Physics Work & Energy ETEA 2018
PMDC Verified Question 85 of 108
A man has a mass of 80 kg. He ties himself to one end of rope which passes over a single fixed pulley. He pulls on the other end of the rope to lift himself up at an average speed of \( 50 \text{ cms}^{-1} \). What is the average useful power at which he is working?
A
40W
B
0.39kW
C
4.0kW
D
39kW
Tap any option to test your recall and reveal the step-by-step Propolis autopsy.

Propolis Cognitive Error Autopsy

Official Correct Choice:
Option B: 0.39kW
Concept:

Power can be calculated as the product of the upward force applied (to overcome gravity) and the constant velocity of the mass.

Formula:

$$ P = F \cdot v = (mg) \cdot v $$

Solution:

  • Mass (\( m \)) = 80 kg


  • Velocity (\( v \)) = \( 50 \text{ cm/s} = 0.5 \text{ m/s} \)


  • Force required = Weight = \( mg = 80 \times 9.8 = 784 \text{ N} \)


  • Power \( P = 784 \times 0.5 = 392 \text{ W} \)


  • Convert to kilowatts: \( \frac{392}{1000} = 0.392 \text{ kW} \)


Why other options are incorrect:

If \( g=10 \) is used, \( P = 800 \times 0.5 = 400 \text{ W} = 0.4 \text{ kW} \). The closest exact answer using 9.8 is 0.39 kW. Failing to convert cm/s to m/s results in large values like 39 kW.

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