14.3: Traditional Direct Marketing
By the end of this section, you will be able to:
- List and describe the various forms of traditional direct marketing.
- Explain how the digital age has impacted direct marketing.
Forms of Traditional Direct Marketing
Direct marketing involves using communication tools to engage directly with individual consumers and call them to take some marketing action (see Figure 14.2). That action can be a consumer visiting a website or calling a phone number. Ultimately, the goal is to motivate the consumer to make a purchase. If you’ve received a catalog in the mail or caught yourself watching an entire infomercial about the newest kitchen gadget or gym equipment, you’ve experienced traditional direct marketing as a consumer.
Direct-Mail Marketing
Direct mail arrives in people’s homes every day and is typically delivered by the U.S. Postal Service. When marketers use direct-mail marketing , they communicate promotional messages and offers directly to people’s homes or places of business. Examples of direct-mail marketing include postcards featuring an offer, discount, or coupon code. Additional examples include seasonal catalogs and glossy lookbooks presenting the latest fashions.
Like all forms of direct marketing, direct mail is designed to call the consumer to take an action, whether to visit a website, scan a QR code, or call a phone number. It is also highly targeted in that companies can send mail based on demographic characteristics such as age, income, zip code, and buying behavior.
Direct mail has some key advantages over other forms of promotion. First, as consumers are inundated with digital messages, direct mail offers the opportunity to stand out and capture attention. Even mostly digital-facing companies such as Warby Parker (see Figure 14.3) and Casper (mattresses) have added direct mail to their promotion portfolios in an attempt to stand out from other brands.
Direct mail also reaches an entire household of people. This is an important advantage for product categories where household members typically discuss and decide on a product together.
Finally, direct mail has the characteristic of lingering. Other forms of promotion, such as advertising and email marketing, don’t have as long a life span as direct mail. According to RetailWire , the average life span of a direct mail piece is 17 days, which means that a household may review that message repeatedly over the life of the mail piece (Ryan, 2019).
The major disadvantage of direct mail is that many consumers consider it junk mail and throw it out without every reading the offer. Also, mail can take time to land in homes. Although the U.S. Postal Service offers speedier delivery options, these come at an increased cost.
Catalog Marketing
Catalog marketing , also known as direct mail order, dates back to the 19th century and is one of the oldest forms of promotion. Catalogs typically include a variety of products that are often vividly displayed in a high-gloss magazine-like format.
Companies such as Lands’ End and IKEA have long used catalogs to entice consumers to call the phone number or visit the website displayed on the catalog. The call to action is precisely what makes catalog marketing direct marketing. Consumers are presented with vivid product images and offers such as free delivery or 20% off if the consumer responds to the call to action.
According to a 2020 article published in Harvard Business Review , catalogs are making a comeback. Consumers report being excited to receive a catalog. In fact, response rates for catalogs have jumped 170% over the last decade (Zhang, 2020).
Unlike emails and advertisements, catalogs remain in consumer homes long after they arrive. Companies such as Target and Amazon have used catalog marketing to connect with customers and present featured products across the seasons.
Telemarketing
Telemarketing is a form of direct marketing that involves a company representative placing or answering customer calls to guide the consumer toward making a purchase. During the calls, the representative or agent typically communicates offers to potential customers. Like other forms of direct marketing, the goal is to motivate the consumer to take some action, such as making a purchase or setting up a follow-up appointment.
Telemarketing can be outbound or inbound. With outbound telemarketing, a company representative contacts the prospective customer directly by phone. With inbound telemarketing, demand for the product or service is generated through other channels such as advertising, email, or direct mail. In response to messages delivered through these channels, the customer is motivated to contact the company directly regarding the product or service.
Companies that manage large volumes of calls typically use a call center , a centralized space where agents answer inbound calls and place outbound calls. The call center serves as the centralized location where customer information is collected or confirmed, and then the customer is directed to the right product or service representative. With the explosion in the use of smartphones to search the web, consumers can direct dial from any web page that presents a phone number for contacting the company. Many inbound calls are routed to agents who are located offshore in India and other countries.
Car dealerships often combine telemarketing with online direct marketing tools to connect with buyers interested in a vehicle listed in the dealership’s online inventory. The dealership website may invite consumers to complete a form, after which a sales representative will call the consumer to set up a test drive appointment or answer questions about availability.
Telemarketing can be effective in cases where the consumer expects a phone call. However, the explosion of unsolicited phone calls from telemarketers has led to a rise in regulation around this direct marketing tool. In 2003, the U.S. government created the National Do Not Call Registry, which bans unsolicited telemarketing calls (Federal Trade Commission Consumer Advice, 2011). Consumers must opt in and give permission for companies to contact them. Businesses that do not comply with the law face a hefty fine for violations.
Direct-Response TV (DRTV)
Direct-response television marketing is a type of direct marketing that is designed to compel viewers to take some immediate action, such as calling a phone number or visiting a website presented during a television commercial. The commercials typically involve a persuasive demonstration of a product, after which consumers are provided with a toll-free number or a website to order. The television stations QVC and HSN are excellent examples of DRTV, selling everything from apparel to appliances.
This movie clip from the film Joy starring Jennifer Lawrence as real-life entrepreneur Joy Mangano shows DRTV in action.
DRTV commercials often run 60 or 120 seconds but can be shorter. DRTV commercials that run for 30 minutes or longer are called infomercials. Dollar Shave Club has garnered 27 million views of its famous direct-response television commercial featuring founder Michael Dubin hilariously identifying all the problems with traditional shave products (see Figure 14.4). The commercial features the website domain several times and a clear call to action to the consumer to visit the site to learn more.
Infomercials often feature a spokesperson promoting the benefits of a product. In many cases, there is a persuasive demonstration of the product, and viewers are called to “act now.” Some of the most well-remembered infomercial products include the Snuggie, Magic Bullet, and Proactiv . A carefully executed commercial, coupled with the right product, can generate billions of dollars for companies. Proactiv, for example, rebranded as Alchemee in 2022, generated $1 billion in sales in 2020 from its famous acne skin-care line (Stych, 2022).
Because it offers the advantage of capturing customers in real time and is easy to measure, DRTV continues to be an effective direct marketing tool.
Seminars
Seminars allow companies to share their expertise and knowledge related to a topic, issue, or industry. These can be done in person or virtually and are a great tactic for developing trust and building relationships with consumers. They have additional advantages, including building greater brand awareness and introducing new products or services, and may ultimately lead to increased sales.
Trade Shows
Trade shows are exhibition events that provide companies the opportunity to present themselves and their products and services to industry peers. Trade shows are suited for the business-to-business (B2B) market and are sponsored and hosted by industry trade organizations. They are an excellent way for industry professionals to network and grow their businesses. They are also wildly popular. For example, one of the most popular trade shows, the Consumer Electronics Show, or CES, attracts thousands of companies that showcase their latest technology. This trade show serves as an intersection for industry professionals in the health, gaming, and automotive spaces, and participants include tech companies such as Google , Microsoft , and E3 , among others.
Companies that participate in trade shows can benefit in the following ways. First, trade shows allow company representatives to visit with existing customers to grow current sales and further solidify their partnership. They also give companies a chance to connect with and present to new buyers.
Every year, MailCon brings together marketing professionals, brands, and agencies to discuss the latest trends in email technology, strategy, and automation. Major brands such as Wayfair , Girl Scouts of the USA , Ford Motor Company , and A&E Networks gather to network and learn about advancements in the email marketing space (MailCon, 2022).
Digital marketing reaches customers where they are at—online. HubSpot answers some of the most common questions it gets about digital marketing in this article .
How Has the Digital Age Impacted Marketing?
The digital age has changed how marketers engage with customers and build relationships. Although the traditional channels of print, television, and radio certainly present advantages, the digital age has created opportunities for marketers to engage with consumers in a highly personalized and interactive way.
Online Direct Marketing Defined
Although traditional forms of direct marketing center on engaging directly with consumers through channels such as mail and television, online direct marketing uses a rich collection of digital tools to target individual consumers with an offer that requests a response or action. The online direct marketing tools covered in this section include website marketing, email marketing, content marketing, online video marketing, blogs, and online forums.
LendingTree is a great example of a fintech (financial tech) company disrupting the traditional banking industry. LendingTree has revolutionized the way consumers and banks participate in the lending process. It excels at matching consumers searching for financing with banks looking for qualified customers. It is LendingTree’s digital marketing tools that make this matching process possible.
A consumer who searches the web and lands on LendingTree’s website is invited to compare quotes and plans that are tailored to their age, income level, and location by filling out an online form. LendingTree then displays consumer-relevant plans and quotes based on their demographics and follows up with an email inviting consumers to view offers from financial institutions. If the customer is a Gmail user, consumers may then see digital ads later on sites such as YouTube and in their Gmail inbox.
Direct Meets Digital: The Evolution of Direct Marketing with Technology
The explosion in internet usage and online shopping coupled with the evolution of digital technologies has resulted in the emergence of online direct marketing. Although traditional forms of direct marketing remain important for engaging with consumers, the channel has evolved as technology has evolved. With 3.5 billion smartphone users worldwide, marketers recognize the value in engaging with consumers through mobile devices. In the United States alone, 65.6% of Americans report that they check smartphones 160 times a day (Georgiev, 2022).
In response to the explosion in smartphones and internet usage, online direct marketing is getting a larger share of advertising spend. In 2020, advertisers spent $139.8 billion on digital marketing, and that number is expected to grow to $200 billion by 2025 (Bangah, 2021).
Forms of Online Direct Marketing
There are several online direct marketing tools that can be used (see Figure 14.5). Let’s take a look at each tool in the following section.
