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.

Q1: How strong of a magnetic field is required to produce the same torque as a regular car engine?

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.

Q2: What is the effective resistance of the motor?

Q3: Determine the voltage of the battery?

Please show all work, I will rate high.

Answer 1

Given:

  

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.

Q1: How strong of a magnetic field is required to produce the same torque as a regular car engine?

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.

Q2: What is the effective resistance of the motor?

Q3: Determine the voltage of the battery?

We are given the torque supplied by a typical car engine is ---    at   --- this must be converted to angular frequency --- :

.

The power supplied by the internal combustion engine is :

   .

  :

They want an electric motor with current , , and cross sectional area    to supply the same torque . In a constant magnetic field of tesla , the electric motor has maximum torque :

     We thus want :

===>

===>

===> The required magnetic field is thus :

--- SOLUTION .

:

They want the power of the electric motor to equal the power of the internal combustion engine:

===>

===>

   . We can then use Ohm's law ---    to compute the resistance of the motor coil :

===>

--- SOLUTION .

:

We already calculated the battery voltage above ---   --- SOLUTION .

I think the power they quoted of the car engine is too high by a facror of 10 :

. I think that around is more reasonable power for a car engine .