Unit 1

Alfredo Ferreira; Wucheng Zhang; David LeBlanc

Main Body

Unit 1 Learning Objectives

Physics

(1) Identify and apply strategies for reading physics word problems

(2) Recognizing the roles of the three meaning-making modes of language, figures and mathematical symbols, including the functions of various types of figures and equations.

Language

(3) Identifying the various terms used to understand language such as word, phrase, clause, text, and genre.

(4) Recognizing the relative scale of the above units, how they relate to each other in terms of scale of meaning-making.

SECTION 1.1

Reading and Solving Word Problems in 1st-year Physics

This introductory unit begins by providing strategies for interpreting and solving physics problems. In the second part of this unit, physics problems are used to learn about how language organizes physics knowledge and practices into units and scales of meaning-making. Both these sections of Unit 1 are foundational for the textbook. As noted above in “How to use this textbook”, this textbook is task-based: after doing the tasks, check the feedback on your work to build on what you know and can do in physics.

Task 1.1.1: Reading Physics Word Problems

Physics problems come in many shapes and sizes; however, they all typically include a mix of language, figures, symbols. Developing strategies to read, organize and interpret a problem will set you up to successfully solve any physics word problem!

Task 1.1.1a Instructions: Read through the Cold Run problem. Use the textbox below to list and organize key information from the problem. List any possible strategies you have used when working with word problems, we will come back to these strategies later in this chapter.

The Cold Run Problem:

You and a friend are getting ready for another day of long-distance running training. However, this morning, it’s a cool −1C° and, with wind chill, −5C°. You both agree to run 10km today as long as neither of you has to wait in the cold. You know that she runs at a very consistent pace with an average speed of 3.0 m/s, while your average speed is consistently 3.5 m/s. You both start at the same location, but she completes her warm-up quickly and leaves first. The plan is that she will arrive at her house first so that she can unlock the door and wait for you inside. Five minutes after she leaves, you notice that she dropped her house keys. If she finishes her run first, she will have to wait for you outside and get uncomfortably cold. How far from your house will you be when you catch up to her if you leave immediately, run at your usual pace, and remember to take her keys?

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Task 1.1.1b Instructions: Below is a word problem that demonstrates some recommended interpretation strategies. Click on the icons to read a description for each strategy used.

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Task 1.1.1c Instructions: Read through the list of recommended strategies below. Using the strategies you listed in task 1.1.1a and the strategies below, determine which strategies will be easier or harder to implement into your work.

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Task 1.1.2: Solving the Problem & Writing a Solution with Rationale

Task 1.1.2 Instructions: As you might be asked to do in a physics exam, solve this Cold Run problem in writing, starting with the information you have extracted from the problem. For each stage of your solution, briefly provide reasons for your choices (“show your thinking”).

The Documentation Tool below can be used to save and submit your solution. Write a complete solution with rationale; later in the textbook, this solution will provide a sample for you to analyze and understand your use of language in written solutions.

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SECTION 1.2: The 5-Stage Strategy to Solving Physics Problems

The first step or stage in approaching a word problem is to extract and organize the necessary information from the problem. To solve the problem using the relevant information from the problem, we recommend the 5-stage strategy. The 5-stage strategy is a powerful tool for solving any physics problems and, more generally, for identifying any areas of strength and weakness that students arrive with in first-year physics.

Task 1.2.1: Thinking Ahead About Problem Solving Methods

Task 1.2.1a Instructions: When writing a formal solution for your instructor what do you consider the correct order for the 5-stages? The next section of this text will discuss our recommended approach to using this strategy.

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Applying the 5-Stage Strategy

The table below gives an outline of the 5-stage strategy to solving physics problems. Each stage is then expanded on by using the Cold Run problem as an example.

Stages of Solving a Physics Problem

1. Extract key elements from the problem: Extract the known and unknown information, organizing and displaying these in a coherent diagram or description. The relevant information may appear in the problem in any of the modes: language, figures, and symbolism.

