a solid ball of inertia m rolls without slipping down a ramp that makes an angle θ with the horizontal. What frictional force is exerted on the ball? As a function of theta, what coefficient of friction is required to prevent slipping?

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09-12-2022
Physics

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a solid ball of inertia m rolls without slipping down a ramp that makes an angle θ with the horizontal. What frictional force is exerted on the ball? As a function of theta, what coefficient of friction is required to prevent slipping?

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jaspreetsharma jaspreetsharma · Answer 1 · 2022-12-19T03:17:52-05:00

The frictional force on the ball is equal to 5/7 mg sin, and the necessary coefficient of friction to keep it from slipping is equal to 5/7 tan. For a solid ball of inertia m to roll down an angled ramp without slipping.

The frictional force only ever produces a negative amount of work. This is because the opposing force of friction.

ma = m g sin - f. [translation]

f r [rotation] = I a / r

In that case, f = m g sin / (1 + m r2 / I).

I = 2/5 m r2 implies that f = 5/7 m g sin must be f = m g cos, where 5/7 m g sin = m g cos.

μ > = 5/7 tanθ

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