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

Question

A simple pendulum, consists of an object suspended by a string. Theobject is assumed to be a particle. The string, with its top endfixed, has negligible mass and does not stretch. In the absence ofair friction, the system oscillates by swinging back and forth in avertical plane. If the string is 2.75m long and makes an initial angle of 28.5° with the vertical, calculate the speedof 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 (a) at the lowest point in its trajectory
m/s
(b) when the angle is 15.0°
m/s

Explanation / Answer

(a)at the lowest point in its trajectory the kinetic energy ofthe particle is equal to the potential energy therefore (1/2)m * v^2 = m * g * S or v = (2g * S)^(1/2) g = 9.8 m/s^2 and S = L * tan,L = 2.75 m and =28.5o (b)When the angle is 1 = 15.0o then v = (2g * S1)^(1/2) S1 = L * tan1 (b)When the angle is 1 = 15.0o then v = (2g * S1)^(1/2) S1 = L * tan1

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