2. Interpret the problem using a physics model: Interpret the problem elements and relationships in terms of known physics terms and models. This stage requires a detailed analysis of the problem in combination with previously learned physics models.

3. Operationalize a Solution Mathematically: Based on models selected, identify the mathematical equations and methods needed to solve for unknown elements. This stage is mathematically-focused, requiring defined symbols and quantities from the problem.

4. Solve the problem: Apply the selected equations and methods, plugging in known values and resolving unknown values. Solving requires clearly defined mathematical symbols and logic in coordination with understanding the physical aspects of the problem.

5. Check you answer: Apply alternative methods to check numerical solutions for physical plausibility and algebraic solutions for limiting cases and trends. Figures and language can help visualize the physical solution to determine the validity of the original solution.

Below we will walk through an example of applying the 5-stage strategy using the Cold Run problem.

Stage 1: Draw out key elements

The Choice Create a list of known and unknown variables.

The Why It is up to the learner to determine which quantities are ‘known’ and which are ‘unknown’. This stage is facilitated by the interpretation strategies listed in 1.1.1.

Known:
- Distance total, $d_{t} = 10 km$
- Velocity of friend, $v_{f} = 3.0 m / s$
- My velocity, $v_{m} = 3.5 m / s$
- Time difference between my start and my friend’s start: $Δ t = 5 mins = 300 s$
Unknown:
- Distance my friend travelled, $d_{f}$
- Distance I travelled, $d_{m}$
- Time my friend spent running, $t_{f}$
- My time spent running, $t_{m}$

Stage 2: Interpret the problem using a physics model

The Choice This is a problem of linear motion in one direction. Assuming acceleration is constant, ( $a = 0$ ), our classic mechanic’s 1D motion physics model (and equations) will be relevant to this problem.

The Why Stage 1 listed the variables of velocity, time, and distance; while the question implies that our motion is in one direction with no stops. 1D motion equations are frequently used for problems containing motion in one direction and containing all three variables we listed. Therefore we will use the 1D motion equations to provide a framework for solving this problem.

Stage 3: Operationalize a Solution Mathematically

The Choice We will use 1D motion equation $d = v t$ to solve the problem.

The Why We have identified the problem will need 1D motion equations to solve. Analyzing our variables in stage 1, there is only one equation relevant to 1D motion that includes constant acceleration:

$d = v t .$

Stage 4: Solve the Problem

The Choice We will apply the equation $d = v t .$ for both my motion and my friend’s motion. We will also use the condition $Δ t + t_{m} = t_{f}$ . We will solve the equation to obtain the unknown $t_{f}$ , $t_{m}$ , and subsequently $d_{f}$ and $d_{m}$ via $d = v t$ .

The Why We can now create two equations and insert the known values for the velocity, $v_{f}$ and $v_{m}$ . This will leaves us with two unknown variables to solve for: $t$ and $d$ . Using the previously defined term of $d_{m} = d_{f}$ we can eliminate the $d$ variable through substitution. Finally, using the equation $t + 300 s = t$ we can use a single variable $t$ to represent time.

The Action Combining the equations of motion of my friend and me, we have

$v_{f} (t_{m} + Δ t) = v_{m} t_{m},$

which solves

$t_{m} = \frac{v_{f} Δ t}{v_{m} - v_{f}} .$

We plug in the number from the problem and evaluate $t_{m} = 1800 s = 6 \min$ . By $d = v_{m} t_{m}$ , we find $d = 6300 m$ .

Stage 5: Check your solution

The Choice Use our friend’s velocity equation to solve for the distance.

The Why Since my distance travelled and my friend‘s distance travelled are equal, we should get the same answer from both equations. By plug the number into

$d = v_{f} (t_{f} + Δ t),$

we obtained $d = 6300 m$ , which is the same as the distance I travelled.

Furthermore, our run is only 10km long and we will meet at 6.3km. This distance is a reasonable answer as it is within the range of our run! It is important to understand that this stage will be different depending on the question asked. It will take some creative problem solving to determine the best method in checking your solution.

