Andy Benton works at the local Starbucks coffee shop and his responsibilities include taking orders, fulfilling orders, and ring
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(a) The total mass of the bicycle+rider system is
m=65 kg+8.8 kg=73.8 kg
And their initial kinetic energy is
For the work-energy theorem, the work done by the brakes to stop the bicycle+rider must be equal to the loss of kinetic energy of the system:
And so, since the final kinetic energy Kf is zero (because the final velocity is zero), then we have
Where the negative sign is due to the fact that the work done by the brakes is against the motion of the bicycle.
(b) First we can calculate the acceleration of the bicyle; since the final speed is zero, we have
where the negative sign means it is a deceleration.
Then we can find the distance covered by using the relationship:
So we have
So, the bike and the rider traveled for 28 meters before to stop.
(c) The work done by the brake force is:
where F is the brake force and d is the distance covered by the bike+rider during the time of application of the force, so it is d=S=28 m.
Therefore, the brake force is (we can neglect signs because we are only interested in the magnitude of the force):