Exercise 10.25 A wheel with a weight of 394 N comes off a moving truck and rolls

Question

Exercise 10.25 A wheel with a weight of 394 N comes off a moving truck and rolls without slipping along a highway. At the bottom of a hill t is rotating at an angular velocity of 28.0 rad/s . The radius of the wheel is 0.557 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 3480 J . Part A Calculate h. Use 9.81 m/s^2 for the acceleration due to gravity.

Explanation / Answer

Here ,

let the height is h

as the wheel rolls without sliping

v = R * w

v = 0.557 * 28 = 15.6 m/s

mass of wheel , m = 394/9.8

m = 40.2 Kg

Using conservation of energy

0.5 * I * w^2 + 0.5 * mv^2 = m * g * h + Wf

0.5 * 0.8 * 40.2* 0.557^2 * 28^2 + 0.5 * 40.2 * 15.6^2 = 40.2 + 9.8 * h + 3480

solving for h

h = 13.51 m

the height of the wheel is 13.51 m

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