Q70PE - College Physics (Urone)

Question

One way to force air into an unconscious person’s lungs is to squeeze on a balloon appropriately connected to the subject. What force must you exert on the balloon with your hands to create a gauge pressure of \[{\rm{4}}{\rm{.00 cm}}\] water, assuming you squeeze on an effective area of \[{\rm{50 c}}{{\rm{m}}^{\rm{2}}}\]?

Step-by-Step Solution

Answer

The force acting into the surface per area is obtained as: \[{\rm{1}}{\rm{.96 N}}\].

Step 1: Conceptual Introduction

Fluid statics, often known as hydrostatics, is a branch of fluid mechanics that investigates the state of balance of a floating and submerged body, as well as the pressure in a fluid, or imposed by a fluid, on an immersed body.

Step 2: Given data

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 pressure given is \[{\rm{4 cm}}\] of water.

The surface area creating the pressure is \[{\rm{50 c}}{{\rm{m}}^{\rm{2}}}\].

The surface area creating the pressure in meter square is: 

\begin{aligned}A &= \frac{{50}}{{10000}}\\ &= 0.005\;\,{{\rm{m}}^2}\end{aligned}

 

 

Step 3: Force acting on the body

By putting all the value into the equation, we get: 

\begin{aligned}F &= P \times A\\F &= h\rho g \times A\\ &= \left( {0.04\;{\rm{m}}} \right)\left( {1000\;{\rm{kg}}/{m^3}} \right)\left( {9.8\;{\rm{m/}}{{\rm{s}}^2}} \right) \times 0.005\;{{\rm{m}}^2}\\ &= 1.96\,\;{\rm{N}}\end{aligned}

 

Therefore, force acting into the surface per area is: \[{\rm{1}}{\rm{.96 N}}\].