Task 1.2.2: Thinking Back about Strategies

Task 1.2.2a Instructions: The Cold Run solution is an application of the 5-stage strategy as used in formal writing. Review your task 1.1.2 where you attempted the cold run problem. Reflect on the similarities and differences between your solution and the formal solution.

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Task 1.2.2b Instructions: Are you ready to use the 5-stage approach to tackle physics word problems? The quiz below will test your knowledge and provide feedback.

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SECTION 1.3: Three Meaning-making Modes in Physics

Let’s discuss the three modes – language, figures, and symbolism – that are used in solving physics problems. While it is possible to express an idea such as “exponential growth” using any of these modes (see the task below), as you probably know, each of these modes specializes in particular ways of making meaning. What does each mode allow us to do especially well? In other words, what are the general affordances – or super powers – of language, figures, and symbolism?

Language: Language is the glue that holds meaning together in science and, indeed, in most kinds of human interaction. Through the vast choices of vocabulary and grammar that language affords us, we are able to represent the world and human experiences in highly detailed and subtle ways. For example, using language it’s possible to describe the very particular ideas and activities of an instructor while they are lecturing, a description that would be much more limited if we used just a figure or mathematical symbols.
Figures: Figures are good at is representing multiple entities and the relationships between them in space. Humans interpret space as meaning, like a line that moves from left to right often signals movement in time. The key point is that by representing multiple entities and their relationships in space, these meanings are available to be interpreted all at once in a non-linear frame.
Symbolism: Symbolism encompasses symbols for entities such as H for height and symbols for carrying out logical operations and patterns of operations. Strict rules are applied when communicating via symbols; for example, H = height, is a strict definition of “H” across that text. As such, symbolism requires pre-work beforehand to define each symbol.

Task 1.3.1: The Three Meaning-Making Modes

Task 1.3.1a Instructions: The same information below is represented in three different ways. Answer the following questions based on this information and receive feedback tailored on your answer.

Verbal: The number of species is exponentially increasing.

Symbolic: $y = C * e^{(\frac{t}{b})}$

Figure:

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Task 1.3.1b Instructions: Which type of learner were you? Save your learner type and feedback, we will re-visit this information later in the textbook!

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Task 1.3.2: Combining Language, Figures, and Symbols

Task 1.3.2a Instructions: You will find an example of each of the three meaning-making modes in the task below. Click and drag each example into their corresponding mode.

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Task 1.3.2b Instructions: The set of tasks below will test your knowledge of the 5-stage strategy and its application with the three modes of communication described above: language, figures, and symbolism.

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If you require more information regarding task 1.3.2b click below to see an explanation of the answers.

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Task 1.3.3: All About Figures and Their Functions

Task 1.3.3a Instructions: In the task below you will find image’s of 5 frequently used figures in physics. These figures are particularly important for stages 2, 3 and 5 of the 5-stage strategy. Complete the task below to introduce yourself with these various figures. Click and drag the appropriate description of each figure into its corresponding box. Note: Hover your mouse over each image to read a detailed description.

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Task 1.3.3b Instructions: In physics, figures can be broadly classified into two categories: qualitative and quantitative. Qualitative figures focus on the relative relationships between entities within a diagram, while quantitative figures depict objects and entities with mathematical accuracy. The following tasks can help you understand the differences between these two types of figures:

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Task 1.3.4: Types of Equations and Their Functions

Task 1.3.4a Instructions: Physics solutions typically employ three types of equations: definition, theorem, and derived equations. Defining equations give you a definition of a new quantity that is consistent across the solution (e.g. $v = \frac{d x}{d t}$ ). Theorem are fundamental in physics and define a universal law; these equations can only be verified through rigorous experimentation (e.g. Newton’s second law for mechanics: $F = m a$ ). Defining and theorem equations are typically found in stage 2 and 3 of the problem solving method where they aid in interpreting and operationalizing the solution mathematically. Finally, derived equations are a variant group generated uniquely for each solution by combining definition equations and theorems (e.g. $2 a x = v_{2}^{2} - v_{1}^{2}$ ). Derived equations are typically found in stage 4 of the problem solving method. At this stage they are used to determine the mathematical answer to the problem.

