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# Chapter 4: Newton's Laws

Difficulty Level: At Grade Created by: CK-12

## Introduction

### The Big Idea

Applied forces may cause objects to accelerate. All forces come in pairs because they arise in the interaction of two objects — you can’t push without being pushed back! The more force applied, the greater the acceleration that is produced. Objects with high masses are difficult to accelerate without a large force. In the absence of applied forces, objects move in a straight line at a constant speed (or remain at rest). In formal language:

Newton's First Law
Every body continues in its state of rest, or of uniform motion in a right (straight) line, unless it is compelled to change that state by forces impressed upon it.
Newton's Second Law
The change of motion is proportional to the motive force impressed; and is made in the direction of the right (straight) line in which that force is impressed.
Newton's Third Law
To every action there is always opposed an equal reaction: or, the mutual actions of two bodies upon each other are always equal, and directed to contrary parts.

(Taken from the Principia in modern English, Isaac Newton, University of California Press, 1934).

Understanding motion comes in two stages. The first stage you’ve already seen: you can figure out where something will go, and how fast it will get there, if you know its acceleration. The second stage is much more interesting: where did the acceleration come from? How can you predict the amount of acceleration? Mastering both stages is the key to understanding motion.

## Summary

In this chapter students will gain an understanding of force and what causes changes in motion. In addition, students will learn how to solve many different types of problems involving vectors, incline planes, friction, etc.

### The Basics

• An object will not change its state of motion (i.e., accelerate) unless an unbalanced force acts on it. Equal and oppositely directed forces on the same object do not produce acceleration.
• The force of gravity is called weight. Near the surface of a planet, it has magnitude \begin{align*} mg \end{align*} and is directed perpendicular to its surface. This \begin{align*} g \end{align*} is different from the Gravitational Constant, and differs from planet to planet.
• Your mass does not change when you move to other planets --- although your weight does --- because mass is a measure of how much matter your body contains, and not how much gravitational force you feel.
• To calculate the net force on an object, you need to calculate all the individual forces acting on the object and then add them as vectors.
• Newton’s Third Law states for every force there is an equal but opposite reaction force. To distinguish a third law pair from merely oppositely directed pairs is difficult, but very important. Third law pairs must obey three rules: (1) Third law force pairs must be of the same type of force. (2) Third law force pairs are exerted on two different objects. (3) Third law force pairs are equal in magnitude and oppositely directed. Example: A block sits on a table. The Earth’s gravity on the block and the force of the table on the block are equal and opposite. But these are not third law pairs, because they are both on the same object and the forces are of different types. The proper third law pairs are: (1) earth’s gravity on block/block’s gravity on earth and (2) table pushes on block/ block pushes on table.

Feb 24, 2012