95. Galileo's Experiment.—The fact that bodies of different weight tend to fall at the same rate was first experimentally shown by Galileo by dropping a 1-lb. and a 100-lb. ball from the top of the leaning tower of Pisa in Italy (represented in Fig. 79). Both starting at the same time struck the ground together. Galileo inferred from this that feathers and other light objects would fall at the same rate as iron or lead were it not for the resistance of the air. After the invention of the air pump this supposition was verified as just explained.
96. Acceleration Due to Gravity.—If a body falls freely, that is without meeting a resistance or a retarding influence, its motion will continually increase. The increase in motion is found to be constant or uniform during each second. This uniform increase in motion or in velocity of a falling body gives one of the best illustrations that we have of uniformly accelerated motion. (Art. 75.) On the other hand, a body thrown upward has uniformly retarded motion, that is, its acceleration is downward. The velocity acquired by a falling body in unit time is called its acceleration, or the acceleration due to gravity, and is equal to 32.16 ft. (980 cm.) per second, downward, each second of time. In one second, therefore, a falling body gains a velocity of 32.16 ft. (980 cm.) per second, downward. In two seconds it gains twice this, and so on.
In formulas, the acceleration of gravity is represented by "g" and the number of seconds by t, therefore the formula for finding the velocity, V,[F] of a falling body starting from rest is V = gt. In studying gravity (Art. 89) we learned that its force varies as one moves toward or away from the equator. (How?) In latitude 38° the acceleration of gravity is 980 cm. per second each second of time.
97. Experimental Study of Falling Bodies.—To study falling bodies experimentally by observing the fall of unobstructed bodies is a difficult matter. Many devices have been used to reduce the motion so that the action of a falling body may be observed within the limits of a laboratory or lecture room. The simplest of these, and in some respects the most satisfactory, was used by Galileo. It consists of an inclined plane which reduces the effective component of the force of gravity so that the motion of a body rolling down the plane may be observed for several seconds. For illustrating this principle a steel piano wire has been selected as being the simplest and the most easily understood. This wire is stretched taut across a room by a turn-buckle so that its slope is about one in sixteen. (See Fig. 80.) Down this wire a weighted pulley is allowed to run and the distance it travels in 1, 2, 3, and 4 seconds is observed. From these observations we can compute the distance covered each second and the velocity at the end of each second.
Fig. 80.—Apparatus to illustrate uniformly accelerated motion.
In Fig. 63, if OG represents the weight of the body or the pull of gravity, then the line OR will represent the effective component along the wire, and OS the non-effective component against the wire. Since the ratio of the height of the plane to its length is as one to sixteen, then the motion along the wire in Fig. 80 will be one-sixteenth that of a falling body.
98. Summary of Results.—The following table gives the results that have been obtained with an apparatus arranged as shown above.
In this table, column 2 is the one which contains the results directly observed by the use of the apparatus. Columns, 3, 4, and 5 are computed from preceding columns.