Question

A 0.600-kg toy car is powered by one D cell (1.50 V) connected directly to a small DC motor. The car has an effective energy conversion efficiency of 52.6%, meaning that 52.6% of the electric energy applied to the motor is converted into translational kinetic energy. After 4.96 seconds, the car, which is initially at rest, reaches a speed of 1.81 m/s. What is the average current supplied to the car\'s motor?

Answer 1

Using Work-energy theorem:

W = dKE

W = KEf - KEi

W = (1/2)*m*Vf^2 - (1/2)*m*Vi^2

W = (1/2)*0.600*(1.81^2 - 0^2)

W = 0.98283 J

Given that car has effective energy conversion efficiency of 52.6% (n = 0.526)

So energy supplied by battery should be equal to

Energy supplied by battery = Work-done/efficiency

Energy supplied by battery = 0.98283/0.526 = 1.8685 W

Now Average power will be:

Power = Energy supplied/time

Power = 1.8685 J/4.96 sec = 0.3767 W

Now relation between power and current is given by:

P = V*I

I = P/V

V = Voltage of battery = 1.50 V

I = 0.3767/1.50 = 0.251 Amp

Average current supplied = 0.251 Amp

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