Question

An engine pump up 200 kg of water through a height

of 20 min 10 second. If the efficiency of the engine
is 80%. Calculate the power of the engine.
(1) 3800 W
(2) 5000 W
(3) 4900 W
(4) 4800 W​

Answer 1

The power of the engine is calculated using the work-energy principle and considering the efficiency of the engine. With the given parameters, the power is found to be 4900 watts (option 3).

Step-by-step explanation:

To calculate the power of the engine, we need to know the amount of work done by the engine and the time taken to do that work. The work done by an engine to lift water can be calculated using the formula work (W) = mass (m) × gravitational acceleration (g) × height (h). Since the provided information includes mass of the water, height, and time, we can calculate the work done by the engine as:

W = 200 kg × 9.8 m/s2 × 20 m

W = 39200 kg·m2/s2 or Joules (J)

The time taken is 10 seconds. Therefore, the ideal power output (Pideal) can be calculated by dividing the work done by the time:

Pideal = 39200 J / 10 s = 3920 W

However, the engine operates at an efficiency of 80%. Considering efficiency, the actual power (P) of the engine is:

P = Pideal / Efficiency

P = 3920 W / 0.80 = 4900 W

Therefore, the power of the engine is 4900 watts (W), which is option (3).