[USMA:23491] New Second of time

[John Nichols]

It is not that the equation is F=ma, but that it is the

sum of the forces = ma.

Now it would have had velocity so the damping factor would have come into play as it contacted Newton's head. The displacement from the point of impact till it was stopped brings the stiffness into play.

So assuming that it feel 1 metre (What else would God pick for such an important experiment) and that g is 9.81 in that place on the earth then

it would have taken the square root of 2/9.81 as the fall time being 0.45 seconds, give or take a thousands of a second.

it would have been travelling with a velocity of 4.4 m/s give or take a smidgen.

given a stiffness of the apple of 0.1 GPa and of the human as 1.0 kPa ignoring the increasing stiffness as bone comes into play, probably taking it up to about 10 GPa, limestone is 40 GPa so I am assuming 0.25 of that.

The displacement into the head was about 1 mm. Which means the apple actually fell 1.001 so we can repeat the whole thing and find out that in reality it penetrated 1.001 mm and so on on so forth. until some one points out that it was actually 39.37 inches falling with a velocity of 778.5 inches per George with a travel time of 0.1 Georges ( I have allowed one Imperial George to equal 4.5 seconds. )

Now I stop because the maths is beyond my University level.

Of course if there had been a stiff breeze no.....................

John Nichols


At 02:27 AM 19-11-2002, you wrote:

At 8:57 +1100 02/11/19, Pat Naughtin wrote:

As a side issue, you might like to compare this last average with the apple
that is supposed to have fallen on Sir Isaac Newton's head in his garden at
Woolsthorpe. Presumably Newton's apple had a weight of one newton, and we
can safely assume that the acceleration due to gravity was about the same as
now (say 9.8 m/s^2). Using the formula F = ma, it follows that the mass of
Newton's apple was m = F/m = 1 � 9.8 = 102 grams. It follows that Isaac
Newton's original apple (allowing certain assumptions) was quite small.

Indeed we were quite lucky: imangine that the famous apple was huge, say 500 g, Isaac Newton could well have been knocked out...

Louis

John Nichols BE, Ph.D. (Newcastle), MIE (Aust), Chartered Professional Engineer
Assistant Professor
Texas A&M University
Department of Construction Science
Langford AC
Rm: A414 MD 3137
College Station, TX 77843-3137

Electronic mail: [EMAIL PROTECTED]
Telephone: 979 845 6541
Facsimile: 979 862 1572
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a fronte praecipitium a tergo lupi

in front a precipice, behind a wolf
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