Website Marketing
Website marketing is the promotion of a website that results in driving traffic or visitors to the site to learn more about the product or company or to make a purchase. The purpose of website marketing is to attract online shoppers who may be interested in a company’s product or service offering.
Developing a website is one of the most important steps a company can take to establish a digital presence online. Websites serve a variety of purposes. Some are designed to nurture consumers and guide them toward making a purchase, whereas others are designed to facilitate transactions. For example, car manufacturers such as Toyota and Honda use their websites to deliver details and options related to their product lines. Consumers can use interactive tools to change out features and colors based on their preferences; however, consumers would likely visit a dealership to make the actual purchase.
Amazon.com is designed to allow third-party sellers to share product details, reviews, and product comparisons. Its purpose is to facilitate a purchase transaction in which the consumer buys something directly from the site. Shopify has recently emerged as the “anti-Amazon” by offering sellers more than a dozen services ranging from e-commerce websites to inventory management and payment processing.
There are still other websites whose purpose is not transactional but that are designed to build community and engagement among customers. Bleacher Report’s website offers sports articles, game scores, and live sports streaming. Fans are invited to comment and engage with one another regarding the latest sports news. The website also offers the option of signing up for its newsletter delivered to consumers’ email inboxes. Whether it’s to communicate information, facilitate a transaction, or build a community, websites should be designed with a positive user experience (UX) in mind.
Email Marketing
Email marketing is a type of direct marketing that is highly personal and designed to build relationships with consumers. Marketers use email to communicate promotions about products and share relevant content. It offers the advantage of connecting companies with highly targeted consumers at a much lower cost than other channels. Email usage statistics are also impressive, making this channel attractive as an online direct marketing tool.
Email boasts over 4 billion daily users; 99% of people report checking their email on a daily basis (Kirsch, 2022). Given the low cost and high usage rate, email marketing can be a profitable way to connect with customers. Marketers generally send two types of emails: transactional emails and marketing emails. A transactional email is a type of email that is sent to customers following a commercial transaction, such as a purchase or a return. When online shoppers purchase athletic apparel from Dick’s Sporting Goods , they receive an email confirmation confirming the order.
Marketing emails are promotional in nature and typically involve a marketing offer. Old Navy sends marketing emails during major sales events. They feature relevant product categories based on past purchases, often including a coupon code or free-shipping promotion.
Buzzfeed provides another great example of a company that optimizes email marketing to reach subscribers. According to Campaign Monitor, it has created a collection of diverse and audience-catered newsletters that are tailored to the preferences of Buzzfeed’s subscribers (Wildt, 2019). Emails feature relevant articles and funny GIFs that prompt subscribers to visit the site to read more. On average, subscribers who visit the site via email spend more time on the site than visitors from other channels.
Regardless of their email marketing strategy, companies utilize email marketing platforms such as Mailchimp to reach target audiences. Mailchimp is built for growing businesses, and in 2022, it launched a Super Bowl advertising campaign to promote its services. As a martech (marketing technology) company, it offers small businesses tools for guiding consumers through a customer journey to a purchase. Mailchimp’s automation tool allows businesses to send email campaigns based on a consumer’s interaction with an email message. The result is a highly personalized email conversation between the small business and the customer.
Learn how Mailchimp’s CEO and cofounder, Ben Chestnut, built and grew the Mailchimp email platform in this podcast: NPR’s How I Built This with Guy Raz .
Check out the 2022 Super Bowl commercial with DJ Khaled here:
Email marketing is also known as permission-based marketing. Permission-based marketing requires that marketers get consent to send email and text messages to consumers before contacting them with a promotional message. Once a consumer opts in to receive an email or text message, they can opt out by clicking on an unsubscribe link or by reply-texting a company to opt out of messages.
Consumers typically opt in to receiving emails when they place an online order so that they may receive order confirmation and shipping updates. In addition, consumers are also opting in to receive other value-added content, such as exclusive discounts, access to a webinar, a free trial, or some other type of value exchange.
Content Marketing
Websites, email, and other forms of online marketing are only as good as the content they carry. Content marketing involves creating and distributing content that is valuable and relevant to a company’s target customers. New York–based Dotdash Meredith is a good example of this. The company’s digital brands include Verywell, The Spruce, Byrdie, and others. Dotdash Meredith is a unit of Barry Diller’s IAC. Company policy: no pop-up ads!
As with other forms of direct marketing, content is about driving customers to take some desired action. Consumers would much rather consume a funny video clip, a highlight reel of their favorite athlete, and an inspiring quote or comment than see banner and pop-up ads. For content marketing to work, it must be useful, relevant, high quality, and engaging to the targeted audience.
When content is delivered through social media, blogs, and email, consumers have the opportunity to engage directly with the company and other content consumers. They can like, share, retweet, and mark as a favorite—all examples of actions taken in response to the content. Marketers can use the data created by these actions to perform sentiment analysis and generate other metrics. The challenge with content marketing is that it is constantly changing. Companies are tasked with constantly updating their content and continuing to tell stories that their audience wants to hear and engage with.
Online Video Marketing
Online video marketing involves creating videos that tell a story about a product, company, or brand designed to drive consumer engagement through activities such as liking, sharing, and retweeting. Video marketing is becoming increasingly popular as a marketing tool because the cost of creating video campaigns has dropped significantly in the last decade due to technological advancements. Biteable , for example, offers marketers a cost-effective way to create brand videos that are quick, simple, and customizable.
Along with the drop in cost to produce online videos, consumer demand for videos has increased. Because of this demand, Instagram , Facebook , and Twitter have pivoted to video-first platforms. Wyzowl ’s annual State of Video Marketing Survey revealed in 2021 that online video watching has doubled since 2018 and that online marketers “feel positive about the return on investment offered by video more than ever as it continues to strongly influence traffic, leads, sales, and audience understanding” (Hayes, 2023).
Read more about the key data points learned by Wyzowl in its 2022 survey. You might be interested to learn that 86% of businesses use video as a marketing tool, 94% of companies believe videos help customers better understand their product, and 99% of video marketers said they will continue using video. You can find the full report here . There’s a ton of interesting information!
Blogs and Online Forums
A blog is an online journal of interests, beliefs, or other topics published by a person, a group of people, or an organization. In its early stages, a blog was a personal journal that someone posted to the web. It’s since evolved into an online marketing tool that is typically a website or a webpage and serves a variety of purposes.
First, a blog’s purpose can be to share valuable and relevant information with targeted audiences. Ultimately, the goal is to attract visitors to the page or site and convert them to customers. In addition, marketers create blog content on sometimes a weekly or even daily basis so that consumers continue to visit the site or the page to access the new content. When the blog content is good, visitors will continue to engage with the articles produced by the company. Ultimately, this helps a company’s organic ranking on Google. In Google, your page or website will rank higher on the Google search results page as it grows in popularity and consumers click on it.
Blogs are also a great way to create and nurture online communities, or groups of people with similar interests connecting to one another online.
Customer relationship management company HubSpot is excellent at creating high-quality blog content for marketing and business professionals. It covers an array of professional topics, from marketing to human resources management to communicating effectively in the workplace. Its content ultimately drives visitors to its website, where they’ll find a suite of programs designed for marketing, sales, customer service, and operations.
Blogging can be an integral part of a content strategy as long as marketers dedicate time and resources to continue updating the content. Visitors appreciate fresh and relevant information, and delaying the delivery of high-quality content may mean a loss of visitor interest.
Learn more about the types of content marketing tools marketers have to work with by reading this HubSpot article . Included are the types you’re probably more familiar with, such as blogs and videos, but also discussed are the ones you may not have as much experience with, such as white papers and case studies.
Advantages of Online Direct Marketing
Several key advantages make online direct marketing an attractive tool for marketers. First, online direct marketing is not restricted by geographical boundaries. The Internet is readily available to most consumers globally, making it practical to market around the globe.
Second, online direct marketing is much less expensive than other forms of marketing when considering its global reach. Imagine how expensive it would be to send direct-mail catalogs to customers all over the world. Establishing an online presence by developing a website and creating video and blog content is relatively inexpensive compared with other forms of promotion.
Third, online direct marketing is easy to measure regarding campaign performance. With advertising tools targeted to mass audiences, it isn't easy to attribute a sale to a particular television or radio commercial. With online direct advertising, marketers can track the performance of their campaigns based on consumers’ interaction with digital tools such as email, online videos, and a company’s website. For example, when Nike creates and posts online video content on YouTube and its website, Nike marketers can track consumers’ engagement with that content and the consumer’s online journey. Online direct marketing reveals real-time insights into the effectiveness of campaigns compared with more traditional forms of promotion.
Fourth, online direct marketing is highly targeted. Marketers can carefully focus promotion efforts on very specific groups of consumers based on their geography, their social media channel preferences, and other variables. Online direct marketing also allows for retargeting, which occurs when consumers visit different websites but are shown similar ads based on their online consumer behavior.
Finally, online direct marketing allows for real-time interaction between brands and consumers. Consumers may start with a Google search and end with the completion of an online purchase. Throughout the online consumer buying process, marketers have the opportunity to engage with the consumer in real time.
Traditional direct marketing and online direct marketing offer a variety of benefits in connecting marketers to targeted consumers.
Digital marketers build and implement a company’s online-related activities and sales. Review this job description and list of qualifications from Glassdoor for more details. There are several additional resources that will help you better understand the digital marketing job role and what it will take to get a job in this field:
- Ahrefs—A Source for Digital Marketing Tutorials: “How to Start a Career in Digital Marketing (Step-by-Step)”
- Neil Patel: “How to Get a Digital Marketing Job with No Experience”
- Digital Marketing Institute: “ 7 of the Hottest Digital Marketing Jobs ”
- Indeed: “ How to Get a Job in Digital Marketing in 7 Steps ”
- American Marketing Association: “ 5 Reasons to Choose a Digital Marketing Career ”
Knowledge Check
It’s time to check your knowledge on the concepts presented in this section. Refer to the Answer Key at the end of the book for feedback.
