Monday, August 18, 2003

A Physics Exercise for the Lead-Footed: Solution

Determining the height of the building Larry would have to throw the child from, in order to inflict injuries comparable to those caused by hitting it with a half tonne vehicle at 60 kph, is a relatively simple problem, which can be solved easily by anyone with a knowledge of high school physics (circa 1971). The simplest solution involves 2 stages:

Stage 1. Calculate the kinetic energy of Larry's car at the time it strikes the child. This is given by the equation:

Ek = 0.5mv2

Before we calculate this quantity, it is convenient to perform the following conversions:

60 kph = 60,000/3600 = 16.67 m/sec
0.5 tonne = 500 kg

substituting these values into the equation for kinetic energy gives the result:

Ek = 0.5 * 500 * 16.672
i.e Ek = 69440 kg m2/sec2

Of this, according to our assumptions, at most 6944 kg m2/sec2 is transferred to the child in the collision, causing injury to the child.

Stage 2. Calculate the distance that the child would have to fall under the influence of gravity to acquire this much kinetic energy. This can be done using the work equation:

w = Fd

which we re-arrange (with one substitution), to give:

d = Ek/F

A body falling under the influence of gravity experiences a force (F) of 9.8 kg m/sec2 for each kilogram of mass. With this piece of information it is easy to calculate d:

d = 6944/(9.8 * 20) = 35m

Finally, dividing this result by 5 gives the answer to our question: Larry would have to throw the child of a building at least 7 storeys tall to produce injuries as serious as those caused by the collision.

Note: As the kinetic energy of the car varies with the square of its speed, halving the speed of the car will the height of the building by a factor of 4, to 8.75 metres or approximately 2 stories. Similarly, Larry need only increase his speed to 85 kph to inflict injuries equivalent to throwing the child off a 14 storey building.

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