p. 745. Graphs. A Way to Express Quantitative Relationships. This section is not about graphs alone, but instead about equations, tables, and graphs. You will encounter all of these ways to convey information in this class. The types of situations in which each are appropriate are summarized here.
pp. 745–746. Cartesian Graphs. This gives examples of several types of mathematical and physical and relationships expressed in x-y coordinates. It also explicitly discusses the information that can be gleaned from looking at the graphs. Make sure that you look at the graph described as you read each description.
pp. 747. Slope and Area Under the Curve. This section is extremely important! The slope of a graph tells how a quantity changes, and the area under a graph tells how changes accumulate. This is exactly the kind of information we are often looking for in physics! We will use these principles over and over again.
The particular example illustrated here is for a very simple case: a graph of constant velocity over time. The slope of such a graph tells the acceleration (zero here), and the area under the graph tells the distance traveled.
Read this section very carefully. Don’t worry too much about the last paragraph’s mention of force-vs.-time and force-vs.-distance graphs, because we haven’t yet fully defined force, momentum, or energy. (For what it’s worth, energy is the area beneath the force-vs.-distance curve and momentum is the area under a force-vs.-time curve: we’ll get there soon.) If any other part of this section is less than absolutely crystal clear, see me, a classmate, a tutor, or somebody else who can help you understand it. This is something you want to know.
pp. 747–748. Graphing with Conceptual Physics. We will not be doing the specific labs cited here. The important part of this section is the series of “Check Yourself” questions at the end. Again, make sure that you understand why the answers given are correct!
p. 41. Motion is Relative. Read this closely. It is an extremely key point.
pp. 41–42. Speed. Read this section to find:
pp. 43–44. Velocity. Read this section to find:
pp. 44–47. Acceleration. This section can be difficult, as acceleration is a fairly abstract concept. Read to answer:
p. 47. “Acceleration on Galileo’s…” Skim this section. The main idea is that if you know the acceleration of an object and the time that it has accelerated, you can find its velocity. The formula is very similar to the formula for finding distance covered from speed and time given at the bottom of page 42.
pp. 47–52. Free Fall. This section is long, but it is a good discussion of the characteristics of motion under conditions of constant acceleration.
pp. 47–49. “How Fast.” Read this sub-section to find:
Recommmended workbook exercise: p. 7, questions 1–8; p. 10, questions 1–2.
pp. 49–51. “How Far.”
I recommend trying the “Check Yourself” questions on page 50.
p. 51. “How Quickly ‘How Fast’ Changes.” Read this section carefully; it’s worth it. It is a good explanation of a confusing point. Understanding acceleration turns out to be quite important.
Recommmended workbook exercise: p. 8.
p. 52. Figure 3.11. This is a good illustration of the concepts of speed, velocity, and acceleration. Pay attention to the units used.
This Appendix goes into a little more detail about the description of motion than is provided in the main text. You do not need to read it now, but you may want to look at it later to check your understanding.
The introduction refers to the distinction between vector and scalar quantities, which is not a major concern of ours until next week. Everything else should make sense. The distinction, though not rigorously defined here, is clear from the context.
pp. 740–743. Computing Velocity and Distance Traveled on an Inclined Plane. This is a particular case of motion with constant acceleration. The lessons of the discussion, however, are general for any motion starting from rest with constant acceleration. Note the formula for velocity. Look at the formula and try to picture what it means. What is it saying about the velocity at different times?
The formula given near the top of page 742 is for instantaneous velocity. Note the distinction made here between the instantaneous velocity and average velocity. If you check the numbers, you’ll see that both instantaneous and average velocities increase by the same amount each second!
I’ll risk making things more confusing by noting that here we’re talking about the average velocity over a Δt = 1 s interval each time. The exact numbers would be different if we used a different time interval Dt or if, God forbid, we used a different Δt each time.
In the specific case described, the distances traveled in each succeeding second are consecutive odd numbers. There is nothing special about odd numbers here; the important thing is that the distance increases by the same amount each second. The increase in this case just happens to be 2 m each second. What is not a coincidence is that this increase is double the distance traveled in the first second, when the ball started from a dead stop. (That is, starting from rest, the ball traveled 1 m in the first second. This is half the distance increase per second, which is 2 m.) That is a general result.
Recommmended workbook exercise: p. 10, question 3.
pp. 743–744. Computing Distance When Acceleration Is Constant. This discussion generalizes the case of the inclined plane to any constantly accelerating system. Find answers to these questions:
The math gets more complicated if the object is moving at the start, that is, not beginning from a dead stop.
Make sure you understand why the answers to the “Check Yourself” questions are correct.
We’ll begin with Newton’s laws of motion instead of exploring Aristotle’s earlier ideas and how Galileo brought them into question. If you are interested in the background, by all means read it.
You’ll soon see that Newton’s first law of motion is actually just a special case of Newton’s second law of motion. But it is important for you to understand the first law fully.
pp. 27–28. Newton’s First Law of Motion. Read this section closely. Does this first law seem true, not just in the sense that you’ve been taught it in science class, but in the sense that it explains the behavior of moving objects that you observe? Think about the cases illustrated in Figure 2.4.
pp. 28–31. Net Force. Read this closely. How can forces add together to give a net force that could have a variety of different magnitudes? It that a little like saying that 5 + 3 = something from 2 to 8? Can you get it to make sense to you? (Figure 2.5 on p. 31 may help.)
p. 29. box Isaac Newton. Interesting stuff about a dead European male. It does not directly tell you any physics. Read it if you want.
pp. 30–31. box Personal Essay. This essay is primarily about Paul Hewitt’s awakening to the wonders of physics and how education can change the way one sees the world. It also raises some questions about forces that I would like you to consider, even though it does not answer all of them right away.
He first notes a relationship between the tension in a string and the pitch of the sound it makes when plucked. We’ll address this phenomenon in a few months.
The rest of the observations concern the distribution of forces between ropes holding up a scaffold as the loads (painters Paul Hewitt and Burl Grey, in this case) on the scaffold move about. Clearly, the tensions do change, even to the point of one rope experiencing no tension at all. The first question that they could not answer was if the increased tension in one rope was exactly compensated by the decrease in tension of the other rope. The question is answered in the essay. Soon, you should feel comfortable reasoning through the situation yourself to reach the same conclusion.
pp. 32–36. The Equilibrium Rule through Equilibrium of Moving Things. These sections are about a very important principle: if an object’s motion does not change, it is in mechanical equilibrium, and all the forces acting on it sum to zero. This is the converse of Newton’s first law. Note the applications of this principle that are mentioned in the book.
Are you comfortable with the “Practicing Physics” questions on p. 33? The answers are given and explained on p. 34.
Recommmended workbook exercise: pp. 3–5.
pp. 34–35. “Support Force.” If something does not accelerate, that means that the net force acting on it is zero. Since everything on Earth experiences the force of gravity, anything not accelerating must also experience a canceling support force.
Note also that here there is nothing special about being at rest; it is just one of an infinite number of possible constant velocities.
Try the “Check Yourself” questions on p. 34 and p. 36.
pp. 36–37. The Moving Earth. This explains how easy it is now for us to see Newton’s first law in operation, but it was not so testable for the ancients.
This reading assignment contained a lot of material. Did you find any of it difficult? If so, what was difficult, and why do you think it was difficult? If not, was any of it new to you?
Copyright © 2008, Richard Barrans
Revised: 11 January 2010. Maintained by Richard Barrans.
URL: http://www.barransclass.com/astr1070/rguides/P1050F10rg_01-14.html