Answer to Question #83778 in Mechanics | Relativity for scotty

Question

A 60 kg bicyclist rides his 9.8 kg bicycle with a speed of 16 m/s.
How much work must be done by the brakes to bring the bike and rider to a stop?
What is the magnitude of the braking force if the bicycle comes to rest in 4.5 s?
.

Answer 1

Total mass is:

m = 60 + 9.8 = 69.8 kg.

Kinetic energy equal work by brakes:

W = mv^2 / 2 = 69.8∙16^2 / 2 = 8.934 kJ

Braking deceleration:

a = v / t = 16 / 4.5 = 3.556 m / s^2

Magnitude of the braking force:

F = m * a = 69.8 * 3.556 = 248 N