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galileo's experiment

Galileo designed and conducted a set of experiments to determine what affect the weight of an object had on the rate of fall. The obvious experiment was simply to measure the time required for objects of different weights to fall from various heights. However at the time there were no devices available to accurately measure time lapse associated with fall time from realistic elevation levels. Galileo realized that he could achieve his objective by using round balls of various weight and a sloped ramp which the balls would roll down.

In this arrangement, the effective force causing the motion was reduced from full weight of the ball to that component of the force (weight) parallel to the surface of the ramp. He could then adjust the slope of the ramp to increase or decrease the effective force and resultant rate of descent sufficiently that he could observe and adequately measure the time required for travel through various amounts of vertical distance. As a time measurement device he let water drip from one container to a lower one, and then measured the quantity of water exchanged as the balls rolled down pre-selected lengths of the ramp. He repeated the experiment with balls of various weight.


His experimental results showed that the rate of fall was unaffected by variations in the weight of the balls, and that the rate of acceleration was unchanged for different fall distances. This was a very clever experimental arrangement, and provided the first logical solution to an age old question. Perhaps one of the very first true scientific 'laboratory' experiments.

Comment

But Galileo's experiments proved much more than has been realized. The experiments proved that the ratio of the applied force (the weight) to the inertial resisting force of all objects is a constant which is independent of the magnitude of the applied force (the component of weight parallel to the surface of the ramp).  And the mathematical value of that constant ratio is simply the factor we call the 'acceleration' of the object:

In equation form:   F/I = A   where F is applied force, I is inertial resisting force, and A is the acceleration rate. When F and I are both recognized as 'force' then it is obvious that the factor A is a dimensionless constant which has a mathematical value otherwise called 'acceleration'.   Since the value of A was a constant (32.2 for vertical fall, or 32.2 times the sine of the slope angle for fall along the surface of the ramp) it is obvious that the inertial resisting force must be simply (1/32.2) times the value of the applied force. Had Galaleo made his measurements in the metric system (not yet created) rather than the English system, then the value of A would have been 980, and the value of I would have been (1/980) of the applied force with the unit of force being in terms of grams rather than pounds.

This unrecognized, but experimentally proven, result would be terribly distorted many years later by a famous mathematician who would hypothesize that   F/M = A   where F is an applied force,  M is an imagined inherent constant for each specific object - named 'mass', and the true constant, A,  must therefore be an independent variable named 'acceleration'. That conclusion would overlook the fact that both M and A are purely mathematical values, which when multiplied together equal the single humanly perceivable factor of 'force'.   This fabulously clever, but terribly wrong, mathematical hypothesis is discussed in a subsequent page dedicated to Newton.


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