Question

Arteriosclerotic plaques forming on the inner walls of arteries can decrease the effective cross-sectional area of an artery. Even small changes in the effective area of an artery can lead to very large changes in the blood pressure in the artery and possibly to the collapse of the blood vessel. Imagine a healthy artery, with blood flow velocity of v0=0.14m/s and mass per unit volume of rho=1050kg/m3. The kinetic energy per unit volume of blood is given by

Answer 1

The kinetic energy per unit volume of blood is 10.29 J/m³

Further explanation

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.

$\large {\boxed {F = ma }$

F = Force ( Newton )

m = Object's Mass ( kg )

a = Acceleration ( m )

Let us now tackle the problem !

$\texttt{ }$

Given:

v = 0.14 m/s

ρ = 1050 kg/m³

Unknown:

Ek/V = ?

Solution:

$Ek = \frac{1}{2} m v^2$

$\frac{Ek}{V} = \frac{1}{2} \frac{ m v^2 }{V}$

$\frac{Ek}{V} = \frac{1}{2} \frac{ m } {V} v^2$

$\frac{Ek}{V} = \frac{1}{2} \rho v^2$

$\frac{Ek}{V} = \frac{1}{2} \times 1050 \times 0.14^2$

$\frac{Ek}{V} = 10.29 \texttt{ Joule/m}^3$

$\texttt{ }$

Conclusion:

The kinetic energy per unit volume of blood is 10.29 J/m³

$\texttt{ }$

Learn more

• Impacts of Gravity : brainly.com/question/5330244
• Effect of Earth’s Gravity on Objects : brainly.com/question/8844454
• The Acceleration Due To Gravity : brainly.com/question/4189441
• Newton's Law of Motion: brainly.com/question/10431582
• Example of Newton's Law: brainly.com/question/498822

Answer details

Grade: High School

Subject: Physics

Chapter: Dynamics

Keywords: Gravity , Unit , Magnitude , Attraction , Distance , Mass , Newton , Law , Gravitational , Constant

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Answer 2

Answer:

The kinetic energy per unit volume of blood is 10.29 $\frac{J}{m^3}$.

Explanation:

The formula for the kinetic energy per unit volume (K) is given as follows:

$K = \frac{1}{2}\rho v^2$ --- (A)

Proof of the above formula: You must be wondering from where the aforementioned formula came, since the kinetic energy (KE) is $\frac{1}{2}mv^2$.

Well, in this case, we need to find the Kinetic energy per unit volume (V).

$K = \frac{KE}{V} = \frac{\frac{1}{2}mv^2 }{V} \\Since,\\Density =\rho= \frac{m}{V} \\Therefore,\ the\ above\ formula\ will\ become:\\K = \frac{1}{2}\rho v^2$

Where,

K = Kinetic energy per unit volume = ?

$\rho$ = Density = Mass per unit volume = $1050\frac{kg}{m^3}$

v = velocity (which in this case is the flow velocity $v_o$) = $0.14\frac{m}{s}$

Plug the values in the equation (A):

$K = \frac{1}{2}(1050) (0.14)^2 = 10.29 \frac{J}{m^3}$

Therefore, the kinetic energy per unit volume of blood is 10.29 $\frac{J}{m^3}$.