A wheel with a weight of 386 N comes off a moving truck and rolls without slippi

Question

A wheel with a weight of 386 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 22.9 rad/s . The radius of the wheel is 0.649 m and its moment of inertia about its rotation axis is 0.800 MR2. 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 3540 J .

Exercise 10.25 Part A A wheel with a weight of 386 comes off truck N a moving and rolls without slipping along a highway. At the bottom of a hill it is rotating at an angular velocity of 22.9 rad/s . The radius of the wheel is 0.649 m and its moment of inertia about its rotation axis is 0.800 MR2. 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 1 magnitude of 3540 J Calculate h. Use 9.81 m/sº for the acceleration due to gravity. O AEP r t Ge ? Submit My Answers Give Up IncorrectTry Again; 4 attempts remaining RENO CD 09 NW 0 P Adob

Explanation / Answer

Mass of wheel = 386/g = 386/9.81 = 39.38 kg.
Velocity at bottom = r = 22.9*0.649 = 14.86 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 = 7826.28 Joules.

Subtracting the magnitude of the work done by 'friction' you are left with 7826.28 - 3540 =4286.28 joules that will be converted into gravitational potential energy:

4286.28 = mgh =386 h or h = 11.10 meters in height.

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