The following task presents a solution to a physics problem. Each step may use different equations. Use your understanding of the three equation types to determine which equation type are used within each stage.

The Problem:

A car begins driving from a stationary position. It accelerates at $8.0 m / s^{2}$ for $15 s$ , then travels at a steady pace for another $15 s$ , all in the same direction. How much distance has it covered since traveling?

Stage 1:

Known:

$d_{t} = 10 km$
$a = 8.0 m / s^{2}$
$t_{1} = 15 s$
$t_{2} = 15 s$

Unkown:

$d_{t} = ? m$

Stage 2:

This is a problem of linear motion in one direction. Acceleration is constant, $a = 5 m / s^{2}$ , for the first 12-seconds, then constant at $a = 0 m / s^{2}$ , for the remainder 12-seconds. Our classic mechanic’s 1D motion physics model (and equations) will be relevant to this problem. First,

$d = v t$

will solve for the distance travelled when when acceleration is 0. Next, the equation

$a = \frac{Δ v}{Δ t}$

will be needed to solve for the final velocity in the second half of the car’s travel. Then we will use the kinematic equation

$d = v_{i} t + \frac{1}{2} a t^{2},$

to determine our distance while accelerating at $a = 5 m / s^{2}$ . Finally we will use the equation

$d_{t} = d_{i} + d_{f}$

to determine the total distance travelled.

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SECTION 1.4: Units and Scales of Meaning-making in Language

Task 1.4.1: Thinking Ahead about Units and Scales of Language

Language is a complex resource. A key feature of language is that it is organized into meaning-making units; for example, words are smaller units of language organized at increasingly larger scales in sentences and whole texts. When working consciously with language choices in real-world situations as we hope to do throughout this textbook, it’s important to be able to identify the role of various language units and make conscious language choices at every scale.

Task 1.4.1a Instructions: Read and order the language units from small to large scale. The following sentence may help: choose one unit for each gap.

The smallest unit here is a __1__, which combines with others to form a __2__, which typically joins with other phrases to form a __3__,

which is also a __4__ or just a of part one, which very often combines with others to form one functional step or __5__ in the message achieving its overall purpose.

Multiple stages typically combine in a whole __6__, which exemplifies one or more type of text or __7__.

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Task 1.4.2: Genre as a Unit of Physics Culture

Genre is the term we use to describe and classify a recognizable cultural convention, which is a pattern of cultural practice involving the making and exchanging of meaning. Because you are a member of contemporary global culture, it’s likely that you recognize different genres of music (such as hip-hop, K-pop, Eurobeat, videogame soundtrack) or films (such as documentaries, action films, love stories, and sci-fi).

The field of physics is a global scientific practice that involves many genres, including spoken genres such as the lecture, lab demonstration, tutorial dialogue, and problem-solving in student groups, as well as written ones such as the lab report, research report, and written solutions to problems. Each of these genres fulfills a different set of purposes in the culture of physics.

Task 1.4.2a Instructions: Read texts 1-4 below (you have already have seen text 1). All four texts are similar in important ways, even if the topics involved in each are very different; however, one of the texts is sufficiently different from the others in its structure and purpose to be classified differently from the other three texts. Identify the text that belongs to a different genre than the three others.

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Task 1.4.3: Stage as a Unit within Genres and Texts

Clearly, texts 1-3 above have the same purposes and share similar features. As such, they are examples of the genre of physics problem. The physics problem genre varies greatly; however, physics problems contain two stages: (1) the physical setting stage, which provides the necessary background information (and sometimes unnecessary and distracting information!) and (2) the task stage, which may also contain key information but, most importantly, contains a question (e.g., “What is the… ?”) or a command (e.g., “Determine the….”).

The question is the obligatory stage of physics problems that text 4 doesn’t have. A stage is an identifiable, purposeful step (whether conscious or not) that contributes to the overall purpose of a text.

