Assume that all of the mass of a bicycle wheel is concentrated at its rim.Such a wheel of mass 1.2 kg and radius 30 cm starts from rest at the top of a hill 100 m long and inclined at 20º to the horizontal.What will be the speed of the wheel at the bottom of the hill if it rolls without slipping?
A)21 m/s
B)26 m/s
C)15 m/s
D)33 m/s
E)37 m/s

Question

Quizplus · Accepted Answer

The potential energy of the wheel at the top of the hill is converted to both translational kinetic energy and rotational kinetic energy as it rolls down the hill without slipping. The total energy is conserved as friction is absent in this ideal situation.

Using conservation of energy, we have:

PE(top) = KE(translational) + KE(rotational)

where PE(top) = mgh, m=1.2 kg, g=9.8 m/s², h=100sin(20º) = 34.2 m

KE(translational) = 0.5mv², KE(rotational) = 0.5Iω², where I=mr²

Substituting the values and rearranging, we get:
v = sqrt(2gh/(1+(r²/h²)))

v = sqrt(2*9.8*34.2/(1+(0.3²/34.2²))) = 14.98 m/s ≈ 15 m/s

Therefore, the answer is choice C, 15 m/s.

Assume That All of the Mass of a Bicycle Wheel