1.
Which of the following best describes the difference between traditional direct marketing and online direct marketing?
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Online direct marketing uses digital tools to individually engage with consumers and call them to take some desired action. Traditional direct marketing does not allow a quick call to action.
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Traditional direct marketing is more effective than online direct marketing.
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Online direct marketing allows marketers to target consumers based on factors such as their location, age, and income. Traditional direct marketing can also be based on demographic factors.
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Traditional direct marketing channels do not include a call to action, and online direct marketing channels do.
2.
Which of the following best summarizes the cause for the emergence of online direct marketing as a promotion tool?
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The explosion of internet usage, online shopping, and smartphone usage and the advancement of digital marketing technologies best explains the emergence of online direct marketing.
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Consumers are spending less time watching movies and shows.
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Traditional direct marketing tools have gotten too expensive and are no longer effective at engaging customers.
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Traditional direct marketing doesn’t offer the same degree of message relevance that online direct marketing does.
3.
Which type of marketing involves creating and distributing content that is valuable and relevant to a company’s target customers?
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Website marketing
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Blog marketing
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Email marketing
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Content marketing
4.
Which form of online marketing is permission-based, meaning that consumers must consent to receiving online messages?
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Website marketing
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Blog marketing
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Content marketing
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Email marketing
5.
Which of the following represents an advantage of using online direct marketing tools?
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Online direct marketing allows marketers to target consumers globally because of worldwide access to the internet.
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Online direct marketing is highly targeted in that marketers can reach customers through a variety of digital channels that are inexpensive compared with other promotion tools.
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Online direct marketing allows for easier measurement of ROI on campaigns.
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All of these are advantages of online direct marketing.


6.2: Basic Concepts
Review of Anatomy and Physiology
The lungs sit to the left and right of the heart within a space called the thoracic cavity. The cavity is protected by the rib cage. A sheet of muscle called the diaphragm sits at the bottom of the thoracic cavity and separates it from the abdominal cavity. For this reason, the thoracic cavity is a closed space with its own intrathoracic pressure. [1]
There are two membranes in the thoracic cavity. The visceral pleura membrane covers the outside of the lungs, and the parietal pleura membrane lines the interior chest wall. The space between these two membranes is called the pleural space (also referred to as the pleural cavity). The pleural space normally contains between 10 to 20 mL of pleural fluid that provides lubrication as the pleura continuously slide against each other during inspiration and expiration. [2] See Figure 6.1 [3] for an illustration of the pleural cavity (i.e., pleural space).
The process of breathing, known as ventilation, is divided into two distinct phases called inspiration and expiration. During inspiration (also called inhalation), the diaphragm contracts and pulls downward while the intercostal muscles between the ribs pull upward. This movement increases the size of the thoracic cavity, thus decreasing the intrathoracic pressure. This change in pressure on inspiration is referred to as negative pressure . As a result, pressure is lower inside the thoracic cavity than atmospheric pressure, creating a vacuum effect that causes air to rush into the lungs on inspiration. [4]
During expiration (also called exhalation), the diaphragm relaxes, and the volume of the thoracic cavity decreases as the chest recoils. As a result, the intrathoracic pressure increases and becomes higher than atmospheric pressure, causing air to be forced out or the lungs.
View the following supplementary Medline Plus video [5] reviewing the physiology of breathing: Breathing
Pleural Disorders and Indications for Chest Tubes
An injury, inflammation, or infection can cause blood, fluid, or air to build up in the pleural space. The buildup of air or fluid can put pressure on the lung and cause all or part of it to collapse. Chest pain, shortness of breath, and coughing are common symptoms of pleural disorders, but the treatment for pleural disorders varies depending on the type of disorder and its seriousness. If left untreated, pleural disorders can lead to serious problems, including complete collapse of the lung, shock, or sepsis. [6]
When a lung collapses due to leaked air into the pleural space, it is called a pneumothorax , and when it collapses due to blood in the pleural space, it is called a hemothorax . [7] See Figure 6.2 [8] for an illustration of a pneumothorax.
There are different types of a pneumothorax: spontaneous pneumothorax, traumatic pneumothorax, and tension pneumothorax. A spontaneous pneumothorax can happen suddenly without any known cause. It can also be caused by medical conditions that affect the lungs, such as chronic obstructive pulmonary disease (COPD). A traumatic pneumothorax is caused by a chest injury, such as a bullet wound that pierces the pleural membranes, causing air to rush into the thoracic cavity.
Tension pneumothorax is a medical emergency caused by large pneumothorax that impacts cardiovascular functioning. The increasing thoracic pressure interferes with blood flow through the inferior vena cava, superior vena cava, and right chambers of the heart, causing the patient’s cardiac output and blood pressure to significantly drop. Due to increasing thoracic pressure, a tension pneumothorax causes the patient’s trachea to shift to the unaffected side. [9]
Other conditions that may require the placement of a chest tube include the following:
- Pleural effusion : Accumulation of fluid in the pleural space, often due to a medical condition such as cancer or heart, kidney, or liver failure
- Chylothorax : A collection of lymph in the pleural space
- Empyema : A pyogenic infection (pus) of the pleural space
- Hydrothorax : Accumulation of serous fluid in the pleural space
Chest tubes are indicated for these pleural disorders to remove air and/or fluid from the pleural space, reestablish negative pressure, and allow the lung to re-expand.
Chest Tube Placement Location
A chest tube is a sterile catheter that is inserted into the pleural space with small drainage holes at the proximal end of the tube to allow for drainage of air or fluid. See Figure 6.3 [10] for an image of the proximal end of the chest tube that is inserted into the patient’s pleural space.
The distal end of the chest tube is connected to a closed drainage system. See Figure 6.4 [11] for an image of a closed chest tube drainage system connected to a mannikin. The closed system drains air and fluid from the patient’s pleural space and prevents air or fluid from entering the pleural space. It is airtight and helps restore negative pressure in the thoracic cavity. [12] The chest tube drainage system must be maintained in an upright position below the patient’s chest to facilitate drainage. It should be placed on a non-movable surface or hung on the bed to prevent accidental dislodgment.
The location where the chest tube is inserted in the patient’s chest is based on the medical condition and the contents that need to be drained from the pleural space. For example, if a patient has a pneumothorax and air needs to be removed from the pleural space, the chest tube is placed higher within the thoracic cavity because air rises. It is typically placed in the second or third intercostal space of the anterior chest. As the air is removed from the patient’s pleural space, it disperses into the atmosphere, so there is little or no drainage collecting in the drainage system. [13]
Conversely, if fluid must be removed from the pleural space, it tends to settle in the lower portion of the lung cavity due to gravity. For this reason, chest tubes are often inserted in the lower posterior or lateral chest to drain blood and fluid. Suction is often applied to help promote the removal of the fluid. See Figure 6.5 [14] for an illustration of common chest tube placement sites.
Chest tubes are also routinely placed postoperatively after cardiac surgery to eliminate mediastinal blood. They are typically placed through incisions near the inferior aspect of the sternotomy incision.
Chest Tube Drainage System Chambers
There is a wide range of chest tube drainage system models that have evolved over time with new technology. However, the basic design principles of these systems are the same: to prevent air from entering the pleural cavity during the various phases of the respiratory cycle and to allow for continuous drainage of air and/or fluid from the pleural cavity. To ensure successful and safe treatment of patients with chest tubes, nurses must have a good understanding of the functioning of the specific models of chest tube drainage systems used in their agency. [15] Always follow agency policy and manufacturer’s directions for setup, monitoring, and use.
In general, traditional chest tube drainage systems have three chambers [16] :
- Collection chamber: The chest tube exits the incision from the patient’s chest wall and connects directly to the collection chamber to collect drainage from the pleural space. The collection chamber is calibrated so that drainage can be directly measured in the device. The outer surface of the chamber has a surface that can be written on to document the date, time, and amount of fluid collected. This chamber is typically on the far right side of the system. [17]
- Water seal chamber: The water seal chamber has a one-way valve that allows air to exit the patient’s pleural cavity during exhalation but does not allow it to reenter during inhalation. The water seal chamber is filled with sterile water and maintained at the 2 cm mark to ensure proper operation. This level should be checked regularly and filled with additional sterile water as needed. The water in the water seal chamber may rise with inhalation and fall with exhalation (referred to as tidaling ). Tidaling indicates the chest tube is patent. However, continuous bubbling in the water seal chamber may indicate an air leak. Some chest drainage systems have a feature that allows for measurements of air leaks. Read more about this feature later in this section. [18]
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Suction control chamber:
Not all patients require suction. If a patient has suction ordered, the amount of suction should be prescribed by the provider. There are two types of suction systems that may be used, referred to as a wet suction system or a dry suction system.
- A wet suction system controls suction by the level of water in the suction control chamber and is typically set at -20 cm for adults. If there is less water in this chamber, there is less suction. There should be gentle bubbling in this chamber because it is directly attached to a suction device. However, excessive bubbling can cause rapid evaporation of the water. See Figure 6.6 [19] for an image of a wet suction chest tube drainage system. In this image note the drainage in the collection chamber in the right compartment labeled “D,” the water seal chamber in the middle compartment labeled “C,” and -20 cm of water in the suction control chamber in the left compartment labeled “A.”
