Final answer:
a) The work done by the brakes to bring the bike and rider to a stop can be found by calculating the change in kinetic energy. b) The distance the bicycle travels before coming to a stop can be calculated using the equation v^2 = u^2 + 2as. c) The magnitude of the braking force can be found using the equation F = ma.
Step-by-step explanation:
a) To find the work done by the brakes to bring the bike and rider to a stop, we need to find the change in kinetic energy. The initial kinetic energy is given by KE = (1/2)mv^2, where m is the total mass of the bike and rider and v is the initial speed. The final kinetic energy is zero since the bike and rider come to a stop. Therefore, the work done by the brakes is equal to the change in kinetic energy:
W = ΔKE = KE_final - KE_initial = 0 - (1/2)(65 kg + 8.8 kg)(14 m/s)^2
b) To find the distance the bicycle travels before coming to a stop, we can use the equation v^2 = u^2 + 2as, where u is the initial velocity, a is the acceleration, and s is the distance traveled. Rearranging the equation, we have s = (v^2 - u^2) / (2a). Since the final velocity is 0, the equation becomes s = (0 - (14 m/s)^2) / (2 * (-a)), where a is the deceleration. Plugging in the given values, we can solve for s.
c) The magnitude of the braking force can be found using the equation F = ma, where m is the total mass of the bike and rider and a is the deceleration. Plugging in the given values, we can solve for F.