Water flows over a section of a waterfall at the rate of 5.1 104 kg/s and falls 40 m. How much power is generated by the falling water?
answer in Watts
thanks
P=5.1*10^4kg/s*9.8N/kg*40=1.9992*10^7J/s
= 1.9993*10^7 Watts.
To determine the power generated by the falling water, we need to use the equation:
Power = Force × velocity
First, let's calculate the force exerted by the falling water using the equation:
Force = mass × acceleration due to gravity
Given that the mass flow rate is 5.1 × 10^4 kg/s and the acceleration due to gravity is approximately 9.8 m/s^2:
Force = (5.1 × 10^4 kg/s) × (9.8 m/s^2)
= 4.998 × 10^5 N
Next, we can find the velocity of the water at the bottom of the waterfall using the equation:
Velocity = √(2 × acceleration due to gravity × height)
Given that the height is 40 m:
Velocity = √(2 × 9.8 m/s^2 × 40 m)
= √(784 m^2/s^2)
= 28 m/s
Now, we can calculate the power:
Power = Force × velocity
= (4.998 × 10^5 N) × (28 m/s)
≈ 1.399 × 10^7 W
Therefore, the power generated by the falling water is approximately 1.399 × 10^7 Watts.