A solid ball of mass M = 2.0 kg and radius R = 0.25 m starts from rest at a height h = 3.0 m above the bottom of the path. It rolls without

Question

A solid ball of mass M = 2.0 kg and radius R = 0.25 m starts from rest at a height h = 3.0 m above the bottom of the path. It rolls without slipping down the left side of the path. The right side of the path is frictionless. Moment of inertia of a hollow sphere is � = ! ! ��!. v What is the linear speed

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Ngọc Hoa 2 months 2021-07-22T12:30:10+00:00 1 Answers 3 views 0

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    2021-07-22T12:31:37+00:00

    Answer:

    6.48 m/s

    Explanation:

    We are given that

    Mass,M=2 kg

    Radius,R=0.25 m

    Height,h=3 m

    Moment of inertia of solid sphere=I=\frac{2}{5}MR^2

    We have to find the linear speed.

    \omega=\frac{v}{R}

    By law of conservation of energy

    mgh=\frac{1}{2}I\omega^2+\frac{1}{2}mv^2

    mgh=\frac{1}{2}I(\frac{v}{R})^2+\frac{1}{2}mv^2=\frac{1}{2}v^2(\frac{I}{R^2}+m)

    Where g=9.8m/s^2

    Substitute the values

    2\times 9.8\times 3=\frac{1}{2}(\frac{2}{5R^2}MR^2+M)=\frac{7}{10}Mv^2=\frac{7}{10}(2)v^2

    v^2=\frac{2\times 9.8\times 3\times 10}{7\times 2}

    v=\sqrt{\frac{2\times 9.8\times 3\times 5}{7}}

    v=6.48m/s

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