/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 5 An office window has dimensions ... [FREE SOLUTION] | 91Ó°ÊÓ

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An office window has dimensions \(3.4 \mathrm{~m}\) by \(2.1 \mathrm{~m}\). As a result of the passage of a storm, the outside air pressure drops to \(0.96\) atm, but inside the pressure is held at \(1.0 \mathrm{~atm} .\) What net force pushes out on the window?

Short Answer

Expert verified
The net force pushing out on the window is approximately \(28944 \mathrm{~N}\).

Step by step solution

01

Identify the Given Values

First, identify the dimensions of the window and the pressures inside and outside. The window dimensions are \(3.4 \mathrm{~m} \times 2.1 \mathrm{~m}\). The outside pressure is \(0.96 \mathrm{~atm}\) and the inside pressure is \(1.0 \mathrm{~atm}\).
02

Calculate the Area of the Window

Multiply the dimensions of the window to find the area: \( \text{Area} = 3.4 \times 2.1 = 7.14 \mathrm{~m^2} \).
03

Convert Atmospheric Pressure to Pascals

Convert both pressures from atmospheres to Pascals using the conversion factor \(1 \mathrm{~atm} = 101325 \mathrm{~Pa}\). Thus, the inside pressure \( P_i = 1.0 \times 101325 = 101325 \mathrm{~Pa} \) and the outside pressure \( P_o = 0.96 \times 101325 = 97272 \mathrm{~Pa} \).
04

Calculate the Pressure Difference

Find the difference in pressure between the inside and outside:\( \Delta P = P_i - P_o = 101325 - 97272 = 4053 \mathrm{~Pa} \).
05

Calculate the Net Force on the Window

Use the formula \( F = \Delta P \times A \) to calculate the force, where \( A \) is the area from Step 2. \( F = 4053 \times 7.14 = 28943.82 \mathrm{~N} \). This is the net force pushing out on the window.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Pressure Difference
Pressure difference refers to the variation in pressure from one side of a surface to the other. In many physics problems, calculating the pressure difference is critical in understanding how forces are applied over areas. For the given exercise, the pressure inside the office remains constant at 1.0 atm, while outside, due to the storm, it drops to 0.96 atm.

To find this pressure difference, we need to subtract the outside pressure from the inside pressure. Converting these pressures from atmospheres to Pascals makes the calculation more consistent with the physical equations we use. With the conversion factor 1 atm = 101325 Pa:

  • Inside pressure: 1.0 atm = 101325 Pa
  • Outside pressure: 0.96 atm = 97272 Pa
Thus, the pressure difference, \( \Delta P \), equals 101325 Pa - 97272 Pa, which results in 4053 Pa. Understanding pressure differences helps us figure out how much force acts on a specific area, which is crucial for solving problems involving forces on windows, doors, and other structures during weather changes.
Atmospheric Pressure
Atmospheric pressure is the force exerted per unit area by the weight of the air above that area. It is a variable factor and can significantly change due to weather conditions like storms. In this context, atmospheric pressure outside the office dropped due to a storm.

Normal atmospheric pressure at sea level is 1 atm or 101325 Pa. During the storm, the outside pressure dropped to 0.96 atm. Such changes can affect anything from windows to weather balloons. To handle calculations involving atmospheric pressure differences, ensure consistency by converting any pressure given in atm to units like Pascals. This allows easier manipulation and control over the physics equations at play.

Atmospheric pressure impacts many physics problems, especially when solving for forces related to pressure changes. It's crucial to remember that lower atmospheric pressure outside means there is less force pushing against structures, possibly causing pressure-induced forces to act outward from inside environments.
Net Force Calculation
Net force calculation involves determining the resultant force acting on an object when various forces are applied. In this particular problem, we're interested in the force exerted on the office window due to the pressure difference across it. This force is calculated using the formula:\[F = \Delta P \times A\]In this formula:
  • \( \Delta P \) is the pressure difference (4053 Pa), already calculated.
  • \( A \) represents the area of the window, calculated by multiplying its dimensions: 3.4 m \( \times \) 2.1 m = 7.14 m².
So, the net force \( F \) pushing out on the window is determined by multiplying the pressure difference by the area of the window:\[F = 4053 \text{ Pa} \times 7.14 \text{ m}^2 = 28943.82 \text{ N}\]Understanding net force calculations is essential as it helps predict how structures will respond under various conditions, such as changes in pressure. It also has wide applications in fields like engineering and meteorology, where pressure and force calculations are routinely involved.

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