Question

Ocean waves carry a lot of energy – according to the Bureau of Ocean Energy Management, about 2,640 TWh/yr (terawatt-hours per year) off the immediate coast of the US. 1 TWh/yr is enough to power 93,850 average U.S. homes. If some of this energy could be harnessed, it could be a great source of clean, renewable energy. Assume that an ocean wave is described by a sinusoidal transverse wave along the surface of the ocean and that has an amplitude of 2.0 m, a frequency of 0.25 Hz, and a wavelength of 130 m. Make a model (i.e. write down an equation and calculate) for the energy that a wave-energy harnessing buoy shown below will generate from those waves per cycle and in one whole day. How many homes could this amount of energy power per year? Assume that the buoy always floats at the surface and that the generator shown on the right will convert all of the gravitational energy of the buoy into usable electric energy. The combined mass of the buoy and the translator is 50.0 kg. Deeper thinking question (write a sentence or two in response): Where does the wave energy come from? What happens to the wave after it has passed the buoy? Why?

Hints: (i) What is the total vertical movement of the buoy in one wave cycle? (ii) How much gravitational potential energy does the buoy gain from the upward movement in each wave cycle?(iii) How many wave cycles pass the buoy in one hour and in one day?

Answer 1

wave equation

.

The bouy goes up to a distance of 2m i.e the amplitude of the wave.

total vertical displacemnt in one complete cycle would be

331.04 m

ii)

energy recieved by the buoy = m * g * total vertical displacement in one cycle.

= 50 * 9.8 * 331.04

= 16.2 KJ

iii)

no of waves passsing = frequency * time

in hour

n= 0.25 * 3600= 900

in one day

n=21600

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