Question

A wheel with a weight of 396N 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 25.4rad/s . The radius of the wheel is 0.651m 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 habove the bottom of the hill; this work has a magnitude of 3464J .

Part A

Calculate h.

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

Answer 1

Ei + W friction = Ef

1/2 mv^2 + 1/2 I w^2 - 3464 = m g h

v = w rand I = 0.8 M R^2

1/2 mv^2 + 0.4 M R^2 w^2 - 3463 = m g h

0.5*(396/9.81)*(25.4*0.651)^2 + 0.4*(396/9.81)*0.651^2*25.4^2 - 3463 = (396/9.81)*9.81*h

h=16.34 m