Answer:
The kinetic energy per unit volume of blood is 10.29 [tex]\frac{J}{m^3}[/tex].
Explanation:
The formula for the kinetic energy per unit volume (K) is given as follows:
[tex]K = \frac{1}{2}\rho v^2[/tex] --- (A)
Proof of the above formula: You must be wondering from where the aforementioned formula came, since the kinetic energy (KE) is [tex]\frac{1}{2}mv^2[/tex].
Well, in this case, we need to find the Kinetic energy per unit volume (V).
[tex]K = \frac{KE}{V} = \frac{\frac{1}{2}mv^2 }{V} \\Since,\\Density =\rho= \frac{m}{V} \\Therefore,\ the\ above\ formula\ will\ become:\\K = \frac{1}{2}\rho v^2[/tex]
Where,
K = Kinetic energy per unit volume = ?
[tex]\rho[/tex] = Density = Mass per unit volume = [tex]1050\frac{kg}{m^3}[/tex]
v = velocity (which in this case is the flow velocity [tex]v_o[/tex]) = [tex]0.14\frac{m}{s}[/tex]
Plug the values in the equation (A):
[tex]K = \frac{1}{2}(1050) (0.14)^2 = 10.29 \frac{J}{m^3}[/tex]
Therefore, the kinetic energy per unit volume of blood is 10.29 [tex]\frac{J}{m^3}[/tex].
The kinetic energy per unit volume of blood is 10.29 J/m³
Newton's second law of motion states that the resultant force applied to an object is directly proportional to the mass and acceleration of the object.
[tex]\large {\boxed {F = ma }[/tex]
F = Force ( Newton )
m = Object's Mass ( kg )
a = Acceleration ( m )
Let us now tackle the problem !
[tex]\texttt{ }[/tex]
Given:
v = 0.14 m/s
ρ = 1050 kg/m³
Unknown:
Ek/V = ?
Solution:
[tex]Ek = \frac{1}{2} m v^2[/tex]
[tex]\frac{Ek}{V} = \frac{1}{2} \frac{ m v^2 }{V}[/tex]
[tex]\frac{Ek}{V} = \frac{1}{2} \frac{ m } {V} v^2[/tex]
[tex]\frac{Ek}{V} = \frac{1}{2} \rho v^2[/tex]
[tex]\frac{Ek}{V} = \frac{1}{2} \times 1050 \times 0.14^2[/tex]
[tex]\frac{Ek}{V} = 10.29 \texttt{ Joule/m}^3[/tex]
[tex]\texttt{ }[/tex]
The kinetic energy per unit volume of blood is 10.29 J/m³
[tex]\texttt{ }[/tex]
Grade: High School
Subject: Physics
Chapter: Dynamics
Keywords: Gravity , Unit , Magnitude , Attraction , Distance , Mass , Newton , Law , Gravitational , Constant
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