PROBLEM 10.25 A wheel with a weight of 395 N comes off a moving truck and rolls

Question

PROBLEM 10.25

A wheel with a weight of 395 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 23.6 rad/s . The radius of the wheel is 0.580 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 3530 J .

Calculate h.

Use 9.81 m/s2 for the acceleration due to gravity.

Explanation / Answer

given,

weight of the wheel = 395 N

so,

mass of the wheel = 395/9.8

mass of the wheel = 40.306 kg

angular velocity = 23.6 rad/sec

radius = 0.58 m

moment of inertia = 0.8 * M * R^2

work done by the friction = 3530 J

initial energy possessed by the wheel

Ei = 0.5 * I * omega^2 + 0.5 * M * v^2

Ei = 0.5 * 0.8 * 40.306 * 0.58^2 * 23.6^2 + 0.5 * 40.306 * (23.6 * 0.58)^2

Ei = 6796.61 J

final energy Ef

Ef = frictional work + mgh

Ef = 3530 + 395 * h

by conservation of energy

initial energy = final energy

6796.61 = 3530 + 395 * h

h = 8.26989 m

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