- A dry suction system uses a regulator to adjust the amount of suction and also responds to air leaks to deliver consistent suction for the patient. [20] See Figure 6.7 [21] for an image of a dry suction chest tube system. Note the collection chamber on the right, the water seal chamber in the middle, and the dry suction regulator on the left.
Air Leak Monitor
Chest tube drainage systems may include many safety features. For example, an air leak in the water seal chamber can indicate that air is reentering the patient’s pleural space, which can indicate worsening of a pneumothorax. Some chest tube drainage systems contain a feature in the water seal chamber that facilitates the measurement of the degree of an air leak from the chest cavity. See Figure 6.8 [22] for an image of an air leak meter. The meter is made up of numbered columns, labeled from 1 (low) to 5 (high). The higher the numbered column through which bubbling occurs, the greater the degree of air leak. By documenting the numbered column through which bubbling is occurring, the nurse can monitor the increase or decrease of the air leak.
There are many different types and manufacturers of chest tube drainage systems. View a supplementary chest drain education video [23] by Gentinge that demonstrates the various components of their dry suction water seal chest drain: Express Dry Suction Dry Seal Chest Drain.
Heimlich Valve
A Heimlich valve is an alternative to a chest tube drainage system. It is a small, specially designed flutter valve that is portable and mobile, allowing a patient with a chest tube to ambulate with ease. The valve functions in any position, never needs to be clamped, and can be hooked up to suction if required. It can also be worn under clothing. [24] See Figure 6.9 [25] for an image of a Heimlich valve.
The blue end of the Heimlich valve attaches to the chest tube inserted into the patient’s chest wall, and the other end can be left open to air or attached to a drainage bag. Air enters the inlet nozzle from the patient’s pleural space and opens a rubber sleeve inside the Heimlich valve. The sleeve collapses near the inlet nozzle, preventing the backflow of air into the patient, and then reopens at the outlet nozzle and allows air to escape. [26] See Figure 6.10 [27] for a visual demonstration of how the Heimlich valve works.
- A.D.A.M. Medical Encyclopedia [Internet]. Atlanta (GA): A.D.A.M., Inc.; c1997-2022. Breathing; [updated 2021, February 12]. https://medlineplus.gov/ency/anatomyvideos/000018.htm#:~:text=The%20second%20phase%20is%20called,and%20air%20is%20forced%20out ↵
- Merkle, A. (2022). Care of a chest tube. StatPearls. https://www.statpearls.com/ArticleLibrary/viewarticle/41781 ↵
- “ 2313_The_Lung_Pleurea.jpg ” by OpenStax College is licensed under CC BY 3.0 ↵
- A.D.A.M. Medical Encyclopedia [Internet]. Atlanta (GA): A.D.A.M., Inc.; c1997-2022. Breathing; [updated 2021, February 12]. https://medlineplus.gov/ency/anatomyvideos/000018.htm#:~:text=The%20second%20phase%20is%20called,and%20air%20is%20forced%20out ↵
- A.D.A.M. Inc. (2021, February 2). Breathing [Video]. Medline Plus. All rights reserved. https://medlineplus.gov/ency/anatomyvideos/000018.htm#:~:text=The%20second%20phase%20is%20called,and%20air%20is%20forced%20out ↵
- National Heart, Lung, and Blood Institute. (2022, March 24). What are pleural disorders? U.S. Department of Health & Human Services. https://www.nhlbi.nih.gov/health/pleural-disorders ↵
- National Heart, Lung, and Blood Institute. (2022, March 24). What are pleural disorders? U.S. Department of Health & Human Services. https://www.nhlbi.nih.gov/health/pleural-disorders ↵
- “ Blausen_0742_Pneumothorax.png ” by Blausen.com staff (2014) at Medical gallery of Blausen Medical 2014 is licensed under CC BY 3.0 ↵
- National Heart, Lung, and Blood Institute. (2022, March 24). What are pleural disorders? U.S. Department of Health & Human Services. https://www.nhlbi.nih.gov/health/pleural-disorders ↵
- “ Chest_Tube_Drainage_Holes.jpg ” by Bentplate84 is licensed under CC BY-SA 3.0 ↵
- “Book-pictures-2015-687-001.jpg” by British Columbia Institute of Technology (BCIT) is licensed under CC BY 4.0 . Access for free at https://opentextbc.ca/clinicalskills/chapter/10-7-chest-drainage-systems/ ↵
- This work is a derivative of StatPearls by Ravi & McKnight and is licensed under CC BY 4.0 ↵
- This work is a derivative of StatPearls by Ravi & McKnight and is licensed under CC BY 4.0 ↵
- “Common-insertion-site-of-chest-tube-for-air-and-fluid” by unknown author is licensed under CC BY-NC-ND 4.0 . Access for free at www.researchgate.net/figure/Common-insertion-site-of-chest-tube-for-air-and-fluid_fig2_279737006 ↵
- “ Chest Drainage Systems in Use ” by Zisis, et al. is licensed under CC BY-NC-ND 4.0 ↵
- This work is a derivative of Clinical Procedures for Safer Patient Care by British Columbia Institute of Technology and is licensed under CC BY 4.0 ↵
- This work is a derivative of Clinical Procedures for Safer Patient Care by British Columbia Institute of Technology and is licensed under CC BY 4.0 ↵
- This work is a derivative of Clinical Procedures for Safer Patient Care by British Columbia Institute of Technology and is licensed under CC BY 4.0 ↵
- “ Chest_drain_-_bedside_with_fluids.jpg ” by Johntex is licensed under CC BY-SA 3.0 ↵
- This work is a derivative of Clinical Procedures for Safer Patient Care by British Columbia Institute of Technology and is licensed under CC BY 4.0 ↵
- “Labelled_chest_tube_drainage_system.png” by British Columbia Institute of Technology (BCIT) is licensed under CC BY-SA 4.0 ↵
- “atm-03-03-43-f2.jpg” by Charalambos Zisis, et al. for Annuals of Translational Medicine is used under Fair Use. Access for free at 10.3978/j.issn.2305-5839.2015.02.09 ↵
- Gentinge. (n.d.) Express dry suction dry seal chest drain [Video]. Getinge. All rights reserved. www2.getinge.com/us/education/chest-drain-education/# ↵
- This work is a derivative of Clinical Procedures for Safer Patient Care by British Columbia Institute of Technology and is licensed under CC BY 4.0 ↵
- “Book-pictures-2015-688.jpg” by unknown author is licensed under CC BY 4.0 . Access for free at https://opentextbc.ca/clinicalskills/chapter/10-7-chest-drainage-systems/ ↵
- This work is a derivative of Clinical Procedures for Safer Patient Care by British Columbia Institute of Technology and is licensed under CC BY 4.0 ↵
- “ Heimlich_valve.GIF ” by Orinoco-w is licensed under CC BY-SA 3.0 ↵


4.9: Circuit Analysis
In this section we use the linear algebra we have developed to find the voltages and currents in a simple electrical circuit, such as the one shown in Figure 1. There are many reasons why this might be necessary; in this example we need to know the current flowing through the lamp to tell whether or not it will glow. Too little current will have no visible effect; too much current will cause the lamp to burn out. We will apply a few physical laws relating the voltages and currents in a circuit, turn these laws into systems of linear equations, and solve the equations for the voltages and currents.
Current, Voltage, and Resistance
We will use three physical quantities in our analysis of electrical circuits: current, voltage, and resistance. Current is the flow of electrical charge from one place to another. Electrons flowing through a wire or through some other electronic device comprise a current. Voltage is a difference in electric potential that makes electrons flow. Voltage is sometimes called electromotive force because it is like a “force” that moves electrons. Resistance is a property of the device through which the electron current flows. The lower the resistance of a device, the more easily current can flow through the device.
The analogy of water flowing through pipes can help you develop intuition about electrical circuits. In this analogy, electrical current corresponds to the flow rate of water. Voltage corresponds to the pressure that forces the water to flow, and resistance is the friction of flow. A small pipe would impede the flow of water more than would a large pipe, so the small pipe would correspond to a higher resistance. While this analogy can be helpful, keep in mind that electricity is not water. All analogies break down at some point.
We measure electrical current in amperes . The standard symbol for current is \(i\), and the direction of positive flow is indicated by an arrow on the circuit diagram. The arrow is for reference only; if the true current is in the opposite direction, we get negative values for \(i\). Because electrons are negatively charged, current is defined as flowing in the opposite direction as electron motion. But to reduce confusion, you should learn to think in terms of current rather than electron motion.
A point in a circuit where several devices are connected together is called a node . The conservation law for current says that “what flows in must flow out of a node,” a principle known as Kirchhoff ' s current law . Kirchhoff's current law states that the sum of all currents leaving a node is zero . In this law, a current entering the node is considered to be a negative current leaving the node.
Voltage is measured in volts and is usually written as \(\nu\) (or \(e\)). Since voltage is a difference in potential between two points (nodes), we can show it on a circuit diagram with a + and a –sign to indicate which two nodes we are comparing and which one of the nodes is considered negative. As with current, the markings are for reference only and we may end up with a negative value of \(\nu\).
In an electrical circuit, one node is usually chosen as a reference node and is considered to have a voltage of zero. Then the voltage at every other node is measured with respect to the reference node. This saves us the trouble of always specifying pairs of nodes for voltage measurements and marking + and – signs for each voltage. Other names for the reference node are common and ground .
A constant voltage source is a device that always forces the voltage between its two terminals to be a constant value. In Figure 1 the circle at the left represents a constant voltage source of 5 volts, so that the voltage at the upper (+) end is always exactly 5 volts higher than the voltage at the lower (-) end. A voltage source is something like a battery, but idealized. Real batteries do not maintain a constant output voltage under all conditions.
