A bicycle and rider are coasting (rider is not pedaling) up a 15 degree hill, th

Question

A bicycle and rider are coasting (rider is not pedaling) up a 15 degree hill, the bike has been modified so it has an electric assist which provides 50 N m moment on the rear wheel. Knowing the bike starts with an initial velocity of 9 m/s at the bottom of the hill, how far up the hill will the bike travel before it stops? The mass of the bike is 15 kg, the mass of the person is 60 kg-m^2 the mass-moment of Inertia of each bike wheel is 0.16 kg -m^2and the radius of each wheel is 0.35 m. You can assume the wheels roll without slipping, and without rolling resistance.

Explanation / Answer

Initial Kinetic Energy   = 0.5 * m * v^2 + 2 * 0.5 * I * w^2

                                 = 0.5 * 75 * 9^2 + 0.16 * (9/0.35)^2     = 3143.296 J

final KE = 0 J

Initial Potential Energy = 0 J

Final Potential Energy   = m * g * s * sin(15)       (where s is the distance travelled up the incline)

                                   = 75 * 9.8 * sin(15) * s      = 190.232 s

Work done by external torque = 50 * s / 0.35

Therefore

- 3143.296 + 190.232 s    = 50 * s / 0.35

s = 53.6 m

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