Potential Energy and electricity question

[ihatebluescrubs]

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I don't get this question:

A marooned physicist creates a crude hydroelectric generator hoping to use the kinetic energy of a small waterfall as a source of energy for his radio. Given a mechanical efficiency of 75%, power and AC cycling frequency requirement of 20 watts and 60 Hz respectively, along with a voltage requirement of 120Vrms, how far below the top of the waterfall should he place his generator? (NOTE: Assume that 1kg of water strikes the surface of the rotor per second, and neglect air resistance)

Given ANSWER:

We can use the principal of conservation of energy because the question instructs us to neglect air resistance. Therefore:

E = K + U and Kfinal should equal Uinitial at the point of contact with the generator Since the units of Power are Joules/Second we need to modify Uinitial to be the rate of potential energy produced by 1kg/sec of water. Also don’t forget to take the mechanical efficiency into account.

3/4 (m/t)gh = Power

h = 4(Power)(t)/3mg

h = 4(20 Watts)(1 sec)/3(1 kg)(9.8 m/s2)

h = 2.72 m

How were they able to determine that Power = (m/t)gh? I get that potential energy =mgh but I don't get how they replaced m with (m/t)

Thanks!

 

[Gauss44]

I don't get this question:




Given ANSWER:



How were they able to determine that Power = (m/t)gh? I get that potential energy =mgh but I don't get how they replaced m with (m/t)

Thanks!

They divided energy by time to convert it to power. Power = Potential Energy divided by time.

 

[Laureatebarrel]

Power is by definition Energy divided by time. Since the question asks for 75% of power you take 3/4 of potential energy divided by time to get power.