Resistance is measured in ohms and is denoted by \(R\). A resistor is shown as a zig-zag line in circuit diagrams and labeled with the value of its resistance in ohms. In this chapter we will consider only devices whose resistance is positive and the same in both directions. Ohm's law , also called the resistor law , relates the voltage and current in a resistor. For the resistor shown in Figure 2, with reference directions assigned to \(\nu\) and \(i\) as shown, Ohm's law is
\[\nu=i R \nonumber \]
Note that current flows from + to - through the resistor.
Ohm's law and Kirchhoff's current law are the only principles we need to write equations that will allow us to find the voltages and currents in the resistive circuit of Figure 1. We begin by choosing a reference node and assigning variables to the voltages at every other node (with respect to the reference node). These choices are shown in Figure 3.
The constant voltage source forces \(\nu _1\) to be exactly 5 volts higher than the reference node. Thus
\[\nu _{1}=5 \nonumber \]
Next we write equations by applying Kirchhoff's current law to each node in the circuit (except the reference node and \(\nu _1\), whose voltages we already know). At the node labeled \(\nu _2\) are three paths for leaving current. The current leaving through the 50 ohm resistor can be found by Ohm's law, where the voltage across that resistor is \(\nu _2 − \nu _1\):
\[i_{50}=\frac{v}{R}=\frac{\left(v_{2}-v_{1}\right)}{50} \nonumber \]
For current leaving through the 300 ohm resistor, the voltage is \(\nu _2\). Pay careful attention to the sign; since we are interested in the current leaving the node labeled \(\nu _2\), Figure 4.14 indicates that to apply Ohm's law we should take the voltage as \(+ \nu _2 −\) reference = \(\nu _2 − 0 = \nu _2\). So
\[i_{300}=\frac{v_{2}}{300} \nonumber \]
For the 100 ohm resistor, we can write
\[i_{100}=\frac{\left(v_{2}-v_{3}\right)}{100} \nonumber \]
According to Kirchhoff's current law, the sum of these three leaving currents is zero:
\[\begin{align}
\quad \tfrac{\left(v_{2}-v_{1}\right)}{50}+\tfrac{v_{2}}{300}+\tfrac{\left(v_{2}-v_{3}\right)}{100}=0 \nonumber \\
\Rightarrow 6\left(v_{2}-v_{1}\right)+v_{2}+3\left(v_{2}-v_{3}\right)=0 \nonumber \\
\Rightarrow \qquad \quad -6 v_{1}+10 v_{2}-3 v_{3}=0 \label{}
\end{align} \nonumber \]
Notice that when we wrote the equation for the node labeled \(\nu _2\), the variable \(\nu _2\) had a + sign each time it occurred in the equation, while the others had a - sign. This is always the case, and watching for it can help you avoid sign errors. Now we apply Kirchhoff's current law at the node labeled \(\nu _3\) to get the equation
\[\begin{align}
\frac{\left(v_{3}-v_{2}\right)}{100}+\frac{v_{3}}{2}=0 \nonumber \\
\Rightarrow \quad\left(v_{3}-v_{2}\right)+50 v_{3}=0 \nonumber \\
\Rightarrow \quad 0 v_{1}-1 v_{2}+51 v_{3}=0 \label{}
\end{align} \nonumber \]
Note that this time it is \(\nu _3\) that always shows up with a + sign.
Equations 2 , 6 , and 7 give us a system of three equations in the three unknown variables \(\nu _1\), \(\nu _2\), and \(\nu _3\). We now write them in matrix form as
\[\left[\begin{array}{lll}
1 & 0 & 0 \\
-6 & 10 & -3 \\
0 & -1 & 51
\end{array}\right]\left[\begin{array}{l}
v_{1} \\
v_{2} \\
v_{3}
\end{array}\right]=\left[\begin{array}{l}
5 \\
0 \\
0
\end{array}\right] \nonumber \]
(MATLAB) Use MATLAB to solve Equation 8 . You should find
\(\nu _1\) = 5.0000 volts
\(\nu _2\) = 3.0178 volts
\(\nu _3\) = 0.0592 volt
What is the determinant of the coefficient matrix \(A\)? Is the solution unique?
We can determine the current flowing through the lamp from \(\nu _3\) to ground in Example 1 by Ohm's law:
\[i=\frac{\nu}{R}=\frac{\nu _{3}}{2}=0.0296 \text { ampere } \nonumber \]
The visible effect will, of course, depend on the lamp. Let us assume that the specifications for our lamp indicate that 0.05 ampere or more is required before it will glow, and more than 0.075 ampere will cause it to burn out. In this case, our circuit would not make the lamp glow.
(MATLAB) Write and solve equations for the circuit in Figure 4. What are the voltages at the nodes labeled \(\nu _1\) through \(\nu _4\)? What is the current labeled \(i_1\)? And \(i_2\)?


16.11: References and Suggested Readings
[1]
Anderson, F. W. and Fuller, K. R.
Rings and Categories of Modules
. 2nd ed. Springer, New York, 1992.
[2]
Atiyah, M. F. and MacDonald, I. G.
Introduction to Commutative Algebra
. Westview Press, Boulder, CO, 1994.
[3]
Herstein, I. N.
Noncommutative Rings
. Mathematical Association of America, Washington, DC, 1994.
[4]
Kaplansky, I.
Commutative Rings
. Revised edition. University of Chicago Press, Chicago, 1974.
[5]
Knuth, D. E.
The Art of Computer Programming: Semi-Numerical Algorithms
, vol. 2. 3rd ed. Addison-Wesley Professional, Boston, 1997.
[6]
Lidl, R. and Pilz, G.
Applied Abstract Algebra
. 2nd ed. Springer, New York, 1998. A good source for applications.
[7]
Mackiw, G.
Applications of Abstract Algebra
. Wiley, New York, 1985.
[8]
McCoy, N. H.
Rings and Ideals
. Carus Monograph Series, No. 8. Mathematical Association of America, Washington, DC, 1968.
[9]
McCoy, N. H.
The Theory of Rings
. Chelsea, New York, 1972.
[10]
Zariski, O. and Samuel, P.
Commutative Algebra
, vols. I and II. Springer, New York, 1975, 1960.


9.2: English as a Lingua Franca in the Hindi Film Industry
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- Tejaswini Ganti
- University of California Press
If I’m making a Hindi film, I’m a Tamilian, but my DOP is a Malayali, and my editor is from Gujarat, so our common language is English.
—Sriram Raghavan, writer-director
When reflecting upon the linguistic history of the Hindi film industry, two features stand out: the relative insignificance of fluency in Hindi/Urdu as a prerequisite for acting, directing, or even writing; and the consistent presence of English as a language of trade discourse, commentary, and professional nomenclature. As mentioned previously, the industry emerged in multilingual Mumbai rather than the regions of northern or central India referred to as the Hindi “heartland” and drew personnel from all over the subcontinent and beyond. While standard histories of Indian cinema point out the diverse ethnic and linguistic backgrounds of actors and directors during the silent era, making special mention of how actors and actresses who could not speak Hindustani were displaced by stage actors and courtesans with the arrival of sound, the scenario is actually more complex. 5
Even with the advent of sound in 1931, directors and actors came from diverse linguistic and national backgrounds. For example, Bombay Talkies, which left an important legacy in the postindependence Hindi film industry in terms of stars and directors, had many Germans in its employ. One of its directors, Franz Osten, who did not know any Hindi, directed some iconic Hindi films from this era. Throughout its history and continuing till the present, there have always been a few directors working in the industry who knew very little or no Hindi at all. This holds true for actresses as well. One of the top stars of the 1930s was the Australian-born Mary Evans, renamed “Fearless Nadia,” who gained fame in action/stunt films despite her heavily accented Hindi. Presently, women from non-Hindi-speaking parts of India as well as from as far afield as Australia, Brazil, Canada, Great Britain, Sweden, and the United States continue to try their luck in Bollywood. 6
Even in the scripting process, English has played an important role starting from the early sound era. During the 1930s, in studios like Bombay Talkies, scripts and dialogues were initially conceived of in English by the writer (who was referred to as a “scenario” writer), after which the dialogue writer translated them into Hindustani. 7 Since scripts were often written by individuals who were not proficient in Hindustani, the autonomous dialogue writer emerged as a staple of Hindi cinema. The credits for a script were broken down into three components: story, screenplay, and dialogue, with each element attributed to a different individual—a practice continuing into the present. As a result of the varying ethno-linguistic backgrounds of Bombay film personnel, writers who were fluent or had a facility in Urdu were in great demand as dialogue and lyric writers, since Persianized Urdu was a valorized register for song lyrics and dialogues. 8 Many well-known Hindi/Urdu poets, playwrights, and novelists supported their literary endeavors by working in the Hindi film industry, and scholars have pointed out that after the partition of British India into India and Pakistan, whereby Urdu became the official language of Pakistan, the only site in India where Urdu was kept alive, and even flourished, was the Hindi film industry. 9
In this multilingual context—Urdu writers, German directors, Bengali actors, Marathi singers, Parsi producers, and so on—it is not surprising that English emerged as a lingua franca for cultural producers based in a British colonial port city. While Hindi was (and remains) important as the language within the diegesis and that of consumption, English served (and continues) as the primary language of professional nomenclature and discourse about Hindi cinema and filmmaking. The English terms director , producer , writer , actor , and film are part of daily parlance within and outside the industry, rather than the Hindi equivalents nirdeshak , nirmata , lekhak , abhineta , and chalchitra . In contrast to films made in other Indian languages, the opening and closing credits for mainstream Hindi films have been in English since the 1930s. The Devanagari (Hindi) and Nasta’liq (Urdu) scripts make an appearance in a film’s title, but only after the prominent appearance of the title first in Roman script. One reason is perhaps because Hindi films are the only ones to have been consistently distributed nationally since the 1930s and internationally since the 1940s.
