Conservation of energy water turbine problem

AI Thread Summary
The discussion focuses on a water turbine problem involving the conservation of energy, specifically calculating kinetic energy using the equation mgh=1/2mv^2. The user calculates the potential energy as 2.9*10^8 J, which is then equated to kinetic energy to find the velocity of the water at 53.8 m/s. An efficiency of 85% is considered, resulting in an electrical power output of 2.5*10^8 J. The conversation emphasizes the importance of maintaining units in calculations and suggests starting with formulas before substituting numbers for clarity. Overall, the calculations and concepts related to energy conservation in the context of turbines are affirmed.
TheRedDevil18
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Homework Statement



a3jsbs.jpg


Homework Equations



mgh=1/2mv^2

The Attempt at a Solution



7.1) 200*1000=200000kg

7.2) Must I use mgh? They asked for kinetic energy but energy is conserved so:
200000*9.8*150
= 2.9*10^8 J

7.3) Ep=Ek
2.9*10^8=1/2*200000*v^2
v=53.8 m.s

7.4) 85% of 2.9*10^8
= 2.5*10^8 J

7.5) It gets converted into heat and sound when it hits the turbine.

All good?
 
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The electrical power output is energy per time, it has Watts as unit.
The numbers look fine, but you should keep their units in the calculations. In addition, it would be easier to understand your solutions if you start with the formulas first, and plug in numbers afterwards.
 
p=w/t, how to find time?, must I use equations of motion?
 
TheRedDevil18 said:
p=w/t, how to find time?, must I use equations of motion?
Nope. You already know that the time is 1sec.
 

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