A 120-V motor has mechanical power output of 2.20 hp. It is 92.0% efficient in converting power that it takes in by electrical transmission into mechanical power.

(a) Find the current in the motor (A)
(b) Find the energy delivered to the motor by electrical transmission in 2.90 h of operation. (J)
(c) If the electric company charges $0.160/kWh, what does it cost to run the motor for 2.90 h?

a. See previous post: 9-5-13,12:33 AM.

b. 1784 Watts = 1784 J/s.
Energy=1784J/s * 2.9h*3600s/h=18,625 J.

c. (1.784*2.9)kWh*0.160/kWh = $0.83

To solve this problem, we can use the formulas for power, current, energy, and cost. Let's break it down step by step:

(a) Find the current in the motor (A):

Given:
Voltage (V) = 120 V
Mechanical Power Output (P_out) = 2.20 hp
Efficiency (η) = 92.0% = 0.92 (as a decimal)

The formula relating power and current is:
Power (P) = Voltage (V) * Current (I)

Since the mechanical power output is given, we can calculate the electrical power input as follows:
Electrical Power Input (P_in) = P_out / η

Substituting the given values:
P_in = 2.20 hp / 0.92

Now, since power is in horsepower, let's convert it to watts (W) to match the standard unit:
1 horsepower (hp) = 746 watts (W)

P_in = (2.20 hp / 0.92) * 746 W/hp

Now we have the electrical power input. To find the current, rearrange the formula:
Current (I) = Power (P) / Voltage (V)

Substituting the values:
I = P_in / V

Calculate the value:
I = [(2.20 hp / 0.92) * 746 W/hp] / 120 V

Now, calculate the current (I).

(b) Find the energy delivered to the motor by electrical transmission in 2.90 h of operation (Joules):

Given:
Operation time (t) = 2.90 hours

The energy delivered can be calculated using the formula:
Energy (E) = Power (P) * Time (t)

Substituting the given values:
E = P_in * t

Calculate the energy delivered (E).

(c) If the electric company charges $0.160/kWh, what does it cost to run the motor for 2.90 h?

First, let's calculate the energy consumption in kilowatt-hours:
Energy (E) in kilowatt-hour (kWh) = Energy (E) / 1000

Now, calculate the cost:
Cost = Energy (E in kWh) * Cost per kWh

Substitute the values and calculate the cost.

By following these steps, you can find the answers to parts (a), (b), and (c) of the question.