A wheel with a weight of 396 N comes off a moving truck and rolls without slippi

Question

A wheel with a weight of 396 N comes off a moving truck and rolls without slipping along a highway. At the bottom of a hill it is rotating at an angular velocity of 22.2 rad/s . The radius of the wheel is 0.585 m and its moment of inertia about its rotation axis is 0.800 MR^2 . Friction does work on the wheel as it rolls up the hill to a stop, at a height of 'h' above the bottom of the hill; this work has a magnitude of 3512 J . Calculate h (Use 9.81 m/s^2 for the acceleration due to gravity)

Explanation / Answer

mgh=1/2mv^2+1/2Iw^2==>396h=0.5*40.4* 0.585^2+0.5*0.8*40.4*0.585^2*22.2^2=6132.5 (w=v/r =22.2==>v= h=15.4m

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