Question

One possibility for a low-pollution automobile is for it to use energy stored in a heavy rotating flywheel. Suppose such a car has a total mass of 1100 kg, uses a uniform cylindrical flywheel of diameter 1.50 m and mass 240 kg, and should be able to travel 350 km without needing a flywheel �spinup.� (a) Make reasonable assumptions (average frictional retarding force = 450 N, twenty acceleration period from rest to 95 km/h, equal uphill and downhill, and that energy can be put back into the flywheel as the car goes downhill), and estimate what total energy needs to be stored in the flywheel. (b) What is the angular velocity of the flywheel when it has full �energy charge�? (c) About how long would it take a 150 hp motor to give the flywheel a full energy charge before a trip?

Answer 1

A flywheel is just a heavy disk that can be rotated and so ithas kinetic energy. The KE of the flywheel can then be used to makeother things move (i.e. when they touch the rotating flywheel...the flywheel can be a large gear than can engage othergears.)

How much energy will you need?

    First, the energy lost to the drag force isthe work done by the drag force. The car will travel 350 km againsta force of 450 N.

The work = Force * distance = 450*350000 = 1.575 x10⁸ Joules

For the twenty acc periods, you are left to assume that theenergy used to acc the car is lost when the car brakes (the energybecomes heat in the brakes). So the energy used to acc the car onceto 90 km/h is the final KE of the car...   (1/2) mv²   

First, convert speed to m/s

     95 km / hr =   95000m / 3600 s = 26.38 m/s

and    KE = (1/2) * 1100 *26.38² = 766010.802 J

This is for one acc... for 20 you need   766010.802 * 20 = 0.513 x 10⁸ Joules

Obviously the energy needed for acceleration is tiny comparedto the energy lost to drag. You can add the two...

1.575 x 10⁸ + 0.513 x 10⁸   = approx 1.728x10⁸ J

So there is the answer to part (a)

(b)

(c)   There are 746 watts to one hp, so a 150 hpmotor puts out 111900watts, or 111900 Joules per second

So

   time = 1.728 x 10⁸Joules   /   74600 J / sec   = 1544.23seconds   or 25.73 minutes