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?

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 &#952; and climbs upward. Assuming that it rolls without slipping, how far up the sphere will travel?

Aicharya · Accepted Answer

From energy conservation mgh = 1 2 mv 0 2 + 1 2 I&#969; 2 &#8658; mgh = 1 2 mv 0 2 + 1 2 &#215; 2 5 ma 2 &#215; v 0 2 a 2 &#8658; gh = 1 2 v 0 2 + 1 5 v 0 2 &#8658; gh = 7 10 v 0 2 From triangle, sin &#160; &#952; = h l Then h = l &#160; sin &#160; &#952; &#8658; l &#160; sin &#160; &#952; = 7 10 v 0 2 &#160; g Thus, the sphere will travel distance, l = 7 10 v 0 2 &#160; g &#160; sin &#160; &#952; .

A sphere of radius a and mass m rolls along a horizontal plane with constant speed v 0 . It encounters an…

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