Question

Suppose you have a device that extracts energy from ocean breakers in direct proportion to their intensity. If the device produces 20.0 kW of power on a day when the breakers are 1.20 m high, how much (in kW) will it produce when they are 0.450 m high?

Answer 1

Answer:

2.81 kW      

Explanation:

Initial power output, P = 20.0 kW

Initial amplitude, A = 1.20 m

Final Amplitude, A = 0.450 m

Power is proportional to extracted energy which is proportional to the intensity of the wave and intensity of the wave is directly proportional to the square of the amplitude.

P ∝ E ∝ I ∝ A²

$\frac{P'}{P}=\frac{A'^2}{A^2}$

Substitute the values to find the value of power produced:

$P'=\frac{0.450^2}{1.20^2}\times 20.0 kW=2.81 kW$