The most prominent forms of journalistic, critical, and trade commentary about the Hindi film industry have been in English since the 1930s. Film reviews, interviews with stars, industry news, celebrity gossip, and trade reports are carried out in English-language periodicals, whether Filmland , Filmindia , or Blitz in the 1930s–1960s; Filmfare , Trade Guide , or Screen since the 1950s; or Film Information or Stardust since the 1970s. While there are several Hindi fanzines and newspapers that cover Hindi cinema, they are quite marginal in terms of their impact or readership within the industry. The main trade journals, Trade Guide , Film Information , and Box Office India , which carry box-office figures and report about the business of the film industry, are in English.
If English has always played a prominent role in the Hindi film industry, how is the contemporary moment distinctive? The most drastic difference is English’s changed status and value relative to Hindi. While English has served as a necessary lingua franca throughout the industry’s history, it is increasingly operating as a language of production, creativity, and decision making since the mid-2000s. This change has to do with key demographic shifts in the film industry: namely, the intensification of kinship networks whereby a significant number of leading actors, directors, and producers represent the second, third, or even fourth generation within the industry; and a larger number of creative personnel drawn from urban social elites whose formal schooling has been wholly in English. Since the turn of the millennium, as Hindi filmmaking became more lucrative and rationalized, taking on an aura of professionalism and respectability that it had not traditionally enjoyed, social elites and film industry progeny gravitated toward the film industry as a viable career path. 10 In the next section I discuss how these shifts are implicated in industry members’ assessments of the state of Hindi within the film industry.


2.2.6: The volume-amount relationship
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Figure \(\PageIndex{1}\) illustrates the effect of the amount of gas on the volume. Adding more gas molecules increases the collision frequency of the molecules with the walls increasing the gas pressure. The gas expands to reduce pressure until the pressure of gas in the chamber is equal to the outside pressure.
Avogadro's law
Avogadro’s law states that the volume of a gas is directly proportional to the amount of gas in moles provided the temperature and pressure of the gas are not changed.
The mathematical forms of Avogadro's law are the following.
\[V\propto {n}\nonumber\]
or
\[V=\mathrm{k}n\nonumber\]
or
\[\dfrac{V}{n}=\mathrm{k}\nonumber\]
where \(V\) is the volume, \(n\) is the number of moles, and \(k\) is the constant for the gas under the conditions of constant temperature and pressure. Since \(\mathrm{V} / \mathrm{n}\) is a constant, it implies that:
\[\dfrac{V_{1}}{n_{1}}=\dfrac{V_{2}}{n_{2}}=\mathrm{k}\nonumber\]
where \(V_{1}\) and \(n_{1}\) is initial volume and the initial amount of gas, respectively, and \(V_{2}\) and \(n_{2}\) is final volume and the final amount of gas in mole, provided the temperature and pressure are not changed.
Example \(\PageIndex{1}\)
A weather balloon containing \(3.0\) moles of helium has a volume of \(66 \mathrm{~L}\). What is the final volume if \(2.0\) moles of helium is added to it. The pressure and temperature of the gas do not change?
Solution
Given \(\quad V_{1}=66 L, \quad n_{1}=3.0 \mathrm{~mol}, \quad V_{2}=?, \quad n_{2}=3.0+2.0=5.0 \mathrm{~mol}\)
Formula:
\[\dfrac{V_{1}}{n_{1}}=\dfrac{V_{2}}{n_{2}}, \nonumber\]
rearrange the formula to isolate the desired variable:
\[V_{2}=\dfrac{V_{1} n_{2}}{n_{1}}. \nonumber\]
Plug in the values and calculate:
\[V_{2}=\dfrac{66 \mathrm{~L} \times \times 5.0 \mathrm{~mol}}{3.0 \mathrm{~mol}}=110 \mathrm{~L}. \nonumber\]


4.0: Introduction
Probability is the study of uncertainty . This may seem like a hopeless endeavor, sort of like knowing the unknowable, but it’s not. The study of probability gives us tools for taming the uncertain world we live and program in, and for reasoning about it in a precise and helpful way.
We may not know exactly how long a particular visitor is willing to wait for our webpage to load in their browser, but we can use probability to estimate how much traffic we’ll lose if this takes longer than a certain average duration. We may not know which specific passwords a hacker will try as he attempts to break our security protocol, but we can use probability to estimate how feasible this approach will be for him. We may not know exactly when a certain program will run out of RAM and have to swap its data out to virtual memory, but we can predict how often this is likely to occur — and how painful it will be for us — given a certain system load and user behavior.
The trick is to use the tools we’ve already built — sets, relations, functions — to characterize and structure our notions of the relative likelihood of various outcomes. Once those underpinnings are secured, a layer of deductive reasoning will help us make good use of that information to begin to predict the future.


4.2: The Ethics of Power and Authority
Law enforcement officers possess enormous amounts of power, which can be used against citizens to deprive them of their freedom, search them and their dwellings, seize their property, and use force against them. These powers are legally permitted under specific circumstances, and law enforcement officers are trained to know when these powers can be legally applied. As law enforcement officers rank among the most powerful occupations in society, what compounds their ability to use their power is that they are often in contact with relatively powerless and disenfranchised citizens who may be unable to resist an officer’s illegitimate use of that power. These powers are legally prescribed, and law enforcement officers are well aware of them. It is important that law enforcement officers not misuse their power for the following reasons.
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Because of the psychology of citizenship.
Citizens, for the most part, want to participate in the “social contract,” to be a part of mainstream society and carry out their citizenship responsibilities. They want to belong to society and will do what they think is required by authorities to accomplish this. As a result, they will often try very hard to respond to what law enforcement requires and may be susceptible to unreasonable requests by law enforcement. -
To maintain due process.
Every law enforcement officer should acknowledge the importance of due process. The abuse of power runs directly contrary to the notion of due process, and officers who misuse their power are creating an environment in which due process cannot flourish. Ideally, all officers in the criminal justice system should be focused on due process, and the police have a role in accomplishing due process by being fact finders and apprehenders (Manning, 2010). Along with this, law enforcement officers who are under pressure to charge a suspect must resist the power they are afforded when charges or other actions such as search and seizure are not warranted (Reiner, 2010). Police officers, in particular, face the challenge of weighing crime control against due process, in which they are faced with opportunities to misuse their power. Officers must make decisions on when and in what situations they should use their power. Officers must reflect on how the use of their power would look in a court of law under close scrutiny. -
To safeguard discretionary power and therefore efficiency.
As mentioned previously, law enforcement officers exercise power through discretion. Radical criminologists propose that the police have too much discretion, with the end result being “too much street justice” for the poor, while ignoring crimes of the powerful, of which the police are a member (Box, 2008, p.274). Box argues that the way to eliminate this lack of due process is to place restrictions on discretion. Should law enforcement officers desire to maintain the discretion that they have, which is critical for efficiency, they must not abuse their power.
Power and authority are tools that law enforcement officers must use judiciously and ethically. Without an ethical life, this power will be misused, creating a power imbalance that is bad for the officer, the agency, and society.


4.5.0: Gramática
Have a look at the following tables. What do you notice about the verbs tener and decir ? What happens for each of the different subjects?
|
Poner ( to put ) |
Hacer ( to do/make ) |
Traer ( to bring ) |
Salir (to get out/to go out) |
Dar (to give) |
|
| yo | pon go | ha go | tra igo | sal go | do y |
| tú | pones | haces | traes | sales | das |
| vos | ponés | hacés | traés | salís | das |
| usted/Ud./ él/ella | pone | hace | trae | sale | da |
| nosotros/nosotras | ponemos | hacemos | traemos | salimos | damos |
| vosotros/vosotras | ponéis | hacéis | traéis | salís | dais |
| ustedes/Uds./ellos/ellas | ponen | hacen | traen | salen | dan |
There are some verbs that are irregular in other subjects. This verb has a stem-change of e –> i . What do you notice about its conjugation? Which subjects have conjugation irregularities?
|
Decir ( to tell, to say ) |
|
|---|---|
| yo | di go |
| tú | d i ces |
| vos | decís |
| usted/Ud./ él/ella | d i ce |
| nosotros/nosotras | decimos |
| vosotros/vosotras | decís |
| ustedes/Uds./ellos/ellas | d i cen |
These verbs have a stem-change of e –> ie . What do you notice about their conjugation? Which subjects have conjugation irregularities?
|
Tener ( to have ) |
Venir ( to come ) |
|
|---|---|---|
| yo | ten go | ven go |
| tú | t ie nes | v ie nes |
| vos | tenés | venís |
| usted/Ud./ él/ella | t ie ne | v ie ne |
| nosotros/nosotras | tenemos | venimos |
| vosotros/vosotras | tenéis | venís |
| ustedes/Uds./ellos/ellas | t ie nen | v ie nen |
Ahora mira este video. It offers a summary of the ways in which we conjugate these verbs, and others that behave in a similar way.
Attribution: By Daniel Hernández Ruiz, licensed under CC BY 4.0.


7.1: Relations
While there is no agreed upon universal definition of mathematics, one could argue that mathematics focuses on the study of patterns and relationships. Certain types of relationships occur over and over in mathematics. One way of formalizing the abstract nature and structure of these relationships is with the notion of relations. In Chapter 8, we will see that a function is a special type of relation.
Recall from Section 3.5 that the Cartesian product of two sets \(A\) and \(B\) , written \(A\times B\) , is the set of all ordered pairs \((a,b)\) , where \(a\in A\) and \(b\in B\) . That is, \(A\times B=\{(a,b)\mid a\in A, b\in B\}\) .
