A wheel with a weight of 385 N comes off a moving truck and rolls without slippi

Question

A wheel with a weight of 385 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 22.7 rad/s . The radius of the wheel is 0.611 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 3508 J .

Part A

Calculate h.

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

A wheel with a weight of 385 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 22.7 rad/s . The radius of the wheel is 0.611 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 3508 J .

Part A

Calculate h.

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

Explanation / Answer

Here the gain in PE = loss in Linaer KE + rot KE - Work done

Fh = 0.5 mv^2 + 0.5 IW^2 -W

also F = mg and V = rW

so

h = (0.5 * F r^2 w^2 /g + 0.4 F r^2 /g -W) F

h = 0.9 r^2 w^2 /g- W/F

h = 0.9 * 0.611* 0.611 * 22.7*22.7 /9.8 - 3508/385

h = 8.55 m

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