Answer:
23.99N
Explanation:
Given:
Pressure created by the heart = 120mm of hg
converting the pressure into the standard unit of N/m²
1mm of hg = [tex]\frac{1}{760}atm=\frac{1}{760}\times 1.013\times10^5N/m^2[/tex]
now, 120 mm of hg in N/m² will be
120mm of hg = [tex]\frac{12}{760}\times 1.013\times10^5N/m^2[/tex]
also
given effective area = 15.0 cm² = 15 × 10⁻⁴m²
Now,
Force = Pressure × Area
thus,
Force exerted will be = [tex]\frac{120}{760}\times 1.013\times10^5N/m^2[/tex] × 15 × 10⁻⁴m²
or
Force exerted will be = 23.99N
The force that it exerts is about 24.0 N
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Let's recall Hydrostatic Pressure formula as follows:
[tex]\boxed{ P = \rho g h}[/tex]
where:
P = hydrosatic pressure ( Pa )
ρ = density of fluid ( kg/m³ )
g = gravitational acceleration ( m/s² )
h = height of a column of liquid ( m )
Let us now tackle the problem!
[tex]\texttt{ }[/tex]
Given:
blood pressure = P = 120 mmHg = 0.12 mHg
effective area = A = 15.0 cm² = 15.0 × 10⁻⁴ m²
density of mercury = ρ = 13600 kg/m³
gravitational acceleration = g = 9.8 m/s²
Asked:
force = ?
Solution:
We will use this following formula to solve this problem:
[tex]P = F \div A[/tex]
[tex]F = P A[/tex]
[tex]F = \rho g h A[/tex]
[tex]F = 13600 \times 9.8 \times 0.12 \times ( 15.0 \times 10^{-4} )[/tex]
[tex]F \approx 24.0 \texttt{ N}[/tex]
[tex]\texttt{ }[/tex]
The force that it exerts is about 24.0 N
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Grade: High School
Subject: Physics
Chapter: Pressure
