Question

powers the fan is converted to the kinetic energy of moving air. A fan is putting 1.9 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?Express your answer with the appropriate units.

Answer 1

Answer:

Explanation:

Given

Power $P=1.9\ J/s$

Also Power is given by

$P=\frac{\rho \times A\times V^3}{2}----1$

Where P=Power delivered

$\rho$=density of air

A=Area

V=Velocity of air

If we increase velocity by a factor of 2 Power changes to P'

$P'=\frac{\rho \times A\times (2V)^3}{2}----2$

Divide 1 and 2

$\frac{P}{P'}=\frac{V^3}{(2V)^3}$

$P'=8 P$

$P'=8\times 1.9=15.2\ J$