A sphere of radius a and mass m rolls along a horizontal plane with constant speed v 0 . It encounters an inclined plane at angle θ and climbs upward. Assuming that it rolls without slipping, how far

Question

A sphere of radius a and mass m rolls along a horizontal plane with constant speed v 0 . It encounters an inclined plane at angle θ and climbs upward. Assuming that it rolls without slipping, how far up the sphere will travel?

TestHub · Accepted Answer

From energy conservation mgh = 1 2 mv 0 2 + 1 2 Iω 2 ⇒ mgh = 1 2 mv 0 2 + 1 2 × 2 5 ma 2 × v 0 2 a 2 ⇒ gh = 1 2 v 0 2 + 1 5 v 0 2 ⇒ gh = 7 10 v 0 2 From triangle, sin θ = h l Then h = l sin θ ⇒ l sin θ = 7 10 v 0 2 g Thus, the sphere will travel distance, l = 7 10 v 0 2 g sin θ .

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