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 26.0 rad/s . The radius of the wheel is 0.650 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 3462 J .

Q1:  

Calculate h.

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

Answer 1

here,

weight of wheel , W = 386 N

mass , m = W/g = 39.3 kg

angular speed , w = 26 rad/s

radius of the wheel , r = 0.65 m

moment of inertia , I = 0.8 * m * r^2

using work energy theorm

work done by friction = intial kinetic energy - final potential energy

W = (0.5 * m * v^2 + 0.5 * I * w^2) - m * g * h

W = (0.5 * m * (r * w)^2 + 0.5 * (0.8 * m * r^2) * w^2) - m * g * h

3462 = (0.5 * 39.3 * (26 * 0.65)^2 + 0.5 * (0.8 * 39.3 * 0.65^2) * 26^2) - 39.3 * 9.81 * h

solving for h

h = 17.2 m

the height is 17.2 m