Chapter 10, Problem 7ICA

Some alternate energy technologies, such as wind and solar, produce more energy than needed during peak production times (windy and sunny days) but produce insufficient energy at other times (calm days and nighttime). Many schemes have been concocted to store the surplus energy generated during peak times for later use when generation decreases. One scheme is to use the energy to spin a massive flywheel at very high speeds, then use the rotational kinetic energy stored to power an electric generator later.

The following worksheet was designed to calculate how much energy is stored in flywheels of various sizes. The speed of the flywheel (revolutions per minute) is to be entered in cell B2 and the density of the flywheel in cell B4. A formula in cell B3 converts the speed into units of radians per second. There are 2π radians per revolution of the wheel.

To simplify the computations, the stored energy was calculated in three steps. The first table calculates the volumes of the flywheels, the second table uses these volumes to calculate the masses of the flywheels, and the third table uses these masses to determine the stored rotational kinetic energy. Note that in all cases, changing the values in cells B2 and/or B4 should cause all appropriate values to be automatically recalculated.

1. a. What should be typed in cell B3 to convert revolutions per minute in cell B2 into radians per second?
2. b. What should be typed into cell E4 that can then be copied through the rest of the first table to calculate the flywheel volumes? Assume the shape of the flywheel to be a cylinder.
3. c. What should be typed into cell E12 that can then be copied through the rest of the second table to calculate the flywheel masses?
4. d. What should be typed into cell E20 that can then be copied through the rest of the third table to calculate the kinetic energies stored in the flywheels? The rotational kinetic energy is given by the formula:

   KE_Rot = (Iω²)/2 = (mr²ω²)/4

5. e. What should be typed into cell E25 that can then be copied through row 25 to determine the average kinetic energy at each height (in each column)?
6. f. What should be typed into cell E26 to determine the difference between the maximum kinetic energy and 800 times the minimum kinetic energy given in the table?