Two identical wheels (A & B) which are disks of mass 2.0kg are moving on horizon

Question

Two identical wheels (A & B) which are disks of mass 2.0kg are moving on horizontal surfaces. On the horizontal surfaces the center of mass of each wheel moves with a linear speed of 6.0 m/s. However, wheel A is rolling, while the wheel B is sliding on a frictionless surface without rolling. Each wheel then encounters an inclined plane. Wheel A continues to roll up while B continues to slide up the incline. Eventually they come to a momentary halt, because the gravitational force slows them down. (a) What is the total kinetic energy of each wheel? (b) Determine the maximum height reached by each wheel as it moves up the incline.

Explanation / Answer

For rolling wheel ; Total energy = angular KE + linear KE = 0.5 * m * v^2 + 0.5 * I * w^2 = 0.75 * m * v^2 = 54 Joules (moment of inertia for disc = m* r^2 /2) For sliding wheel ; Total energy = 0.5 * m * v^2 = 36 J as there is no rolling motion . For max height of sliding wheel; m*g*h = 36 J thus the height h = 1.83 m For max height of rolling wheel; m*g*h = 54 J thus the height h = 2.75 m

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