A basketball rolls without slipping (starting from rest) down a ramp. If the ramp is sloped by an angle of 4 degrees above the horizontal an

Question

A basketball rolls without slipping (starting from rest) down a ramp. If the ramp is sloped by an angle of 4 degrees above the horizontal and the ball rolls for a distance of 60 m along the ramp, what is its speed after rolling this far?The moment of inertia of a basketball is 1.

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Euphemia 4 years 2021-07-16T03:09:40+00:00 1 Answers 23 views 0

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  1. Philomena
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    2021-07-16T03:11:13+00:00
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    Answer:

    11.7 m/s

    Explanation:

    To find its speed, we first find the acceleration of the center of mass of a rolling object is given by

    a = gsinθ/(1 + I/MR²) where θ = angle of slope = 4, I = moment of inertia of basketball = 2/3MR²

    a = 9.8 m/s²sin4(1 + 2/3MR²/MR²)

      = 9.8 m/s²sin4(1 + 2/3)

      = 9.8 m/s²sin4 × (5/3)

      = 1.14 m/s²

    To find its speed v after rolling for 60 m, we use

    v² = u² + 2as where u = initial speed = 0 (since it starts from rest), s = 60 m

    v = √(u² + 2as) = √(0² + 2 × 1.14 m/s × 60 m) = √136.8 = 11.7 m/s

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