TBR Physics - Section 3 - Q26 and Q28

[SKaminski]

Q26)

Relevant information:
Water flows from the reservoir and falls over the dam. At the bottom of the dam is a water wheel. When the falling water strikes the wheel, the wheel will rotate, causing a conducting coil in the generator to rotate through a magnetic field...
Let the height of the dam be 150 meters and the width of the dam be 500 meters. The water is moving at a speed of 5 m/s and has a depth of 2 meters.

Question:
For the entire process described in the passage, the BEST description of energy conversion is:
A) kinetic energy to potential energy, electrical energy, and heat.
B) potential energy to electrical energy and kinetic energy.
C) kinetic and potential energy to electrical energy, kinetic energy, and heat.
D) electrical energy to kinetic energy.

Correct Answer: C.
Justification: As the water leaves the top of the dam, it is moving, so it has initial kinetic energy. it is 150 meters above the hydraulic generator, so it also has initial potential energy. The final outcome is the conversion of the mechanical energy to electrical energy.

My problem with this explanation:
My answer was B. It is the same as answer C, except it does not include INITIAL KINETIC energy, nor FINAL HEAT (internal energy?).

I had narrowed it down to answers B and C and ruled out C for two reasons: 1. I assumed that the forward velocity (Vx) was having no effect on the generator, which may have been an erroneous assumption on my part, and was only considering Vy.

Secondly, the question no where mentions/brings up heat. For these two reasons I eliminate answer C. What was wrong with my thinking here?

Q28)
Background Information: Which of the following graphs BEST represents the relationship between the magnetic field strength and the area of the coil, if the maximum voltage and coil rotation frequency are held fixed?
Equation given:
Eo=(En)sin(omega)t
with Eo=BA(omega)
B=magnetic field, A=area of coil.

Only two important graphs:
B(my answer), a straight line with a negative slope from 5,0 to 0,5. It resembles a linear relationship.

And answer A, which has a graph that looks like http://img15.imageshack.us/img15/2619/motortor.jpg (with different values for the X and Y, of course.) That's an asympotic relationship,

I guess I don't understand how the graph A represents an inversely proportional relationship? Maybe I'm not thinking about it right.

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[Yorick]

At the top, the water is at a height, 150, and is flowing so it has kinetic AND potential energy. The bottom is at a height 0 so there is no potential energy at the bottom and the water is moving in the wheel, so it has kinetic energy. This alone eliminates choices A,B, and D, so C is the best answer.

The reason heat becomes part of the total energy is because of the conducting coil rotating through the magnetic field, which generates and electrical current (heat and electrical energy).

Q28:

The graph is asymptotic because if you set Eo=Eo, then (En)sin(omega)t=BA(omega) and solving for B, B=(En)sin(omega)t / A(omega), so A can never be 0 since it is in the denominator, so B is inversely proportional to A. B will approach 0 as A approaches infinity and B will approach infinity as A approaches 0, so answer A has the best graph, asymptotic to the positive X and Y axis.

 

[SKaminski]

Thank you, that makes complete sense.

The graph they showed DID have each axis touch 0. Without the graph reaching up towards infinity, i should have known it was a mistake. Thank you.

 

[Rucap09]

Bump.

On this question (which I've got listed as Q1 of TBR Physics Book 1 Ch3), isn't it still inaccurate to state that the kinetic energy is being "converted" to these three? The horizontal velocity of the water has no bearing on the y-axis velocity, which is the velocity that contributes to turning the dam. If water were to simply fall off the top as opposed to having an initial velocity, would it make any difference in the force produced?