p. 58. Force Causes Acceleration. The main idea here is that acceleration is proportional to net force. This is an extremely important idea! Recall from Newton’s first law that constant-velocity motion is the consequence of zero net force. Any deviation from constant velocity means that the net force is not zero. Here, we recognize a direct relation between the net force on an object and the rate of change of its velocity.
Take a little time to remind yourself what velocity and acceleration are. Also recall what Newton’s first law states, and what it means. Reflect as well that net force is proportional to acceleration, not to velocity. Does this make sense to you? If it doesn’t, try to clearly and concisely state your objections, and keep them in mind through the rest of this reading.
pp. 59–61. Friction. While reading this section, bear in mind that friction is a very complicated phenomenon, which is still not fully understood. It is discussed in this section because friction shows up almost everywhere in the real world, and you absolutely must take it into account to understand the net forces on real-world objects.
Read this section to find:
Be aware that these relations are approximations; they are not 100% correct.
Recommmended workbook exercise: p. 19, questions 1–5.
pp. 61–63. Mass and Weight. This section gives a physics-based definition of mass. What the definition means will be made clearer in a few pages.
The discussion of the proportionality between mass and weight means that w = mg (see Footnote 2 on p. 61), where w is an object’s weight, m is its mass, and g is a constant depending on the object causing the gravitational field (star, planet etc.). So if you know an object’s mass m, just multiply it by g to find w. (This means that the same mass will have different weights in environments where g is different.)
Recommmended workbook exercise: p. 11; p. 12.
The discussion on p. 62 stresses the inertial effect of mass, which is present even in the absence of gravity. The section doesn’t explain why mass is responsible for both weight and inertia; it turns out that you need the General Theory of Relativity to do that.
Try the “Check Yourself” questions on p. 63.
pp. 63–64. Mass Resists Acceleration. The key point of this section is that the acceleration of an object depends on the net force acting on the object and on the object’s mass. It doesn’t depend on anything else! Ever! (Well, not unless velocity is a significant fraction of the speed of light, in which case relativistic effects become important.)
pp. 64–65. Newton’s Second Law of Motion. This is the key point of the chapter. However, I find the presentation a little confusing. Never mind the talk about proportionality; the key point is
a = Fnet/m.
Also don’t be concerned with the stuff about “consistent units;” if you use mass units for m and acceleration units for a, F will automatically be in force units. You just may need to do some conversions to get it in units you want.
Recommmended workbook exercise: p. 13.
pp. 65–66: When Acceleration Is g… While reading this section, keep in mind that the weight of an object depends on its mass: w = mg. Since force causes acceleration and mass resists acceleration from a force, the two effects cancel out for the acceleration caused by an object’s weight. Another way to see this is:
From Newton’s second law, F = ma.
The force on an object from its weight is F = mg.
So, the acceleration of an object due to its weight can be found by setting these two forces equal:
ma = mg
a = mg/m
a = g
p. 66–68. When Acceleration Is Less… The key point here is that objects falling on earth have more than just the force of gravity acting on them: air resistance also contributes to the net force. The net force is the sum of the object’s weight pushing down and air resistance pushing up. Since air resistance increases as velocity increases, a falling object will accelerate until the force of drag cancels its weight. Then the object falls at constant velocity (remember Newton’s first law).
Recommmended workbook exercise: p. 20.
What is the relationship between Newton’s first law and Newton’s second law?
Is it possible for an object’s velocity to change if its acceleration is constant? For its acceleration to change if its velocity is constant? Is it possible for an object’s velocity to increase while its acceleration decreases? For its velocity to decrease while its acceleration increases?
Don’t worry that we are jumping ahead in the book. The part of this chapter that now concerns us follows directly from Chapter 4. The book uses it as an introduction to the motion of satellites, which we will address much later. So it makes the most sense for us to examine projectiles now.
This part describes how objects (projectiles) move when accelerated by only the force of gravity. Some of this we have already covered, and some of it we will not address in class at all. The key points for us in this chapter are to understand how the gravitational force, which acts only toward the attracting object, gives rise to such characteristic motion.
pp. 184–185. Projectile Motion. In the approximate case where gravity is always directed straight down and its magnitude does not vary with height, the vertical and horizontal components of a projectile’s motion are independent of each other. The acceleration is exclusively in the vertical direction (straight down), and there is no acceleration (the velocity is constant) in the horizontal direction.
pp. 185–186. “Projectiles Launched Horizontally.” In this case, the initial vertical velocity is zero, so the projectile accelerates in the vertical direction essentially from rest. Definitely check out Figures 10.4 and 10.5.
Recommmended workbook exercise: p. 25; p. 55.
pp. 186–191. “Projectiles Launched at an Angle.” These differ from the horizontally- launched projectiles only in that the initial vertical velocity is not zero.
The “Practicing Physics” box at the top of p. 188 gives a nice way to understand the path of a projectile launched at an angle. See how it works?
Recommmended workbook exercise: p. 56.
On p. 189, there is an analysis of how the range of a projectile depends on its launch angle. Then on p. 190, it gets a bit more complicated, because the book says that if you throw something, its initial speed depends on launch angle. You should read this to get the general idea, but in this class you will not be required to calculate a projectile’s flight distance from its launch angle.
Recommended workbook exercise: p. 57. The problem tells you how to find the magnitude of the resultant (speed of the projectile).
How does an object move:
Copyright © 2008, Richard Barrans
Revised: 11 January 2010. Maintained by Richard Barrans.
URL: http://www.barransclass.com/astr1070/rguides/P1050F10rg_01-21.html