A 120-V motor has mechanical power output of 2.00 hp. It is 82.0% efficient in converting power that it takes in by electrical transmission into mechanical power.
(a) Find the current in the motor
(b) Find the energy delivered to the motor by electrical transmission in 3.30 h of operation
(c) If the electric company charges $0.160/kWh, what does it cost to run the motor for 3.30 h?
Ok so I started the problem by manipulating the power equation (P=IV) to get I=P/V and I got 10.2 A but it says that that's not correct. I assume the other parts aren't correct because I don't have part (a) right. What am I doing wrong. The power I used was 1.22kW
electricalpower*.82=mechanicalpower
electrical power= 2hp(746watts/hp)/.82
IV= 2*746/.82
I= 2*746/(.82*120)
I get about 15 amps
thanks! i was multiplying by 0.82 instead of dividing
To find the current in the motor, you correctly used the equation I = P/V, where P is the power output in watts and V is the voltage. However, you made a mistake while converting the power from horsepower (hp) to watts (W).
In order to convert horsepower to watts, you should use the conversion factor 1 hp = 745.7 W.
Given that the mechanical power output of the motor is 2.00 hp, the correct conversion is:
P = 2.00 hp * 745.7 W/hp = 1,491.4 W
Now, we can substitute the values into the equation:
I = P/V = 1,491.4 W / 120 V = 12.43 A
Therefore, the current in the motor is approximately 12.43 A, not 10.2 A.
Now let's move on to part (b) to find the energy delivered to the motor by electrical transmission in 3.30 hours.
The formula to calculate energy is E = Pt, where P is power and t is time.
Given that the power is 1,491.4 W and the time is 3.30 hours, we can calculate:
E = 1,491.4 W * 3.30 h = 4,914.42 Wh
Since 1 kWh is equal to 1,000 Wh, we can convert the energy to kilowatt-hours:
E = 4,914.42 Wh / 1,000 = 4.91442 kWh
Therefore, the energy delivered to the motor by electrical transmission in 3.30 hours is approximately 4.91442 kWh.
Finally, let's find the cost to run the motor for 3.30 hours, as given in part (c).
The cost can be calculated using the formula cost = energy * cost per unit.
Given that the electric company charges $0.160/kWh, we can substitute the values:
Cost = 4.91442 kWh * $0.160/kWh = $0.7863
Therefore, it will cost approximately $0.7863 to run the motor for 3.30 hours.
To find the correct answers to parts (a), (b), and (c), let's go step by step. First, let's correct part (a) where you calculated the current incorrectly.
Given:
- Voltage (V) = 120 V
- Mechanical power output (P) = 2.00 hp
We are asked to find the current (I) in the motor. We can use the formula:
P = VI
To convert horsepower (hp) to watts (W), we need to use the conversion factor: 1 hp = 746 W.
So, the mechanical power output in watts is:
P = 2.00 hp * 746 W/hp = 1492 W
Now, we can rearrange the formula P = VI to solve for I:
I = P / V = 1492 W / 120 V = 12.43 A (rounded to two decimal places)
Therefore, the correct answer for part (a) is 12.43 A.
Moving on to part (b), we need to find the energy delivered to the motor in 3.30 hours of operation. The formula to calculate energy is:
Energy = Power * Time
Given:
- Time (t) = 3.30 h
- Power (P) = 1492 W (calculated above)
Substituting the values into the formula:
Energy = 1492 W * 3.30 h = 4916.4 Wh
Note: 1 Wh = 1 watt-hour = 1 W * 1 h
Therefore, the energy delivered to the motor is 4916.4 Wh.
Finally, let's move on to part (c) where we need to calculate the cost of running the motor for 3.30 hours, given the electric company charges $0.160/kWh.
To calculate the cost, we can first convert the energy from watt-hours (Wh) to kilowatt-hours (kWh) using the conversion factor: 1 kWh = 1000 Wh.
Energy in kWh = 4916.4 Wh / 1000 = 4.9164 kWh (rounded to four decimal places)
Next, we can calculate the cost by multiplying the energy in kWh by the cost rate:
Cost = Energy * Cost rate = 4.9164 kWh * $0.160/kWh = $0.7866
Therefore, it would cost $0.7866 (rounded to four decimal places) to run the motor for 3.30 hours.
Now, you have the correct answers for all three parts:
(a) The current in the motor is 12.43 A.
(b) The energy delivered to the motor in 3.30 hours of operation is 4916.4 Wh.
(c) It would cost $0.7866 to run the motor for 3.30 hours.