Two bowling balls, of equal size and unequal mass, are hanging
from strings as shown in the diagram. The strings are simultaneously
cut. Compare the velocities of the two balls as they fall toward the
ground.
Since both balls are being accelerated at
the same rate (see below), they will fall to the earth side by side
with equal velocities. This assumes that there is no air resistance,
which is common in introductory classes.
The free body diagram of each ball is given
by:
where WEB is the weight force which the
earth exerts on the bowling ball. It's magnitude is given by the
product of the mass of the bowling ball and the magnitude of the
gravitational field (g = 9.8 N/m). By Newton's Second Law this single
force is equal to the product of the mass of the bowling ball and the
bowling ball's acceleration. Since the mass appears on both side of
this equality, the acceleration of each ball is equal in magnitude
(and direction) to the gravitational field (which is the same for
both balls.
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