. Apr 11, 2010

### Staff: Mentor

Looks good to me!

20. Apr 11, 2010

### wirenut67

Again Al many thanks!

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