A pendulum bob of mass 3.0 kg is released from rest such that the (massless, tau

Question

A pendulum bob of mass 3.0 kg is released from rest such that the (massless, taut) string of length 2.0 m is horizontal. The bob is released and swings down in a circular arc. Immediately after the bob is released, what is the magnitude of the centripetal acceleration of the bob. Immediately after the bob is released, what is the magnitude of the tangential acceleration of the bob. What is the speed of the bob when it reaches its lowest point (the bottom of the circular arc)? What is the magnitude of the centripetal acceleration of the bob when it reaches its lowest point? What is the tension in the string when the bob is at its lowest point?

Explanation / Answer

1) Since the tangential velocity of the bob is zero, centripetal acceleration is zero.

2) Tangential acceleration = g = 9.81 m/s2

3) Potetial energy of the bob is converted to its kinetic energy.

mgh = mv2/2

=> v = (2gh)1/2 = (2 * 9.81* 2)1/2 = 6.26 m/s

4) Centripetal acceleration = v2/L = 6.262 / 2 = 19.6 m/s2

5) T = mv2/L = 3 * 6.262 / 2 = 58.8 N

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