Two identical wheels are moving on horizontal surfaces. The center of mass of ea

Question

Two identical wheels are moving on horizontal surfaces. The center of mass of each has the same linear speed. However, one wheel is rolling, while the other is sliding on a frictionless surface without rolling. Each wheel then encounters an incline plane. One continues to roll up the incline, while the other continues to slide up. Eventually they come to a momentary halt, because the gravitational force slows them down. Each wheel is a disk of mass 3.81 kg. On the horizontal surfaces the center of mass of each wheel moves with a linear speed of 5.45 m/s. (a),(b) What is the total kinetic energy of each wheel? (c), (d) Determine the maximum height reached by each wheel as it moves up the incline.

(a) KEr = __________ Units _______
(b) KEs = __________ Units _______
(c) hr = ___________ Units _______
(d) hs = ___________ Units _______

Explanation / Answer

a) K.E = 1/2 m v^2           = 1/2 * (3.81 kg ) ( 5.45 m/s )^2            = 56.5J conservation of energy for sliding wheel
b) mgh = 1/2 m v^2 + 1/2 I w^2 = 1/2 m v^2 + 1/4 m R^2 w^2 = 3/4 m v^2
= 3/4 * 3.81 kg * ( 5.45 m/s)^2 = 84.8J
c) h = 1/2 v^2 / g         = 1/ 2( 5.45 m/s)^2 / 9.8          = 1.51m for sliding wheel
d) h = 3 v^2 / (4 g)           = 3 ( 5.45 m/s)^2 / 4 *9.8            = 2.27m for rolling wheel

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