Question

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​

Answer 1

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°