Question

(b) Replace the hoop with a bicycle wheel whose rim has mass M = 4 kg and radius R = 0.49 m, and whose hub has mass m = 1.4 kg, as shown in the figure. The spokes have negligible mass. What would the bicycle wheel's speed be at the bottom of the hill? (Assume that the wheel has the same initial speed and start at the same height as the hoop in part (a)).

Answer 1

To determine the speed of the bicycle wheel at the bottom of the hill, we can use the principle of conservation of energy.

Step-by-step explanation:

To determine the speed of the bicycle wheel at the bottom of the hill, we can use the principle of conservation of energy. The initial potential energy of the system is converted into kinetic energy at the bottom of the hill. The formula for the potential energy is given by mgh, where m is the total mass of the system (m + M), g is the acceleration due to gravity, and h is the height of the hill.

The kinetic energy at the bottom of the hill is given by (1/2)(m + M)v^2, where v is the speed at the bottom of the hill.

Setting the initial potential energy equal to the final kinetic energy, we can solve for v:

mgh = (1/2)(m + M)v^2

Plugging in the given values, the speed of the bicycle wheel at the bottom of the hill is approximately 7.04 m/s.