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 2.71 kg. on the horizontal surfaces the center of mass of each wheel moves with a linear speed of 5.89 m/s. () 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) 70.5117 J

b) 47.01 J

c) 7.05 m

d) 4.7 m

Explanation:

a)The rotating wheel has both translational K.E. (linear kinetic energy) and rotational kinetic energy.

Total K.E. of rotating wheel = ω²

                                                =(mu² + mr²×[u/r]²)

where ω = angular velocity and r = radius of the wheel

we get K.E. =

                   = 0.75×2.71×(5.89)²

                   = 70.5117 J

b) for sliding wheel, it has just translational K.E.

Total K.E. of sliding wheel =

  = 0.75×2.71×(5.89)²/10

  = 7.05 m

d) derivation of the following equation is in the attachment,

if H = height climbed by the sliding wheel

H =

  = 0.5×2.71×(5.89)²/10

  = 4.7 m

here we know that ball will drop down by total distance 3.2 m

so here we know that

now using kinematics

now in the same time it will cover horizontal distance of 0.75 m

so speed of the ball will be

gravity

explanation: