OBJECT: To study the motion of a freely falling body; in particular, to measure g, the acceleration due to gravity.
METHOD: An object is allowed to fall freely, and its positions at the ends of successive equal intervals are recorded on a coated paper strip by means of electric sparks. From these data graphs of distance-time and velocity-time are plotted. The acceleration is determined from the slope of the velocity-time graph.
THEORY: The average speed v of a body is the quotient of the distance s which it traverses and the time t required to travel that distance. In symbols (equation 1):
v = s/t
The instantaneous speed v of an object is defined as the limit of this ratio as the time is made vanishingly small. Symbolically (equation 2):
v = Δs/Δt
where Δs represents a small increment of distance traversed in the corresponding increment of time Δt.
In Fig. 2 curve (a) shows the distance-time relationship for a freely falling body. In any such curve Eq. (2) states that the instantaneous speed is given by the slope of a tangent drawn to the curve at the point for the instant in question. If the speed were constant the slope would be constant and the curve would be a straight line. For a freely falling body this is evidently not true, as the speed, and hence the slope of the curve, is continually increasing.
When the velocity of a body varies, the motion is said to be accelerated. Acceleration is defined as the time rate of change of velocity; in symbols (equation 3):
a = (vt−vo)/t
where a represents the average acceleration of a body which changes its velocity from vo to vt in the time t. Since acceleration has the dimensions of a velocity divided by a time, the absolute unit in the metric system will be the centimeter per second per second and in the British system the foot per second per second; usually written, cm/sec² and ft/sec².
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