CATAGORY: Mechanics
QUESTION: I seem to get different answers from this for this question.
A small car travelling at a constant speed of 20ms-1 on a horizontal road
is subjected to air resistance of 570N and road friction of 150N.
a) What power providded by the engine of the car is used to keep it in
motion at this speed?
b) If the effieciency of the car’s engine is 25%, at what rate is the
chemical energy in the fuel being transformed?
c) If 1 Litre of fuel provides 3.3 ´ 107 J of chemical energy when it is
burned, how much fuel is used by the car if it travels at this speed for
100km?

Back to catalog.

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(1)     Power = Force * velocity

Because the force is in the opposite direction as the velocity the
Power is negative meaning a power drain.  The total frictional force
is 570N + 150N = 720N so at 20m/s the Power loss is

(2)    Power = -(720N) 20m/s = -14400 J/s

The car engine must then generate +14400 J/s to compensate for the
loss.  Since the car engine is only 25% efficient the then four times
as much (1/.25) chemical energy must be transformed so the rate of
chemical energy conversion is 4(14400 J/s) = 57600 J/s.
At 20m/s 100km is traveled in

(3) t = (100km x 1000m/km)/20m/s = 5000 s ~ 1.38 hours

During this time the amount of chemical energy used up is

(4)  E = 57600 J/s x 5000 s = 2.88 x 10^8 J

If 1 litre of fuel provides 3.3 x 10^7 J then the number of litres
used up is

(5)    L = 2.88 x 10^8 J/ (3.3 x 10^7 J/l) = 8.73 lietres


         *********************
         *                   *
         * (a) 14400 J/s     *
         *                   *
         * (b) 57600 J/s     *
         *                   *
         * (c) 8.73 lietres  *
         *                   *
         *********************