Giancoli Chapter 4 Guide & Recommended Problems

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A chapter with 20 pages, 8 Sections. The seventeen worked-out examples should tell you where the emphasis is here. There are very few new equations, in fact, just two. The "working equation" is Newton's second law of motion, and 95% of the problems will involve this law. There are three of "Newton's laws of motion," but the first is simply a statement (and is a special case of the second anyway) and the third is extremely simple when expressed as an equation.

The history here is fascinating, and I will talk about it in class, but the fact is that the first law (see p. 85) is simply a direct declaration that Aristotle was wrong, and the law really amounts to a definition of "force" as "anything that can change the velocity of an object." I will not get hung-up on definitions of force and mass: there is some arbitrariness here, but (as Einstein later pointed out) really fundamental quantities in science (mass, time) are only "defined" by specifying how to measure them. Thus "time" is something you measure with a clock, and "mass" is something you measure by measuring how much velocity change is produced by some standard force. The word "inertia" (see p. 85) is simply a description of this quality of mass to resist a change in velocity.

The problem-solving starts in Section 4 with the second law, given in Eqn. 4-1. The really, really, REALLY important things to note about this law are:

1. F and a are vector quantities; m is a scalar.

2. There can be only one mass in this equation, and one acceleration (although a, being a vector, can have up to 3 components, of course).

3. There can be many forces acting on the mass. It is the vector sum of the forces that goes into the left-hand-side (LHS) of Eqn. 4-1.

4. Again: Eqn. 4-1 is a vector equation. This means that there are really three equation; one for the x-components, one for the y-components, and one for the z-components:

F_x = ma_x

F_y = ma_y

F_z = ma_z

Section 5 presents the third law, which is a pretty sophisticated concept, but can be written as a really simple equation: F_AB = - F_BA. In words: the force exerted on object A by object B is equal in magnitude and opposite in direction to the force exerted on object B byobject A. The " problems" involving this law tend to actually be "questions," BUT there are instances in working second-law problems when you need to remember (and use) this simple third law to "find" one of the forces (as in Example 4-12, p. 98).

Section 6 talks about a specific force: weight is simply the local name we give to the force on an object due to earth's gravity. (If you are "on" a different planet than earth, the "weight" would be the gravitational force of the that planet.) This force always acts "downward" and is equal to mg where m is the mass of the object in question and g is the familiar (from previous chapters) 9.8 m/s2. I will explain in class why g has this value on earth.

Clearly the most important section in this chapter is Section 7; it is the longest and consists almost entirely of worked-out examples. You need to carefully look at these examples and then start practicing on the problems. I sincerely believe that the learning in this course, and especially in this chapter and the next takes place mostly during the time that the student (you, that is) spend working out the problems. You need to struggle with them, get stuck, ask for help, try different things, and, finally, get the right answer. There is an adage that goes with this:

Success comes from experience Experience comes from failure

Not failure in the course (obviously), but failure to get the right answer on problems. It is in finding the wrong techniques that don't work (and why they don't) that you learn and remember the right techniques that do work. There is no short-cut to this. Your performance on the tests will be directly related to how much time you spend in practice. Tutors are available. I encourage working problems in groups after you try them individually. I am available during office hours, and there are other students and faculty who can help you.

Recommended Questions and Problems for Chapter 4:

(There are a lot but you don't need to do them all. Do enough to build confidence that you can do them. Many are just slight variations of others - once you get the idea, the others will come easier.)

Question: Q3 (not necessarily), Q4 (yes), Q5 (no, yes for an instant), Q7, Q11, Q20

Sections 4 & 5: P5, P7, P10, P18, P22

Section 7: P27, P33, P35, P37, P40, P46, P48, P49, P51, P52, P53, 54

General Problems: P67, P69, P70, P74, P78, P81