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
[tex]P=\dfrac{\rho AV^3}{2}[/tex]
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
14.4 J of kinetic energy goes into the air every second.
[tex]\texttt{ }[/tex]
Let's recall the Kinetic Energy formula:
[tex]\boxed {E_k = \frac{1}{2}mv^2 }[/tex]
Ek = kinetic energy ( J )
m = mass of object ( kg )
v = speed of object ( m/s )
[tex]\texttt{ }[/tex]
Acceleration is rate of change of velocity.
[tex]\large {\boxed {a = \frac{v - u}{t} } }[/tex]
[tex]\large {\boxed {d = \frac{v + u}{2}~t } }[/tex]
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!
[tex]\texttt{ }[/tex]
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:
[tex]Ek' : Ek = \frac{1}{2}m'(v')^2 : \frac{1}{2}mv^2[/tex]
[tex]Ek' : Ek = m'(v')^2 : mv^2[/tex]
[tex]Ek' : 1.8 = 2m(2v)^2 : mv^2[/tex]
[tex]Ek' : 1.8 = 8 : 1[/tex]
[tex]Ek' = 8 \times 1.8[/tex]
[tex]\boxed{Ek' = 14.4 \texttt{ J}}[/tex]
[tex]\texttt{ }[/tex]
[tex]\texttt{ }[/tex]
Grade: High School
Subject: Mathematics
Chapter: Energy
