Final answer:
The work done by the brakes to bring the bike and rider to a stop is 7852.5 joules.
Step-by-step explanation:
To find the work done by the brakes, we need to calculate the initial kinetic energy of the bike and rider and the final kinetic energy when they come to a stop.
Given: Mass of the bicyclist (m1) = 60 kg, Mass of the bicycle (m2) = 9.8 kg, Initial speed (v) = 15 m/s.
The initial kinetic energy (KE1) = 0.5 * m1 * v^2 + 0.5 * m2 * v^2
The final kinetic energy (KE2) will be 0, as the bike and rider come to a stop.
Therefore, the work done by the brakes will be equal to the change in kinetic energy:
Work = KE1 - KE2
Substituting the values, we get:
Work = (0.5 * 60 * 15^2) + (0.5 * 9.8 * 15^2) - 0
Work = 6750 + 1102.5 - 0
Work = 7852.5 joules