Question

A 0.600 kg toy car is powered by one 9V battery (9.00 V) connected directly to a small DC motor. The car has an effective energy conversion efficiency of 30.6 % , meaning that 30.6 % of the electric energy applied to the motor is converted into translational kinetic energy. After 5.69 s , the car, which is initially at rest, reaches a speed of 3.43 m / s . What is the average current supplied to the car's motor

Answer 1

The average current I supplied to the cars motor is 0.225 Amperes.

Step-by-step explanation:

The mass of the toy car is given as, m = 0.6 kg

The toy car operates at a steady speed of, v = 3.43 m/s.

It achieves the steady speed after a time, t = 5.69 seconds.

The total kinetic energy of the car is given by,

E =
`(1)/(2) m v^2`

= 0.5 × 0.6 ×
`(3.43)^2`

= 3.53 Joules

Since the efficiency of the motor is 30.6% = 0.306

The electrical energy equivalent is supplied to motor =
`(3.53)/(0.306) = 11.54 Joules`.

The electrical energy is given by P × t = I × V × t = 11.54 Joules

P is the electric power where P = I × V where V is the voltage of the cell and is the average current, I.

Therefore we can write I × 9 × 5.69 = 11.54 Joules.

So the average current I =
`(11.54)/(9 * 5.69 )` = 0.225 Amperes.