Question

A 200 kg concrete culvert (a hollow cylinder with radius 0.50 m) rolls from rest without slipping 50 m down a road with inclination 10°. What is the culvert's linear speed at the bottom? (The moment of inertia is I=MR²). Assume that gravity is the only force that is acting in initiating the motion of the culvert (creates torque).

Answer 1

using conservation of energy

mgh = 0.5 Iw^2 + 0.5 m v^2

mgh = 0.5( m r^2) (v^2/r^2) + 0.5 mv^2

9.8* 50 sin 10 = v^2

v = 0.9224 m/s

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Answer 2