Question

A.) A challenge gaining prominence throughout the planet is the increased need for "green" or sustainable energy. In certain parts of the country, wind farms are a viable alternative to conventional energy sources. An average wind turbine, the device which converts rotational motion to electricity, has a maximum capacity of 1.80 MW1.80 MW . However, the wind turbine realistically never runs at full power. If a wind turbine runs at 26.4%26.4% capacity for 1.00 year1.00 year , how much energy does the wind turbine generate?

E=______kWh

B.)

Suppose that the average U.S. household uses 14100 kWh (kilowatt‑hours) of energy in a year. If the average rate of energy consumed by the house was instead diverted to lift a 2020 kg car10.8 m into the air, how long would it take?

car:________s

Using the same rate of energy consumption, how long would it take to lift a loaded Boeing 747 airplane, with a mass of 4.15×105 kg , to a cruising altitude of 9.67 km ?

airplane:______S

Answer 1

Given,

Capacity, P = 1.80 MW = 1.8 * 10³ kW

Efficiency, n = 26.4%

Time, t = 1 yr = (365 * 24) hrs

             = 8760 hrs

Thus,

Energy generated by turbine, E = P*n*t = 1.8 * 10³ * (26.4/100) * 8760

                                                   = 4.16 * 10⁶ kWh

(B)

Average consumption, P' = 14100 kWh / yr

                                = [ (14100 * 10³ * 3600) / (365*24*3600) ] J/s (Convert kWh in Joules and year in seconds)

                                = 1609.6 J/s

Now,

mass of car, m = 2020 kg

height to raised, h = 10.8 m

Energy required, E' = m*g*h = 2020*9.8*10.8

                                = 213796.8 J

Now,

time required, t' = E' / P' = 213796.8 / 1609.6

                           = 132.8 s

(C)

Given,

Mass, M = 4.15 * 10⁵ kg

height, H = 9.67 km = 9.67 * 10³ m

Energy required, E'' = M*g*H = 4.15 * 10⁵ * 9.8 * 9.67 * 10³

                                = 393.3 * 10⁸ J

Now,

time required, t'' = 393.3 * 10⁸ / 1609.6

                            = 2.44 *10⁷ s   = (2.44 * 10⁷ / 3.6 * 10³) hrs

                            = 6780 hours