Two identical wheels are moving on horizontal surfaces. The centerof mass of eac

Question

Two identical wheels are moving on horizontal surfaces. The centerof mass of each has the same linear speed. However, one wheel isrolling, while the other is sliding on a frictionless surfacewithout rolling. Each wheel then encounters an incline plane. Onecontinues to roll up the incline, while the other continues toslide up. Eventually they come to a momentary halt, because thegravitational force slows them down. Each wheel is a disk of mass3.38 kg. On the horizontal surfaces the center of mass of eachwheel moves with a linear speed of 6.49 m/s.(a),(b) What is the total kineticenergy of each wheel? (c), (d)Determine the maximum height reached by each wheel as it moves upthe incline.


I know part B which is just 1/2mv^2.. and I also know part D. Ifyou could just help me find part A and D thank you

Explanation / Answer

The kinetic energy of the sliding wheel is 1/2 m v2 The kinetic energy of the rolling wheel is 1/2 m v2+ 1/2 I 2 = 1/2 m v2 + 1/2 (1/2m R2) v2/ R2 = 3 mv2 / 4 If the plane is frictionless then both reach the same heightbecause they each have the same translational energy. If the plane is not frictionless then the rolling wheelreaches a greater height due to its rotational energy beingexpended. KE = m g h The kinetic energy of the rolling wheel is 1/2 m v2+ 1/2 I 2 = 1/2 m v2 + 1/2 (1/2m R2) v2/ R2 = 3 mv2 / 4 If the plane is frictionless then both reach the same heightbecause they each have the same translational energy. If the plane is not frictionless then the rolling wheelreaches a greater height due to its rotational energy beingexpended. KE = m g h

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