Definition 7.1. Let \(A\) and \(B\) be sets. A relation \(R\) from \(A\) to \(B\) is a subset of \(A \times B\) . If \(R\) is a relation from \(A\) to \(B\) and \((a,b)\in {R}\) , then we say that \(a\) is related to \(b\) and we may write \(aR\) \(b\) in place of \((a,b)\in{R}\) . If \(R\) is a relation from \(A\) to the same set \(A\) , then we say that \(R\) is a relation on \(A\) .
Example 7.2. The set \(\mathbb{N}\times \mathbb{R}\) from Problem 3.55 is an example of a relation on \(\mathbb{R}\) since \(\mathbb{N}\times \mathbb{R}\) is a subset of \(\mathbb{R}\times \mathbb{R}\) .
It is important to notice that the order in which we write things for relations matters. In particular, if \(R\) is a relation from \(A\) to \(B\) and \(a R b\) , then it may or may not be the case that \(bR a\) .
Example 7.3. If \(A=\{a,b,c,d,e\}\) and \(B=\{1,2,3,4\}\) , then the set of ordered pairs \[R=\{(a,1),(a,2),(a,4),(c,2),(d,2),(e,2),(e,4)\}\] is an example of a relation from \(A\) to \(B\) . In this case, we could write \((c,2)\in{R}\) or \(cR 2\) . We could also say that \(a\) is related to 1, 2, and 4.
Example 7.4. As in the previous example, let \(A=\{a,b,c,d,e\}\) . One possible relation on \(A\) is given by \[R=\{(a,a),(a,b),(a,c),(b,b),(b,a),(b,c),(c,d),(c,e),(d,d),(d,a),(d,c),(e,a)\}.\]
Example 7.5. Consider the set of accounts \(A\) on the social media platform Twitter. On Twitter, each account has a set of accounts that they follow. We can model this situation mathematically using a relation on \(A\) . Define \(T\) on \(A\) via \(xTy\) if \(x\) follows \(y\) on Twitter. As a set \[T=\{(x,y)\in A\times A\mid x\text{ follows }y\text{ on Twitter}\}.\]
Example 7.6. You are already familiar with many relations. For example, \(=\) , \(\leq\) , and \(<\) are each examples of relations on the real numbers. We could say that \((3,\pi)\) is in the relation \(\leq\) and the relation \(<\) since \(3\leq \pi\) and \(3<\pi\) . However, \((3,\pi)\) is not in the relation \(=\) since \(3\neq \pi\) . Also, notice that order matters for the relations \(\leq\) and \(<\) yet does not for \(=\) . For example, \((-\sqrt{2}, 4)\) is in the relation \(\leq\) while \((4,-\sqrt{2})\) is not.
Example 7.7. Define the relation \(S\) from \(\{-1,1\}\) to \(\mathbb{Z}\) via \(1Sx\) if \(x\) is even and \(-1Sx\) if \(x\) is odd. That is, \(1\) is related to all even integers and \(-1\) is related to all odd integers.
Example 7.8. Let \(A\) be any set. Since \(\emptyset \subseteq A\times A\) , the empty set forms a relation on \(A\) . This relation is called the empty relation on \(A\) .
Relations can be represented using digraphs. A digraph (short for directed graph ) is a discrete graph that consists of a set of vertices connected by edges, where the edges have a direction associated with them. If \(R\) is a relation from \(A\) to \(B\) , then the elements of \(A\) and \(B\) are the vertices of the digraph and there is a directed edge from \(a\in A\) to \(b\in B\) if \((a,b)\) is in the relation \(R\) (i.e., \(aR b\) ). We can visually represent digraphs by using dots to represent the vertices and arrows to represent directed edges. We will not make a distinction between a digraph and its visual representation. Utilizing a digraph to represent a relation may be impractical if there is a large number of vertices or directed edges.
Example 7.9. Consider the relation given in Example 7.3. The corresponding digraph is depicted in Figure 7.1. Notice that we have placed the vertices corresponding to elements of \(A\) on the left and the elements of \(B\) on the right. This is standard practice, but what really matters is the edge connections not how the vertices are placed on the page.
= [circle, draw, fill=grey,inner sep=0pt, minimum size=5mm] = [draw,-stealth]
Problem 7.10. Let \(A=\{1,2,3,4,5,6\}\) and \(B=\{1,2,3,4\}\) and define \(D\) from \(A\) to \(B\) via \((a,b)\in D\) if \(a-b\) is divisible by 2. List the ordered pairs in \(D\) and draw the corresponding digraph.
If \(R\) is a relation on \(A\) (i.e., a relation from \(A\) to \(A\) ), then we can simplify the structure of the digraph by only utilizing one copy of \(A\) for the vertices. In this case, we may have directed edges that point from a vertex to itself. When drawing digraphs for a relation on a set, we will default to this simplified digraph (like the one depicted in Figure 7.2(b)).
Example 7.11. Figure 7.2(a) represents the relation of Example 7.4 as a digraph from \(A\) to \(A\) while the digraph in Figure 7.2(b) provides a streamlined representation of the same relation that uses the elements in \(A\) only once instead of twice.
Problem 7.12. Let \(A=\{1,2,3,4,5,6\}\) and define \(|\) on \(A\) via \(x|y\) if \(x\) divides \(y\) . List the ordered pairs in \(|\) and draw the corresponding digraph.
Problem 7.13. Let \(A=\{a,b,c,d\}\) and define \(R\) on \(A\) via \[{R}=\{(a,a),(a,b),(a,c),(b,b),(b,a),(b,c),(c,c),(c,a),(c,b),(d,d)\}.\]
- Draw the digraph for \(R\) .
- Draw the digraph for the empty relation on \(A\) .
We can also visually represent a relation by plotting the points in the relation. In particular, if \(R\) is a relation from \(A\) to \(B\) and \(aR b\) , we can plot all points \((a,b)\) that satisfy \(aR b\) in two dimensions, where we interpret the set \(A\) to be the horizontal axis and \(B\) to be the vertical axis. We will refer to this visual representation of a relation as the graph of the relation.
Example 7.14. When we write \(x^2+y^2=1\) , we are implicitly defining a relation. In particular, the relation is the set of ordered pairs \((x,y)\) satisfying \(x^2+y^2=1\) , namely \(\{(x,y)\in \mathbb{R}^2 \mid x^2+y^2=1\}\) . The graph of this relation in \(\mathbb{R}^2\) is the unit circle centered at the origin in the plane as shown in Figure 7.3.
Problem 7.15. For each of the following, draw a portion of the graph that represents the relation as a subset of \(\mathbb{R}^2\) .
- \(\{(x,y)\in \mathbb{R}^2 \mid y=x^2\}\)
- \(\{(x,y)\in \mathbb{Z}^2 \mid y=x^2\}\)
- \(\{(x,y)\in \mathbb{R}^2 \mid y^2=x\}\)
- \(\{(x,y)\in \mathbb{N}\times \mathbb{R} \mid y^2=x\}\)
Problem 7.16. Draw a portion of the graph that represents the relation \(\leq\) on \(\mathbb{R}\) .
For a relation on a set, it is natural to consider the collection of elements that a given element is related to. For example, a user’s “Following List" on Twitter is the set of accounts on Twitter that the user is following.
Definition 7.17. Let \(R\) be a relation on a set \(A\) . For each \(a\in A\) , we define the set of relatives of \(a\) with respect to \(R\) via \[rel(a,R):= \{b\in A\mid aR b\}.\] We also define the collection of the sets of relatives with respect to \(R\) by \[Rel(R):= \{rel(a)\mid a\in A\}.\]
If \(R\) is clear from the context, we will usually write \(rel(a)\) in place of \(rel(a,R)\) . In terms of digraphs, \(rel(a)\) is the collection of vertices that have a directed edge pointing towards them from the vertex labeled by \(a\) . In graph theory, this collection of vertices is called the out neighborhood of \(a\) and each such vertex is called an out neighbor . Notice that \(Rel(R)\) is a set of sets. In particular, an element in \(Rel(R)\) is a subset of \(A\) —equivalently, an element of \(\mathcal{P}(A)\) .
Problem 7.18. Consider the relation given in Example 7.4. By inspecting the ordered pairs in \(R\) or by looking at the digraph in Figure 7.2(b), we see that \[rel(a) = \{a,b,c\},\ rel(b) = \{a,b,c\},\ rel(c) = \{d,e\},\ rel(d) = \{a,c,d\},\ rel(e) = \{a\},\] so that \(Rel(R) = \{\{a,b,c\},\{d,e\},\{a,c,d\},\{a\}\}\) .
Problem 7.19. Consider the relation given in Problem 7.13(a). Find \(Rel(R)\) by determining \(rel(x)\) for each \(x\in A\) .
Problem 7.20. Describe the collection of the sets of relatives with respect to the empty relation from Problem 7.13(b).
Problem 7.21. Let \(P\) denote the set of all people with accounts on Facebook and define the relation \(F\) on \(P\) via \(xFy\) if \(x\) is friends with \(y\) . Describe \(rel(\text{Maria})\) , where Maria is the name of a specific Facebook user. What is \(Rel(F)\) ?
Problem 7.22. Define the relation \(\equiv_5\) on \(\mathbb{Z}\) via \(a\equiv_5 b\) if \(a-b\) is divisible by 5. Find \(rel(1)\) , \(rel(2)\) , and \(rel(6)\) . How many distinct sets are in \(Rel(\equiv_5)\) ? List the distinct sets in \(Rel(\equiv_5)\) .
