A 120-V motor has mechanical power output of 3.20 hp. It is 81.0% efficient in converting power that it takes in by electrical transmission into mechanical power.
(a) Find the current in the motor.
Answer: 24.6A
(b) Find the energy delivered to the motor by electrical transmission in 3.60 h of operation.
?J
(c) If the electric company charges $0.160/kWh, what does it cost to run the motor for 3.60 h?
$
(b) Output power = 3.20 hp = 2387 Watts
Input power = 2387/0.81 = 2947 W
Electrical energy delivered in 3.60 h
= 2947 J/s*3.2 h*3600 s/h = 3.395*10^7 J
(c) 2.947 kW*3.2 h = ___ kWh
Multiply that by the cost per kWh
(a) To find the current in the motor, we can use the formula:
Power = Voltage * Current
In this case, the power output of the motor is given as 3.20 hp, which can be converted to watts using the conversion factor: 1 hp = 746 W. So, the power output in watts is:
Power_output = 3.20 hp * 746 W/hp = 2387.2 W
The efficiency of the motor is given as 81.0%, which means that only 81.0% of the electrical power input is converted into mechanical power output. So, the electrical power input can be calculated by dividing the mechanical power output by the efficiency:
Power_input = Power_output / Efficiency = 2387.2 W / 0.810 = 2946.67 W
Now, we can use the formula for power to find the current in the motor:
Power = Voltage * Current
Plugging in the values:
2946.67 W = 120 V * Current
Solving for Current:
Current = 2946.67 W / 120 V = 24.6 A
Therefore, the current in the motor is 24.6 A.
(b) To find the energy delivered to the motor by electrical transmission in 3.60 hours of operation, we can use the formula:
Energy = Power * Time
Plugging in the values:
Energy = 2946.67 W * 3.60 h = 10608 J
Therefore, the energy delivered to the motor by electrical transmission in 3.60 hours of operation is 10,608 J.
(c) To find the cost of running the motor for 3.60 hours, we need to determine the total energy consumed by the motor in kilowatt-hours (kWh). Since 1 kilowatt-hour is equal to 3,600,000 J, we can convert the energy (in joules) to kilowatt-hours:
Energy_in_kWh = Energy / (3,600,000 J/kWh)
Plugging in the value for energy:
Energy_in_kWh = 10,608 J / (3,600,000 J/kWh) = 0.002946667 kWh
The cost of running the motor can be calculated by multiplying the energy consumed in kilowatt-hours by the cost per kilowatt-hour:
Cost = Energy_in_kWh * Cost_per_kWh
Plugging in the values:
Cost = 0.002946667 kWh * $0.160/kWh = $0.000471467
Therefore, it costs approximately $0.000471467 to run the motor for 3.60 hours.