Question:
A person lifts 60 kg load to a vertical height of 30 m over a duration of 20 seconds. If the power of the man is 1323 W, the mass of the man is:
A person lifts 60 kg load to a vertical height of 30 m over a duration of 20 seconds. If the power of the man is 1323 W, the mass of the man is:
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Remember to include the mass of the person when calculating power for lifting tasks.
Updated On: Jun 9, 2026
- \( 30 \text{ kg} \)
- \( 40 \text{ kg} \)
- \( 50 \text{ kg} \)
- \( 60 \text{ kg} \)
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The Correct Option is A
Solution and Explanation
Concept:
Power is defined as the work done per unit time. When a man climbs a height, he does work against gravity for both his own mass and the load mass. \( P = \frac{(M_{man} + M_{load})gh}{t} \).
Step 1: Set up the power equation.
Given \( P = 1323 \text{ W} \), \( M_{load} = 60 \text{ kg} \), \( h = 30 \text{ m} \), \( t = 20 \text{ s} \), and assuming \( g = 9.81 \text{ ms}^{-2} \): $$ 1323 = \frac{(M_{man} + 60) \times 9.81 \times 30}{20} $$
Step 2: Simplify the equation.
$$ 1323 = (M_{man} + 60) \times 9.81 \times 1.5 $$ $$ 1323 = (M_{man} + 60) \times 14.715 $$ $$ M_{man} + 60 = \frac{1323}{14.715} \approx 90 $$
Step 3: Solve for \( M_{man} \).
$$ M_{man} = 90 - 60 = 30 \text{ kg} $$ $$\boxed{30 \text{ kg}}$$
Step 1: Set up the power equation.
Given \( P = 1323 \text{ W} \), \( M_{load} = 60 \text{ kg} \), \( h = 30 \text{ m} \), \( t = 20 \text{ s} \), and assuming \( g = 9.81 \text{ ms}^{-2} \): $$ 1323 = \frac{(M_{man} + 60) \times 9.81 \times 30}{20} $$
Step 2: Simplify the equation.
$$ 1323 = (M_{man} + 60) \times 9.81 \times 1.5 $$ $$ 1323 = (M_{man} + 60) \times 14.715 $$ $$ M_{man} + 60 = \frac{1323}{14.715} \approx 90 $$
Step 3: Solve for \( M_{man} \).
$$ M_{man} = 90 - 60 = 30 \text{ kg} $$ $$\boxed{30 \text{ kg}}$$
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