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Chapter 9: Problem 4

Atmospheric pressure is about \(1.0 \times 10^{5} \mathrm{Pa}\) on average. (a) What is the downward force of the air on a desktop with surface area $1.0 \mathrm{m}^{2} ?$ (b) Convert this force to pounds so you really understand how large it is. (c) Why does this huge force not crush the desk?

Short Answer

Expert verified
Question: Calculate the downward force of air in pounds exerted on a desktop with a surface area of 1.0 m^2, and explain why this force does not crush the desk. Answer: The downward force of air on the desktop is approximately 22480 lbs. This huge force does not crush the desk because there is an equivalent upward force from the air pressure acting on the bottom side of the desk. These two opposing forces cancel each other out, resulting in a net force of zero on the desk. Furthermore, the desk is made of materials that can resist these forces, allowing it to maintain its shape and support the pressure from the air.

Step by step solution

01

Find the formula for force exerted by air pressure

We will use the formula for force exerted by air pressure: \(F = P \times A\) where F is the force exerted, P is the atmospheric pressure, and A is the surface area of the object.
02

Insert given values and calculate the downward force of air

We have the atmospheric pressure, P = \(1.0 \times 10^{5} \mathrm{Pa}\), and the surface area, A = $1.0 \mathrm{m}^{2}$. Plug these values into the formula and solve for F: \(F = (1.0 \times 10^{5} \mathrm{Pa}) \times (1.0 \mathrm{m}^2)\) \(F = 1.0 \times 10^5 \mathrm{N}\) (Newtons) (b) Convert the force to pounds
03

Convert the force from Newtons to pounds

To convert the force from Newtons to pounds, use the conversion factor: 1 N = 0.2248 lbs Multiply the force exerted in Newtons by the conversion factor: \(F = (1.0 \times 10^5 \mathrm{N}) \times (0.2248 \mathrm{lbs/N})\) \(F \approx 22480 \mathrm{lbs}\) (c) Explain why the huge force does not crush the desk
04

Understand the forces acting on the desk

The large downward force caused by air pressure does not crush the desk because there is also an equivalent upward force from the air pressure acting on the bottom side of the desk. These two opposing forces cancel each other out, resulting in a net force of zero on the desk. Additionally, the desk is constructed with materials that can resist the forces exerted on it, managing to hold its shape and support the pressure from the air.

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