A 34 kg bowling ball with a radius of 22 cm starts from rest at the top of an incline 4.4 m in height. Find the translational speed of the b

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A 34 kg bowling ball with a radius of 22 cm starts from rest at the top of an incline 4.4 m in height. Find the translational speed of the bowling ball after it has rolled to the bottom of the incline. (Assume that the ball is a uniform solid sphere.)The acceleration of gravity is 9.81 m/s 2 . Answer in units of m/s.

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  1. Answer:

    7.85 m/s.

    Explanation:

    Given,

    Mass of the bowling ball, m = 34 Kg

    radius, r = 0.22 cm

    height of the inclination, h = 4.4 m

    transnational velocity = ?

    Moment of inertia of bowling ball,

    [tex]I = \dfrac{2}{5}mr^2[/tex]

    Using conservation of energy

    [tex]mgh = \dfrac{1}{2}I\omega^2 + \dfrac{1}{2}mv^2[/tex]

    We know that [tex]v = r\omega[/tex]

    [tex]mgh = \dfrac{1}{2}( \dfrac{2}{5}mr^2)(\dfrac{v}{r})^2 + \dfrac{1}{2}mv^2[/tex]

    [tex] m gh = 0.7 m v^2[/tex]

    [tex]v =\sqrt{\dfrac{gh}{0.7}}[/tex]

    [tex]v =\sqrt{\dfrac{9.81\times 4.4}{0.7}}[/tex]

    [tex]v = 7.85\ m/s[/tex]

    Speed of the bowling ball is equal to 7.85 m/s.

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