M&S Problem 2.47 (extended) An electric motor operating at steady state draws a current of 20 ap at a voltage of 110 V. The output shaft rotates at a constant speed of 2000 RPM and exerts a torque of 9.07 N-m. Determine (a) the magnitude of the power input in W; (b) the output power, in W; (c) the magnitude and direction of any heat transfer that must be present, in W; and (d) the cost of 224 hours of operation if electricity is valued at $0.11 per kW-hr.

a) 2.2 KW

b) 1899.616 W

c) 300.383 W

d) $54.208

Explanation:

Given:

- current drawn by motor i = 20 Amps

- Voltage supplied V = 110 V

- speed of shaft N = 2000 rpm

- Torque of the shaft T = 9.07 N-m

Find:

(a) the magnitude of the power input in W

(b) the output power, in W

(c) the magnitude and direction of any heat transfer that must be present, in W

(d) the cost of 224 hours of operation if electricity is valued at $0.11 per kW-hr.

Solution:

(a)

W_in = P = i * V

W_in = (20 Amps) * (110 V) = 2200 W

(b)

W_out = T*w

W_out = (2*pi*N*T) / 60 = (2*pi*2000*9.07) / 60

W_out = 1899.616 W

(c)

Q_loss = W_in - W_out

Q_loss = 2200 - 1899.616

Q_loss = 300.383 W

(d)

Cost = Rate * W_in*time

Cost = ($ 0.11 / KW-h) * (2.2 KW) * (224 h)

Cost = $54.208