Final answer:
To calculate the torque developed by the motor, subtract the heat energy from the total energy consumed, then use the power equation P = torque * angular velocity with the motor's rotational speed in radians per second. The calculated torque for the motor running at 2200 rpm is approximately 0.5596 N·m.
Step-by-step explanation:
The question asks us to calculate the torque developed by an electric motor given the amount of electrical energy consumed, the energy conversion efficiency, and the motor's rotational speed. To find the torque, we use the relation between power, torque, and angular velocity.
The power output can be calculated by subtracting the energy lost to heat from the total electrical energy consumed. We then convert the power to watts (W), knowing that 1 kilojoule per second equals 1 kilowatt (1000 W), and using the rotational speed in revolutions per minute (rpm) to find the angular velocity in radians per second (rad/s)
The motor consumes 11.6 kJ of energy in 1 minute, which is 11.6 kJ/60 s = 193.3 J/s or 193.3 W. Since two-thirds of this energy is used for the motor output, the power output of the motor is (2/3) * 193.3 W = 128.9 W. The motor's rotational speed is 2200 rpm, which is equivalent to 2200/60 = 36.67 revolutions per second (rps). To get the angular velocity (ω), we multiply the revolutions per second by 2π (to convert to radians): ω = 36.67 rps * 2π = 230.38 rad/s.
To calculate the torque (τ), we use the power equation: P = τ * ω. Rearranging for torque gives us τ = P / ω. Substituting the values we have, τ = 128.9 W / 230.38 rad/s = 0.5596 N·m. Therefore, the torque developed by this motor at 2200 rpm is approximately 0.5596 N·m