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27 June, 08:34

7. A pendulum of mass 5.0 kg hangs in equilibrium. A frustrated student walks up to it and kicks the bob with a horizontal force of 30.0? applied over 0.30 seconds. What is the length of the pendulum if it has a period of 5.0 seconds? What is the maximum angle of displacement of the swinging pendulum?

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  1. 27 June, 09:02
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    For pendulum, time period is

    T = 2π √ l / g

    T² = 4π² l / g

    l = / g T² / 4π²

    = 9.8 x 5² / 4π²

    = 6.21 m

    Angular impulse = Torque x time

    = 30 x 6.21 x. 3 = increase in angular momentum

    30 x 6.21 x. 3 = I ω; I is moment of inertia and ω is angular velocity.

    I ω = 55.89

    I = 1/3 m l²

    = 1/3 x 5 x 6.21²

    = 64.27

    Angular kinetic energy = 1/2 I ω²

    = 1/2 (I ω) ² / I

    =.5x 55.89² / 64.27

    = 24.30 J

    Due to it, the centre of mass of pendulum increases by height h so that

    h = l/2 (1 - cos θ)

    1/2 I ω² = mg l/2 (1 - cos θ)

    24.3 = 5 x 9.8 x 3.1 (1 - cos θ)

    (1 - cos θ) =.16

    cos θ =.84

    θ = 33 degree.
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