The time taken by an engine of power 10 kW to lift a mass of 200 kg to the height 440 m is
Correct answer: C. 86 s
- A. 2 s
- B. 4 s
- C. 86 s
- D. 16 s
Explanation
First, we need to calculate the work done (W) to lift the mass. The work done is equal to the change in gravitational potential energy, which is given by the formula:W = mghwhere:m = 200 kg (mass)g = 9.8 , m/s^2 (acceleration due to gravity)h = 440 m (height)Substituting the values:W = (200)(9.8)(440) = 862400 JNext, we use the relationship between power (P), work (W), and time (t):P = W/tWe are given the power as P = 10 kW, which is equal to 10^4 = 10000 W.Rearranging the formula to solve for time (t):t = W/PSubstituting the values for work and power:t = 862400/10000 = 86.24 sThus, the time taken is 86.24 seconds.
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Work transfers energy when a force causes displacement, while kinetic energy, gravitational potential energy and power describe motion, position and the rate of energy transfer. The work-energy theorem links net work with change in kinetic energy, and efficiency accounts for energy losses rather than treating them as energy destruction.
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