While changing a flat tire, a motorist accidentally let the spare tire go, and i

Question

While changing a flat tire, a motorist accidentally let the spare tire go, and it rolled down the hill shown below, which has an elastic element approximated as the spring at the bottom. The tire has a mass, M = 20kg, and radius, r = 0.5m, and is spinning at 20^rad/s It has a radius of gyration of 0.25m. It started at point 0 at rest (upsilon_0 = 0m/s) and immediately began rolling without slipping (with omega_0). There is no friction on the path nor energy loss in the spring. Point 0 and Point 1 are at equal heights, and Point 5 is just before hitting the spring. What is the velocity of the tire at point 1 b. Where does the maximum velocity of the center of the tire occur (points 0, 1, 2, 3, 4, 5) and what Ls this maximum velocity? Assume that the tire is small compared to the curvature of the hills. What is the maximum deflection of the spring, which Ls initially unstretched with k = 100N/m? Assume that there Ls no energy lost when the tire comes into contact with the spring and that the spring/wheel contact is frictionless.

Explanation / Answer

a) v2 =2gh/1+k2/r2

V = 8.96 m/s

b) maximum velocity at point 2,4,5

c)

x =2*20*9.8*5/100 =4.427

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