How do you calculate work done by brakes to bring a bike and the rider to a stop?

A 70kg bicyclist rides a 10kg bike with speed 10m/s. How much work must be done by the brakes to bring the bike and rider to a stop? How far does the bicycle travel if it takes 5secs to come to rest. What is the magnitude of the braking force?How do you calculate work done by brakes to bring a bike and the rider to a stop?Work = energy = force * distance



The energy of a moving bike + biker is in the form of kinetic energy.



Kinetic Energy = (1/2) m v^2



m = mass = mass of bike + mass of biker

m = 10 + 70

m = 80kgs



v = 10m/s



Kinetic energy = 0.5 * 80 * 10 * 10

Work done = 4000 J



Find the distance travelled by an accelerating body:

We know that final velocity (v) = initial velocity (u) + acceleration (a) * time (t)

v = u + at

Final velocity = 0 - we've stopped.

Initial velocity = 10 m/s

Time = 5 seconds

0 = 10 + 5a

a = -2 m/s^2



Now we know the acceleration, we can find the distance we went in those 5 seconds.



Distance (s) = ut + (1/2)at^2

s = 10 *5 + (1/2) (-2) (5 * 5)

s = 50 - 25

s = 25m



Work = Force * distance

4000 = F * 25

F = 4000 / 25

F = 160 N



The other way to get force is from the equation

Force (F) = mass (m) * acceleration (a)

F = ma

F = 80 * -2 = -160 N



Magnitude of Force = 160 N