A simple pendulum consists of an object suspended by a string. The object is ass

Question

A simple pendulum consists of an object suspended by a string. The object is assumed to be a particle. The string, with its top end fixed, has negligible mass and does not stretch. In the absence of air friction, the system oscillates by swinging back and forth in a vertical plane. If the string is 1.10 m long and makes an initial angle of 26.0° with the vertical, calculate the speed of the particle at the following positions.
(a) at the lowest point in its trajectory
________m/s
(b) when the angle is 15.0°
_________m/s

Explanation / Answer

The length of the pendulum, l = 1.1 m

(a) The initial angle, = 26 degrees

From law of conservation of energy we have

m g l (1 - cos ) = (1/2) m v^2

v = [ 2 g l (1 - cos ) ] ^ (1/2) = [ 2* 9.8 * 1.1 (1 - cos 26 ) ] ^ (1/2) = 1.5 m/s

(b) If the initial angle, = 15 degrees, then again from the above equation

v = [ 2 g l (1 - cos ) ] ^ (1/2) = [ 2* 9.8 * 1.1 (1 - cos 15 ) ] ^ (1/2) = 0.86 m/s

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