You will recall our recommendation of a 5-stage strategy for solving physics word problems where each of the stages contributes uniquely to the effectiveness of the solution. Are you able to recall the 5 stages and their individual purposes?

Stages are a key way to identify genres. We’ve discussed the staging of physics solutions; another example of staging in post-secondary education separate from physics problems and solutions is the argumentative essay, a genre that involves an Introduction stage with a thesis statement, followed by a Supporting Evidence stage, and a Conclusion stage, where the thesis is restated. As with the stages of physics problems and solutions, each stage is necessary if the text is to be effective.

Although text 4 above is not a physics problem because it lacks a task stage, it is clearly related to physics culture. The approach to genre taken in this textbook has to cope with more complex, mixed-genre texts like this that arise in physics and indeed all cultures. This point raises the next question: in which of the following genres would you classify text 4?

Task 1.4.3a Instructions: In the blank space below, type the name of the genre that best describes the purpose and features of text 4.

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Task 1.4.4: Using Staging to Help Check for Distractors in Problems

As you probably know, physics instructors sometimes include distractors in the problem, information that is not necessary to solve the problem. They do this in order to develop your critical abilities to assess all the information in problems towards your solution. While distractors can occur anywhere in a problem, they are more likely to occur in one of the stages; this point is the focus of this task.

The Trolley Problem is broken down below by its physical setting and task stages. As shown in the four yellow highlighted phrases, both these stages can contain assumptions and quantities for solving the problem. For now, we are not concerned with solving this problem or even considering the specific highlighted values; our interest is in comparing the reliability of the background information provided in the physical setting stage versus in the task stage.

Staging of Problem 3

Physical Setting

Consider a square box with uniform mass m1=0.3kg placed on a trolley with mass m2=0.7kg . The friction coefficient between the box and the trolley is s=0.6 kgsm2 and k=0.3 kgsm2 . We assume there is no friction between the ground and the trolley.

Task

Considering g = 10m/s2, what is the range of horizontal force applied on the trolley such that the box will not slide off the trolley.

Task 1.4.4a Instructions: In which stage of the problem, the physical setting stage or task stage, are distractors (unnecessary or unreliable information) more likely to appear?

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Task 1.4.5: Identifying Units of Language Use in Examples

Task 1.4.5a and Task 1.4.5b Instructions: Match the highlighted section of the text with the unit of language (task or physical setting).

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Task 1.4.5c, 1.4.5d, and 1.4.5e Instructions: Within each task, choose the text that best matches the prompt given.

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Task 1.4.6: Words, Phrases, Clauses, Sentences and the (Re)Distribution of Meaning Among Them

The table below shows how a very similar statement (in this case, a statement explaining the use of a kinematic equation) can be expressed in different ways (rows A – C) depending on the way the ideas and logical connections are distributed among various units of language. The increase in shading of each row reflects the increase in the density of information per grammatical unit; we will explore the many uses of this variation in information density in subsequent units. Review the table and complete the tasks below.

Task 1.4.6a Instructions: Fill in the blanks from the following four choices. Type your choices in the blanks to complete the statement describing the table:

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Task 1.4.6b Instructions: If the information in rows A-C changes only in terms of its density, you should be able to identify how ideas are expressed differently, using different units of language, between the rows. Type in the information: spelling and spacing matter!

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Task 1.4.7 (Optional) Instructions: Attempt to pack the explanation about using the kinematic equation into an informationally dense noun phrase, as would appear in row D.

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Archived - Speaking and Writing Physics 101: The Language of Solvig First-Year Physics Problems Copyright © by Alfredo Ferreira is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License, except where otherwise noted.

SECTION 1.1

Reading and Solving Word Problems in 1st-year Physics

SECTION 1.2: The 5-Stage Strategy to Solving Physics Problems

SECTION 1.3: Three Meaning-making Modes in Physics

SECTION 1.4: Units and Scales of Meaning-making in Language

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