Water flows over the edge of a waterfall at a rate of 1.2 x 106 kg/s. There are 50.0 m between the top and bottom of the waterfall. How much power is generated by the falling water by the time it reaches bottom?
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To determine the power generated by the falling water, we need to use the formula:
Power = Force × Velocity.
In this case, the force we will use is the weight of the water, and the velocity will be the speed at which it falls. Let's break down the steps to find the answer:
Step 1: Calculate the weight of the water:
Weight = mass × gravity.
Given that the flow rate of water is 1.2 x 10^6 kg/s, and the acceleration due to gravity is approximately 9.8 m/s^2, we can calculate the weight as follows:
Weight = (1.2 x 10^6 kg/s) × (9.8 m/s^2).
Step 2: Calculate the distance the water falls:
The distance between the top and bottom of the waterfall is given as 50.0 m.
Step 3: Calculate the time it takes for the water to fall:
The time can be calculated by dividing the distance by the velocity.
Since it is not explicitly given, we need to find the velocity.
The velocity can be calculated using the equation of motion:
v^2 = u^2 + 2as,
where:
v = final velocity (0 m/s at the bottom),
u = initial velocity (which we assume to be 0 m/s as it starts from rest),
a = acceleration due to gravity (9.8 m/s^2),
s = distance (50.0 m).
Thus,
0^2 = 0^2 + 2(9.8 m/s^2)(50.0 m).
0 = 0 + 2(9.8 m/s^2)(50.0 m).
0 = 2(9.8 m/s^2)(50.0 m).
0 = 980 m^2/s^2.
We find that the final velocity is 0 m/s.
Step 4: Calculate the time using the equation:
time = distance / velocity.
Since the velocity is 0 m/s, the time for the water to fall is infinite.
Step 5: Calculate the power using the formula:
Power = Force × Velocity.
In this case, since the time is infinite, the power generated by the falling water as it reaches the bottom of the waterfall is 0 watts (or 0 joules per second).
Therefore, no power is generated by the falling water by the time it reaches the bottom due to the infinitely slow velocity because it never actually reaches the bottom.