Free Fall
When you let go of a ball, it falls. When it falls, it falls faster and faster. So a body accelerates when it falls.
When you drop a feather, it falls very slowly. This seems to tell us that lighter bodies fall less quickly. In fact, this is because the air resists the movement of a falling body. It is like friction. If the body has a large surface, like feather or paper, then there is more resistance.
If we can somehow remove the resistance, we would find that a piece of paper and a hammer falls at exactly the same rate. This very famous experiment was carried out by an astronaut on the moon, where there is very little air. He dropped a feather and a hammer together, the feather reached the ground at the same time as the hammer. If you see this on video for the first time, you would be surprised, because it is so unexpected in everyday experience.
A less exotic experiment, but no less interesting story, is that of Galileo dropping two iron balls from the Leaning Tower of Pisa. He released a heavy and a light ball from the top of the tower, and showed that they hit the ground at the same time. In this case, the air resistances were small compared with the weights of the balls.
An experiment that Galileo actually did and recorded, was the measurement of the acceleration of a falling body on an inclined plane. Since there was a plane, it was not exactly free fall. Anyway, by measuring the time and distances of a ball rolling down the plane, he showed that the acceleration was uniform.
Measuring the times and distances of a body under free fall is more difficult because the fall is very fast. Using modern electronic sensors and computers, this can be done and the results would show that the acceleration of free fall is also constant, and is 9.81 m/s2.
Whether it is inclined plane or free fall, we want to look at what data we must take, how to use these to show that the acceleration is constant, and how to obtain the acceleration from the data. The way is to use the acceleration equations.
The acceleration equations contains the quantities s, t, u, v, a. Using simple setup, like ruler and timer, we can normally measure s and t, but not u, v or a. So we need an equation with which we can determine a from s and t. The only one that contains s, t and a is
In principle, if we drop a ball over a distance s and measure t, then initial u = 0 and we can use the equation to solve for a. If we want to check that a is constant, just repeat the measurement for a few different s, and check that the a that are calculated are always the same. There is a more accurate way of doing it - by taking the measurements for a number of s and t, and plotting a graph
Suppose we have 6 electronic detectors, positioned along a vertical line at 20 cm intervals. If a body passes close to a detector, this detector sends a signal to the computer, which records the time. I release a ball 20 cm above the highest detector. As it falls, the computer records the time that it passes each detector. I can then make a table of the measured time:
s (m): 0.000, 0.200, 0.400, 0.600, 0.800, 1.000
t (s): 0.000, 0.084, 0.148, 0.202, 0.250, 0.293
It is difficult to measure the time when I let go of the ball, so take the time and displacement at the first detector as t = 0 and s = 0. I now plot a graph of s/t against t. If the acceleration a is constant, I would get a straight line. Try it.
t (s): 0.000, 0.084, 0.148, 0.202, 0.250, 0.293
s/t (m/s): 2.392, 2.703, 2.9703, 3.200, 3.413
The reason is that if I divide the above equation by t, I have
So if I get a straight line from the measurement, that shows that the acceleration of free fall is constant. Since m = a/2, I can find the gradient and multiply it by 2 to get the acceleration. This is more accurate than making a single measurement of s and t, because drawing the best straight line through the points on the graph averages out the errors.
Copyright 2010 by Kai Hock. All rights reserved.
Last updated: 1 December 2010.