A simple pendulum of length 20 cm and of
mass 0.1 kg is pulled to one side through
an angle'O' and released. If its maximum
velocity is 1.4 ms-', the value of 'o'is
Answers
The maximum angle of the pendulum from the vertical position is, Ф = 60°
Explanation:
Given data,
The length of the simple pendulum, l = 20 cm
l = 0.2 m
The mass of the pendulum, m = 0.1 kg
The maximum velocity of the pendulum, v = 1.4 m/s
The maximum angle of the pendulum, Ф = ?
According to the law of conservation of energy, the potential energy at Ф maximum is equal to the maximum kinetic energy.
The P.E of pendulum,
P.E = mgl(1-cosФ) ∵ h = l(1-cosФ)
The K.E of the pendulum,
K.E = ½ mv²
Since,
P.E = K.E
mgl(1-cosФ) = ½ mv²
1 - cosФ = ½ ( v²/gl)
cosФ = 1 - ½ (v²/gl)
Ф = cos⁻¹ [1 - ½ (v²/gl)]
Substituting the values,
Ф = cos⁻¹ [1 - ½ (1.4²/9.8 x 0.2)]
= 60°
Hence, the maximum angle of the pendulum from the vertical position is, Ф = 60°