physics

A block of mass m = 5 kg is attached to a spring (k = 35 N/m) by a rope that hangs over a pulley of mass M = 7 kg and radius R = 4 cm, as shown in the figure. Treating the pulley as a solid homogeneous disk, neglecting friction at the axle of the pulley, and assuming the system starts from rest with the spring at its natural length, answer the following.

(a) Find the speed of the block after it falls 1 m.

(b) Find the maximum extension of the spring

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  1. (a) MgX - (1/2)kX^2 = increase in kinetic energy = (1/2) M V^2 + (1/2) I w^2

    Solve for V

    M = 5 kg
    g = 9.8 m/s^2
    X = 1 m
    k = 35 N/m
    I = (1/2)*Mpulley)*Rpulley^2
    w = V/Rpulley
    b) Maximum extension Xmax occurs when V = 0

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