A wheel with a weight of 390 N comes off a moving truck and rolls without slippi

Question

A wheel with a weight of 390 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 26.7 rad/s. The radius of the wheel is 0.596 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 3478 J. Calculate h (height) in meters. Use 9.81 m/s^2 for the acceleration due to gravity.

Explanation / Answer

Mass of wheel = 390/g = 390/9.8 = 39.79 kg. Velocity at bottom = ?r = 26.7*.596 = 15.9 m/s Total KE at the bottom of the hill = translational KE of CM plus rotational KE about the CM. = (1/2)mv^2 + (1/2) I ?^2 = (1/2)mv^2 + (1/2)(.8)mv^2 = 0.9mv^2 = 9053.37 Joules. Subtracting the magnitude of the work done by 'friction' you are left with 9053.37 - 3478 =5575.37 joules that will be converted into gravitational potential energy: 5575.37 = mgh = 390 h or h = 14.29 meters in height.

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