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A simple pendulum is made of a small blob of mass m=7.000 kg attached to the end of an inextensible wire. The angular amplitude of oscillation is θ=5.730°. Consider that the gravitational acceleration is g=9.807 m/[tex]s^{2}[/tex]. What is the magnitude of the tension in the wire when the blob is directly below its point of support?

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Answer:

The tension must be equal to the weight of the bob plus the centripetal force that is provided at eth end of the motion.

h = L (1 - cos theta)  where h is the height to which the bob is raised

cos 5.730 = .995

h = .005 L

Also    1/2 m v^2 = m g h    speed of the bob at the bottom

v^2 = 2 g h = .01 g L    where 2 h = .01 L

v^2 / L = .01 g

m v^2 / L = .010 g m = .07 g    since m = 7

Total tension = m g (1 + .07) = 1.07 m g

T = 9.807 * 1.07 * 7 = 73.45 kg m / s^2

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