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 15.0m 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.

Part A -
If we model each of these two blades as a thin uniform steel bar 15.0m long and 25.0cm 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/m3 (Recall that density is equal to an object's mass divided by its volume.)
w=____ rad/s



Part B -
w=____ rpm

Explanation / Answer

The rotational energy of a system is given by

RE = 1/2 * I * ^2

I is the moment of Inertia

If we assume that the blades are on opposite sides of the point of rotation, we can model them as a 30.0m bar, rotating about its center.

From tables of moments of inertia,

I = m * L^2 / 12

The volume of the rod is =    * 0.125^2 * 30 = 1.472 m^3

Mass= V*p = 1.472*7800 = 11486.44 kg

Thus, the moment of Inertia= m * L^2 / 12 = 861483.61 kg/m2

If we need to store 1.00 MJ, then we have

^2 = (2*Energy)/I = 2 * 10^6 / 861483.61
= 1.523 rad/s
= 14.56 pm

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