A large amount of energy is lost each time a car is brought to a stop by applying the brakes. The kinetic energy is converted into heat energy, which is useless in getting the car going again. For this reason, some engineers have experimented with the idea of storing energy in a flywheel when a car comes to a stop.
A flywheel is a massive ring which is free to spin about its center, like a bicycle wheel. The kinetic energy of a flywheel is given by
EK = Iω2/2
where I is the moment of inertia and ωis the angular frequency in radians per unit time. Thus the frequency f (in cycles per unit time) is f = ω/2π. The moment of inertia is given by
I = MR2
where M is the mass of the flywheel and R is the radius.
Ideally the kinetic energy of the car would be transferred to the flywheel as the car comes to a stop. When the driver wants to go again, the energy would be transferred back to forward kinetic motion. Unfortunately, the efficiency of the two transfers will be less than 100%, so energy will be lost to heat. This energy can, of course, be made up by conventional means, such as burning gasoline.
For the following questions, use the notation:
Mcar is mass of the car
Mis mass of the flywheel
Ris radius of the flywheel
ω = 2πf = angular frequency of the flywheel
If the mass of the brake pads is mbrake, and the heat capacity is CV (in J/kg K), which expression gives an approximate temperature change in the brake pads if a car going velocity v slows to a stop?