A thin hoop of radius r = 0.56 m and mass M = 6.6 kg rolls without slipping acro

Question

A thin hoop of radius r = 0.56 m and mass M = 6.6 kg rolls without slipping across a horizontal floor with a velocity v = 1.5 m/s. It then rolls up an incline with an angle of inclination theta = 29o. What is the maximum height h reached by the hoop before rolling back down the incline?

A thin hoop of radius r = 0.56 m and mass M = 6.6 kg rolls without slipping across a horizontal floor with a velocity v = 1.5 m/s. It then rolls up an incline with an angle of inclination theta = 29o. What is the maximum height h reached by the hoop before rolling back down the incline?

Explanation / Answer

let u is the initial speed and v is the speed at top of the hill.

Apply energy consrvation

0.5*m*v^2 + 0.5*I*wo^2 = m*g*H

0.5*m*v^2 + 0.5*m*r^2*wo^2 = m*g*H

0.5*m*v^2 + 0.5*m*v^2 = + m*g*H

m*v^2 = m*g*H

H = u^2/g

= 1.5^2/9.8

= 0.23 m <<<<<<----------------Answer

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