# F = ma in free falling?

According to F = ma, the force acts on an object would be a constant when free falling. Then what kills a person when he falls from 100 m while not injured if the height is 0.1 m ?

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The energy of the deceleration.

The Force acting on a falling body is its weight. On Earth, this will result in an acceleration of 9,8 m/s per second.

Falling from 100 m, it will take you 4,5 seconds.

Therefore, your speed (when you reach one millimetre above the sidewalk) is a tiny bit over 44 m/s (almost 160 km/h, approx. 100 mph).

The constant force needed 4.5 seconds to bring you up to that speed.

However, the sidewalk will stop you in the time it takes to squish your body by (less than) half your thickness; let's say a quarter of a metre.

Your speed will have to go from 44 m/s to 0 m/s over that distance of 0,25 m.

The time it takes for the sidewalk to stop you depends on the upwards acceleration imposed by the sidewalk.

0,25 = (1/2) a t^2

44 = a t

solving both equations for a, we get

a = 2 * 0,25 / t^2

a = 44/t

Since a has the same value for both equations:

0,5 / t^2 = 44/t

cross multiply

t/2 = 44 t^2

t = 88 t^2

since t is not zero (you cannot stop instantaneously - your body does take some time to go squish), we can divide both sides by t

1 = 88 t

t = 1/88 of a second

Then, going back to v = a t, and knowing the values v=44 and t = 1/88, we get

a = v/t = 44 / (1/88) = 3872 m/s^2

The force with which the sidewalk stops your body is almost 400 times your weight.

THAT is the force that stops you.

It is not so much the fall that kills you... it is the sudden stop.

• oldprof
Lv 7
1 month agoReport

It is the upward force of the impact that smooshes you.  When your downward momentum decreases suddenly over time, that's due to the braking or impact force F = dP/dT where dP = mdV is that change in momentum.  But Dixon is right in that dP = F dT is the impulse of the falling object.

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• No one dies during the fall when F=ma.  They die when they stop.  No one dies when sitting in a car moving at 100 km/hr.  They die if the stop is SUDDEN. They don't die if the brakes are applied and the car slows gently.   People don't die shooting a bullet.  They die when the bullet is stopped SUDDENLY ( by you).

The factors that create the high force are the speed involved, the mass and the TIME taken in which to stop.  F = m*v / t

People have died from falling a very small distance if they hit a hard head onto a hard cement pavement because the time of collision is small.

People survive a 10 m fall from a diving platform ( or even 30 + m at Acapulco) because the time of collision with the water is quite large.  But don't try a bellywhacker from the same heights

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• Anonymous
1 month ago

not at all in my opinion

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• The "a" value is much higher. (At impact)

• Tom S
Lv 7
1 month agoReport

"a" is generic acceleration, "g" is specific to "falling body" the acceleration of gravity near Earth's surface. When a falling object hits the ground its acceleration is defined by the distance at which it goes from its speed just before hitting the ground to stopping, deceleration if you will.

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• Generally a person is killed when the entire F is expended in less than a second by the sudden stop at the bottom.

• 56 Ya1 month agoReport

What entire F ? The F is the same from falling 100m and 0.1m.

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• What injures you is the force that the ground exerts to decelerate you upon landing. The greater the speed you have when hitting the ground, the greater the deceleration needed to stop you over a few centimeters, the greater the force.

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• Δp, where p = mv

• oldprof
Lv 7
1 month agoReport

Actually impulse is dP = mdV + dm V = F dT where dm = 0 most of the time; so we have m dV = F dT or ta da, F = m dV/dT = mA where A is the deceleration upon impact.

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• It is your speed when you hit the ground that matters. You accelerate as you fall. The longer you fall, the greater your speed. if your speed is very high when you hit the ground, you are squashed.

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• F = ma

then

a = F/m

that is, the object falling accelerates (at the rate of 9.8 m/s²) while it is falling, that means it falls faster and faster. at 100 m, the speed is about

v = √(2gh) = √(2•9.8•100) = 33 m/s

whereas from 0.1 m

v = √(2gh) = √(2•9.8•0.1) = 1.40 m/s

much slower, less prone to cause injury.

note that injury has nothing to do with the force of gravity while falling, but the speed at which it hits the ground, when all that speed has to change to 0 in a fraction of a second, causing huge de-accelerations, which breaks bones etc.

• billrussell42
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