A simple pendulum, which you will consider in detail in Chapter 12, consists of

Question

A simple pendulum, which you will consider in detail in Chapter 12, 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. The string is 2.00 m long and makes an initial angle of 30.0 degree with the vertical. Calculate the speed of the particle (a) a the lowest point in its trajectory and (b) when the angle is 15.0 degree.

Explanation / Answer

Here ,

a)

length of string , L = 2 m

theta = 30 degree

let the speed of particle is v

Using conservation of energy

0.5 * m * v^2 = m * g * L * (1 - cos(theta))

0.5* v^2 = 9.8 * 2 * (1 - cos(30))

v = 2.29 m/s

the speed of the particle at the lowest point is 2.29 m/s

b) at the angle = 15 degree

Using conservation of energy

0.5 * m * v^2 = m * g * L * (cos(15) - cos(theta))

0.5* v^2 = 9.8 * 2 * (cos(15) - cos(30))

v = 1.98 m/s

the speed of particle is 1.98 m/s

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