Question

The opposite of a wind turbine is an electric fan: The electric energy that powers the fan is converted to the kinetic energy of moving air. A fan is putting 1.0 J of kinetic energy into the air every second. Then the fan speed is increased by a factor of 2. Air moves through the fan faster, so the fan moves twice as much air at twice the speed.

How much kinetic energy goes into the air every second?

Note: Express your answer with the appropriate units.

Answer 1

Given that

Energy per sec = 1.0 J

We know that energy per unit time is known as power.

The power of wind turbine given as

P = (d*A*V³)/2

where P is the power,d is density,A is area and V is the velocity.

P is directly proportional to the cube of velocity of fan.

so we increases the velocity by factor of 2.

therefore power increases by (2)³ = 8.

The Energy per second going into air becomes 8 times.

P' = 8 * 1.0 = 8 Joules per second

8 joules of kinetic energy goes into air in every second.