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21 December, 17:45

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.

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  1. 21 December, 19:55
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    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
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