Andrzej's electric bike is equipped with a motor built into the front wheel hub. The stator of the electric motor (stationary part with the coils) is fixed solidly to the axle and the magnets are attached to the wheel. He made the following measurements on the bike:
1. If he runs it on a horizontal road at 20 km/h and then switches the motor off, it takes the bike 50 m to stop.
2. At full power, it can accelerate up a 5° slope from 5 to 20 km/h in 6 seconds.
3. The total mass of the bike plus the rider, is 106 kg.
4. The diameter of the wheels is 66 cm.
5. The diameter of the front wheel axle is 11 mm.
6. The bike uses a 48 V battery with a capacity of 8 Ah (ampere-hour).
7. The motor is 85% efficient.
Find out:
(a) What is the current flowing through the motor when the bike is driven at 20 km/h on a horizontal road without pedaling?
(b) How far can it go on one battery charge at 20 km/h?
(c) What is the net torque acting on the front axle?
(d) What is the current flowing through the motor when the bike is accelerating up a 5° slope from 0 to 20 km/h in 20 seconds?
(e) What is the full mechanical power of this motor?
(f) What is the maximum slope one can bike up