Weight of Swinging Pendulum
How and why does the weight of a pendulum (tension in
the cable) change in relation to the movement of its bob?
The tension in the cable is only equal to the ball’s weight when the bob
is not moving. The bob is affected by two forces. The weight of the bob
pulls straight downward. The cable pulls toward the pivot. Together they
produce the motion of the pendulum.
Consider spinning a rock on a string over your head. To keep the rock on
its circular path, you have to pull inward. The faster the rock moves, the
harder you must pull. Length of the string also has an effect. This same
thing happens when a pendulum bob swings. It is moving very fast at the
bottom. Speed drops to zero at the top of the swing. The tension is greatest
at the bottom, where speed is greatest. If the tension matched the bob’s
weight, this would be enough to keep the bob from curving downward, to keep
it on a straight path. To make the bob curve upward requires even greater
pull. As speed and direction change, so does the tension.
Dr. Ken Mellendorf
Illinois Central College
The tension in the cable changes due to the centripetal force needed to move
the bob in a circular path. The centripetal force varies both in magnitude
as the speed of the bob changes (F = mvv/r) and direction (perpendicular to
the velocity of the bob and parallel to the cable. The gravitational force
of the bob(mg) is, of course, always vertically down. To find the total
tension in the cable, you must vectorially add these two forces.
Best, Richard J. Plano...
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Update: June 2012