The Power supplied by a torque, ?, to rotate an object at angular frequency, ?,

Question

The Power supplied by a torque, ?, to rotate an object at angular frequency, ?, is P = ??. A common car engine produces ?= 3000NM at ?= 3000 RPM (rotations per minute). Suppose you want to create an electric car that runs on a battery and electric motor. Typically electric car motors utilize a current of 100A and have a cross sectional area of 0.5m2. Suppose also that the number of wire turns in the coil of the motor is N = 100.

When the motor is connected in series with the battery that powers it, we can treat it like a generic circuit element with effective resistance R that causes a voltage drop V = IR. By setting the electrical power consumed by the motor equal to the mechanical power used to push the car, P = ??, the effective resistance of the motor can be determined.

What is the effective resistance of the motor, and determine the voltage of the battery.

Explanation / Answer

a)

angular frequency

W=3000*(2pi/60) =314.16 rad/s

Power supplied

P=T*W=3000*314.16

P=942,778 Watts

Effective resistance

R=P/I2 =942,778/1002

R=94.25 ohms

b)

Voltage of battery

V=IR =100*94.25

V=9424.8 Volts

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