Problem 7.23. Consider the relation \(\leq\) on \(\mathbb{R}\) . If \(x\in \mathbb{R}\) , what is \(rel(x)\) ?
Problem 7.24. Suppose \(R\) is a relation on \(A=\{1,2,3,4,5\}\) such that \(rel(1)=\{1,3,4\}\) , \(rel(2)=\{4\}\) , \(rel(3)=\{3,4,5\}\) , \(rel(4)=\{1,2\}\) , and \(rel(5)=\emptyset\) . List the ordered pairs in \(R\) and draw the corresponding digraph.
We will now examine three important properties that a relation on a set may or may not possess.
Definition 7.25. Let \(R\) be a relation on a set \(A\) .
- The relation \(R\) is reflexive if for all \(a\in A\) , \(aR a\) .
- The relation \(R\) is symmetric if for all \(a,b\in A\) , if \(aR b\) , then \(bR a\) .
- The relation \(R\) is transitive if for all \(a,b,c\in A\) , if \(aR b\) and \(bR c\) , then \(aR c\) .
Example 7.26. Here are a few examples that illustrate the concepts in the previous definition.
- The relation \(=\) on \(\mathbb{R}\) is reflexive, symmetric, and transitive.
- The relation \(\leq\) is reflexive and transitive on \(\mathbb{R}\) , but not symmetric. However, notice that \(<\) is transitive on \(\mathbb{R}\) , but neither symmetric nor reflexive.
- If \(S\) is a set, then \(\subseteq\) on \(\mathcal{P}(S)\) is reflexive and transitive, but not symmetric.
Problem 7.27. Determine whether the relations given in each of the following is reflexive, symmetric, or transitive.
- Example 7.4
- Problem 7.13
Problem 7.28. Suppose \(R\) is a relation on a set \(A\) .
- Explain what it means for \(R\) to not be reflexive.
- Explain what it means for \(R\) to not be symmetric.
- Explain what it means for \(R\) to not be transitive.
Problem 7.29. Let \(A=\{a,b,c,d,e\}\) .
- Define a relation \(R\) on \(A\) that is reflexive but not symmetric nor transitive.
- Define a relation \(S\) on \(A\) that is symmetric but not reflexive nor transitive.
- Define a relation \(T\) on \(A\) that is transitive but not reflexive nor symmetric.
Problem 7.39. Given a relation \(R\) on a finite set \(A\) , describe what each of reflexive, symmetric, and transitive look like in terms of a digraph. That is, draw pictures that represent each of reflexive, symmetric, and transitive. One thing to keep in mind is that the elements used in the definitions of symmetric and transitive do not have to be distinct. So, you might need to consider multiple cases.
Below, we provide skeleton proofs for proving that a relation is reflexive, symmetric, or transitive. Notice that the skeleton proof for proving that a relation is reflexive is a special case of Skeleton Proof 2.81. Similarly, the skeleton proofs involving symmetric and transitive are both special cases of Skeleton Proof 2.82. It is important to point out that every relation on the empty set is vacuously reflexive, symmetric, and transitive. In the skeleton proofs below, we are implicitly assuming that the set in question is nonempty. In some circumstances, it may be necessary to mention the possibility of the empty set.
Skeleton Proof 7.31. Here is the general structure for proving that a relation is reflexive.
Assume \(R\) is a relation on \(A\) defined by (or satisfying)… [Use the given definition (or describe the given property) of \(R\) ] . Let \(a\in A\) .
\(\ldots\) [Use the definition (or property) of \(R\) to verify that \(aR a\) ] \(\ldots\)
Therefore, the relation \(R\) is reflexive on \(A\) .
Skeleton Proof 7.32. Here is the general structure for proving that a relation is symmetric.
Assume \(R\) is a relation on \(A\) defined by (or satisfying)… [Use the given definition (or describe the given property) of \(R\) ] . Let \(a, b\in A\) and suppose \(aR b\) .
\(\ldots\) [Use assumption that \(aR b\) with definition (or property) of \(R\) to verify that \(bR a\) ] \(\ldots\)
Therefore, the relation \(R\) is symmetric on \(A\) .
Skeleton Proof 7.33. Here is the general structure for proving that a relation is transitive.
Assume \(R\) is a relation on \(A\) defined by (or satisfying)… [Use the given definition (or describe the given property) of \(R\) ] . Let \(a, b, c\in A\) and suppose \(aR b\) and \(bR c\) .
\(\ldots\) [Use assumption that \(aR b\) and \(bR c\) with definition (or property) of \(R\) to verify that \(aR c\) ] \(\ldots\)
Therefore, the relation \(R\) is transitive on \(A\) .
Problem 7.34. Determine whether each of the following relations is reflexive, symmetric, or transitive. In each case, you should either provide a specific counterexample or a proof.
- Consider the relation \(T\) described in Example 7.5.
- Consider the relation \(F\) described in Problem 7.21.
- Consider the relation \(\equiv_5\) described in Problem 7.22.
- Let \(P\) be the set of all people and define \(H\) via \(xHy\) if \(x\) and \(y\) have the same height.
- Let \(P\) be the set of all people and define \(T\) via \(xTy\) if \(x\) is taller than \(y\) .
- Consider the relation “divides" on \(\mathbb{N}\) .
- Let \(L\) be the set of lines and define \(||\) via \(l_1||l_2\) if \(l_1\) is parallel to \(l_2\) .
- Let \(C[0,1]\) be the set of continuous functions on \([0,1]\) . Define \(f\sim g\) if \[\int_0^1|f(x)|\ dx=\int_0^1|g(x)|\ dx.\]
- Define \(R\) on \(\mathbb{N}\) via \(nR m\) if \(n+m\) is even.
- Define \(D\) on \(\mathbb{R}\) via \((x,y)\in D\) if \(x=2y\) .
- Define \(F\) on \(\mathbb{Z}\times \left(\mathbb{Z}\setminus \{0\}\right)\) via \((a,b)F(c,d)\) if \(ad=bc\) . Do you recognize this relation? Think about fractions.
- Define \(\sim\) on \(\mathbb{R}^2\) via \((x_1,y_1)\sim (x_2,y_2)\) if \(x_1^2+y_1^2=x_2^2+y_2^2\) .
- Define \(S\) on \(\mathbb{R}\) via \(xS y\) if \(\lfloor x\rfloor =\lfloor y\rfloor\) , where \(\lfloor x\rfloor\) is the greatest integer less than or equal to \(x\) (e.g., \(\lfloor \pi\rfloor=3\) , \(\lfloor -1.5\rfloor=-2\) , and \(\lfloor 4\rfloor=4\) ).
- Define \(C\) on \(\mathbb{R}\) via \(xCy\) if \(|x-y|<1\) .


Linguistics is part of the broad field of cognitive science, which studies the human mind. Linguistics focus specifically on the mental grammar: the system that all speakers of a language have in their minds, which allows them to understand each other. The mental grammar of every language includes phonetics, phonology, morphology, syntax, and semantics.
A YouTube element has been excluded from this version of the text. You can view it online here:
https://ecampusontario.pressbooks.pub/essentialsoflinguistics/?p=24
Check Yourself
1. Newspaper headlines occasionally have unexpectedly funny interpretations. One example is:
Two cars were reported stolen by the police yesterday
. Which part of your mental grammar leads to the possibility that the police could have done the stealing or the reporting in this headline?
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Phonetics.
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Phonology.
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Morphology.
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Syntax.
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Semantics.
2. Newfoundland English has some characteristic differences to standard Canadian English. The following sentences are grammatical in Newfoundland English:
I eats toast for breakfast every day. You knows the answer to that question
. What part of the mental grammar of Newfoundland English is different to Canadian English in these examples?
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Phonetics.
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Phonology.
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Morphology.
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Syntax.
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Semantics.
3. When speakers of Hawaiian pronounce the English phrase, “Merry Christmas”, it sounds like:
mele kalikimaka
. What part of the mental grammar of Hawaiian is responsible for how the English phrase gets pronounced?
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Phonetics.
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Phonology.
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Morphology.
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Syntax.
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Semantics.
Answers


11: Fall Protection
“Do not think because an accident hasn’t happened to you that it can’t happen.” – Safety saying, early 1900’s
Overview
Slips, trips, and Falls account for 20% of all accidents, injuries, and fatalities in the workplace and up to 37% in construction environments. There is probably no one who has escaped a stumble, slip, or trip whether at work or play. Walking and working surfaces must be in conditions that do not contribute to falls. Elevated working surfaces which include rooftops, scaffolds, elevated platforms, and even ladders must meet the same standards for cleanliness, evenness, and capacity.
The first duty is to prevent a fall from occurring at all. The discussion that follows focuses on protecting workers if a fall should occur and describing the options for managing fall hazards.
Chapter Objective:
- Understand the Purpose of Fall Protection.
- Determine the Proper use of Floor Coverings to Prevent Falls.
- Be Aware of when Fall Protection is required.
- Apply the Provisions of the Fall Protection Standard.
- Discuss the Various Systems and Practices for Meeting the Fall Protection Standard.
Learning Outcome:
- Apply the hierarchy of controls to fall prevention methods.
- Describe the requirements for training and certification under Subpart M.
Standards: 1926 Subpart M-Fall Protection, 1910 Subpart D Walking-Working Surfaces, 1910 Subpart F Powered Platforms, Man lifts, Vehicle-Mounted Work Platforms
Key Terms:
Anchorage, Controlled Access Zones, Fall positioning device, Leading Edge, PFA
Mini-Lecture: Fall Hazards, Fall Protection
Topic Required Time: 2 hrs; Independent Study and reflection 1 3/4 hour.
Thumbnail: Falling, Pixabay free license