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Q72PE

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Found in: Page 398

College Physics (Urone)

Book edition 1st Edition
Author(s) Paul Peter Urone
Pages 1272 pages
ISBN 9781938168000

Gauge pressure in the fluid surrounding an infant’s brain may rise as high as ${\rm{85}}{\rm{.0 mm Hg}}$ (${\rm{5 to 12 mm Hg}}$ is normal), creating an outward force large enough to make the skull grow abnormally large. (a) Calculate this outward force in newton on each side of an infant’s skull if the effective area of each side is ${\rm{70 c}}{{\rm{m}}^{\rm{2}}}$ . (b) What is the net force acting on the skull?

(a) outward force acting on each side of the brain is obtained is ${\rm{79}}{\rm{.3 N}}$.

(b) The net force acting on the skull is obtained as zero.

See the step by step solution

Step 1: Conceptual Introduction

The force per unit perpendicular area across which the force is exerted is known as pressure. Pressure is defined as follows in equation form:

$P = \frac{F}{A}$

Here $$P$$ is the pressure, $$F$$ is the force and $$A$$ is the area.

Step 2: Calculate the outward force in Newton on each side of an infant’s skull

(a)

The force per unit perpendicular area across which the force is exerted is known as pressure. Pressure is defined as follows in equation form:

$P = \frac{F}{A}$

The surface area is ${\rm{70 c}}{{\rm{m}}^{\rm{2}}}$.

The surface area in meter square is ${\rm{0}}{\rm{.0070 }}{{\rm{m}}^{\rm{2}}}$.

The pressure exerted by the liquid is ${\rm{85 mm Hg}}$.

The pressure in Pascal is:

$$\begin{array}{c}P = \frac{{85 \times 1.01 \times 1{0^5}}}{{760}}\\ = 1.129 \times 1{0^4}\,Pa\end{array}$$

Hence, the pressure is ${\rm{1}}{\rm{.13 \times 1}}{{\rm{0}}^{\rm{4}}}{\rm{ Pa}}$.

By putting all the value into the equation we get:

$\begin{array}{l}F = P \times A\\F = 1.129 \times 1{0^4}\, \times 0.007\\F = 79.3\,N\end{array}$

Therefore, outward force acting on each side of the brain is ${\rm{79}}{\rm{.3 N}}$. The net force acting on the skull is zero.

Step 3: Calculate the force acting on the skull.

Net force acting on skull is zero because equal force is applied on both sides of the brain, so it cancels out.

Hence the net force on the brain is $$0\,{\rm{N}}$$.