In March 2004, a British company successfully tested a power system to tap the e

Question

In March 2004, a British company successfully tested a power system to tap the energy of ocean tides. The energy will be stored in an underwater turbine consisting of two metal blades, each 15.0 m long. The movement of the water due to the tides will give kinetic energy to the turbine blades, causing them to spin. In the calculations that follow, ignore any frictional drag due to the seawater.

If we model each of these two blades as a thin uniform steel bar 15.0 m long and 25.0 cm in diameter, at what rate (in rad/s and rpm ) must they spin for the turbine to store 1.00 MJ of energy? The density of steel is 7800 kg/m^3 (Recall that density is equal to an object's mass divided by its volume.)

Omega=______________rad/s

Omega=______________rpm

Explanation / Answer

Rotational energy: (E = 0.5Iomega ^2 = (rac{1}{3}ml^2)omega^2 = 10^6 J) = 2.15rad/s = 20.58rpm

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