Math Question

[philodynia]

How much impact force would a 200 pound person have on a surface, if they were falling from one foot above it. Is it doubled for two feet? Three feet?

[ASEI]

Well, the force (N, lbf) would depend on the impulse distribution as they hit the surface.

The momentum a person has after falling 1 ft onto the surface is proportional to their mass times their velocity.

p = mv.

Their velocity after falling one foot would be
v = gt
d = 1/2*gt^2

v = (2*g*d)^0.5

(2*32 ft/sec^2*1ft)^0.5 = 8 ft/sec.
p = 200 lbm ft/sec = (200/32) slug ft/sec

The impact impulse actually rises with the square root of height.

[philodynia]

If I could read and understand that all, and come up with my answer, I'm guessing I wouldn't have had to ask in the first place. :wacko:

[Littlemews]

Let me try :
By using Newton's simple equation
Impact Force = kg x m /s^2

200 pound (lb) = 90.72 kilogram
1 ft = 0.3048 m
Second, let's pretend it as 1 sec.

LOL 27.65 kg.m/s2

If the ft is double : 55.30 kg.m/s2

Triple : 82.95 kg.m/s2

Well sry if I am wrong... I am suck in Math/physic, but anyway...

[tony873004]

Originally posted by philodynia@Aug 21 2004, 12:04 PM
How much impact force would a 200 pound person have on a surface, if they were falling from one foot above it. Is it doubled for two feet? Three feet?

Since you're asking for force,

f = m / a

you need to know mass and acceleration

your mass is 200 pounds * 0.45, or appx 90 kg.

your acceleration is how fast your speed changes from your final velocity from the fall, to 0.

so this implies that you need to know what kind of surface you're landing on. A matress would give you less force than a concrete floor. Also, the type of shoes you were wearing would make a difference. Hard soled shoes would produce a greater force than a sneaker. That's why a hard sole shoe makes a louder noise. It's also why a sneaker is called a sneaker.

[damienpaul]

Isn't f = ma i.e. Newton's Second Law is force is equal to mass multiplied by acceleration

[Tinaa]

If he is falling down to Earth wouldn't his acceleration be 9.8 m/s^2?

[JESMKS]

Mass is not the same as weight. Mass is weight divided by the acceleration of gravity. The 200 pound man weighs 90.9 kilograms. His mass would be 90.8 divided by 9.8m/s2
Jack

[tony873004]

Originally posted by damienpaul@Aug 22 2004, 09:00 AM
Isn't f = ma i.e. Newton's Second Law is force is equal to mass multiplied by acceleration

You're right, I made a typo. It's f=ma, not f=m/a.