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 1.8 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?

Answer 1

14.4 J of kinetic energy goes into the air every second.

$\texttt{ }$

Further explanation

Let's recall the Kinetic Energy formula:

$\boxed {E_k = \frac{1}{2}mv^2 }$

Ek = kinetic energy ( J )

m = mass of object ( kg )

v = speed of object ( m/s )

$\texttt{ }$

Acceleration is rate of change of velocity.

$\large {\boxed {a = \frac{v - u}{t} } }$

$\large {\boxed {d = \frac{v + u}{2}~t } }$

a = acceleration (m / s²)v = final velocity (m / s)

u = initial velocity (m / s)

t = time taken (s)

d = distance (m)

Let us now tackle the problem!

$\texttt{ }$

Given:

initial kinetic energy = Ek = 1.8 J

initial speed of air = v

initial mass of air = m

final speed of air = v' = 2v

final mass of air = m' = 2m

Asked:

final kinetic energy = Ek' = ?

Solution:

$Ek' : Ek = \frac{1}{2}m'(v')^2 : \frac{1}{2}mv^2$

$Ek' : Ek = m'(v')^2 : mv^2$

$Ek' : 1.8 = 2m(2v)^2 : mv^2$

$Ek' : 1.8 = 8 : 1$

$Ek' = 8 \times 1.8$

$\boxed{Ek' = 14.4 \texttt{ J}}$

$\texttt{ }$

Learn more

• Velocity of Runner : brainly.com/question/3813437

• Kinetic Energy : brainly.com/question/692781

• Acceleration : brainly.com/question/2283922

• The Speed of Car : brainly.com/question/568302

$\texttt{ }$

Answer details

Grade: High School

Subject: Mathematics

Chapter: Energy

Answer 2

Answer:

14.4 J

Explanation:

Given that

Energy per sec = 1.8 J

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

The power of wind turbine given as

$P=\dfrac{\rho AV^3}{2}$

A= Area

V= Velocity

ρ=Density

We can say that

P ∝V³

P'∝V'³

P'∝(2V)³

P'= 8 x 1.8 J

P'=14.4 J

Now when speed become 2 time then the power P will become 8 times

So the new kinetic energy per sec = 8 x 1.8  J

                                                           = 14.4 J