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Force and Motion -- Introduction

Module by: R.G. (Dick) Baldwin. E-mail the author

Summary: This module introduces force and motion in a format that is accessible to blind students.

Preface

General

This module is part of a collection (see http://cnx.org/content/col11294/latest/ ) of modules designed to make physics concepts accessible to blind students. The collection is intended to supplement but not to replace the textbook in an introductory course in high school or college physics.

This module introduces force and motion in a format that is accessible to blind students.

Prerequisites

In addition to an Internet connection and a browser, you will need the following tools (as a minimum) to work through the exercises in these modules:

The minimum prerequisites for understanding the material in these modules include:

Supplemental material

I recommend that you also study the other lessons in my extensive collection of online programming tutorials. You will find a consolidated index at www.DickBaldwin.com .

Discussion

We dealt with bodies in equilibrium in earlier modules. By equilibrium, I mean that we dealt with forces acting on bodies at rest or forces acting on bodies in uniform motion. A body in equilibrium does not accelerate as a result of the forces acting on it.

An example of a body experiencing forces while at rest

A highway bridge is an example of a body at rest being acted upon by a variety of forces. As vehicles enter and exit the bridge, those vehicles exert forces on the bridge. The impact of those forces is "felt" by all the structural members that make up the bridge. The tension and compression in the various members of the bridge change as vehicles enter and leave the bridge, but the bridge remains in the same fixed location. If properly designed, the bridge doesn't experience acceleration and crash into the river below as a result of those changing forces.

Unbalanced forces

In this module, we begin a study of the influence of unbalanced forces acting on bodies along with a study of the motion produced in bodies as a result of unbalanced forces.

Statics versus dynamics

The earlier modules dealt with statics . We now begin a study of dynamics . The study of dynamics hinges largely on three important laws of motion, which were stated by Sir Issac Newton in 1686.

Making bodies move

We know from experience that we can cause small bodies to move by pulling or pushing them with our hands. In other words, we can cause a body to move by exerting a force on the body. We also know that larger bodies can be caused to move by pulling or pushing them with a machine or with a beast of burden.

We are also familiar with the idea of falling bodies that move independently of someone pushing or pulling. We have come to know this as the result of the gravitational attraction between masses.

Aristotle's contribution, or lack thereof

I have never forgotten my physics professor, Brother Rudolph, at St. Mary's University in San Antonio, Texas, telling the class that Aristotle was a hindrance to science.

Aristotle taught that heavier bodies fall faster than lighter bodies, but he was wrong. It has been proven that all bodies fall towards the earth at the same acceleration when the effects of air resistance are eliminated.

This is not too difficult to prove for yourself. A small piece of paper will fall to the ground much more slowly than a coin when the paper is in its normal state. However, if the paper is crumpled into a very tight ball, greatly reducing the effect of air resistance, it will fall to the ground almost as fast as the coin.

Galileo's contribution

Galileo and Newton clarified the ideas of motion through a series of experiments. For example, Galileo discovered the important relationship between force and acceleration. He concluded that in the absence of air resistance, freely falling objects have the same acceleration regardless of their differing weights.

Acceleration of gravity is constant

By rolling balls down inclined planes, Galileo discovered that the distance covered under a steady force is proportional to the square of the time of descent. By this, he concluded that acceleration is constant, at least near the surface of the earth.

Two cannon balls

The story goes that Galileo dropped two cannon balls of different weights off the Leaning Tower of Pisa and observed that they struck the ground below at exactly the same time. From this, he concluded that falling bodies are subject to the same acceleration regardless of their weight.

Inertia

By rolling a ball down one inclined plane and up a facing incline plane, Galileo observed that the ball tended to rise to (almost) the original height on the second inclined plane. This was true even if the second incline plane was less steep than the first.

This suggested that if the second inclined plane were perfectly flat, the ball would roll forever trying to regain its original height. From this, Galileo is said to have concluded that objects at rest tend to remain at rest, and objects in motion tend to remain in motion with the same velocity. (Recall that a change in direction is a change in velocity.)

This property of matter not to change its state of rest or of uniform motion at a constant velocity is called inertia .

Force is required to cause a change

Whenever a body changes from a state of rest to a state of motion, or changes its motion from one velocity to a different velocity, a force is required to cause that change.

Newton's contribution

Newton continued Galileo's study of motion and formulated his findings in three laws of motion. The first two laws were formal statements of Galileo's earlier conclusions. The third law formulated a finding that was original to Newton.

Three laws of motion

Unlike those before them, Galileo and Newton saw that in the absence of friction, force was required to change motion, not to maintain it.

The Principia

As mentioned earlier, Newton formulated the earlier findings of Galileo in two laws of motion and added a third law based on his own findings. He published those laws in a document which, when translated from the original Latin, was titled something like: "Mathematical Principles of Natural Philosophy." This document is often referred to simply as the Principia.

The three laws are paraphrased in the following sections.

Law 1

Every body remains in a state of rest or of uniform motion in a straight line unless compelled to change that state by external force acting upon it.

Another interpretation of this law reads as follows:

Every object in a state of uniform motion tends to remain in that state of motion unless an external force is applied to it. (This suggests that a state of rest is motion with zero velocity.)

This law is generally regarded as recognition of Galileo's concept of inertia and is often referred to as the "Law of Inertia."

The law explains what force does, but does not suggest how force should be measured.

Law 2

Rate of change of momentum is proportional to the impressed force and takes place in the direction of that force.

Another interpretation of the second law is:

The relationship between an object's mass m, its acceleration a, and the applied force F is F = m*a (where the * indicates multiplication) . Acceleration and force are vectors; in this law the direction of the force vector is the same as the direction of the acceleration vector.

This law, in conjunction with the third law, allows quantitative calculations of dynamics and a definition of mass. In particular, how do velocities change when forces are applied.

The relationships among momentum, force, mass, and accelerations will be explained later.

Law 3

Action and reaction are equal and opposite, and act on different bodies.

Another interpretation of this law is:

For every action there is an equal and opposite reaction.

This law means that forces act in equal and opposite pairs. Whenever two bodies act upon one another, equal and opposite changes of momentum occur in the two bodies.

An example of the effect of this law occurs when a person attempts to jump from a small boat to a pier. If the boat is free to move, it will tend to move away from the pier as the person attempts to launch himself in the direction of the pier. This may leave the person momentarily hanging in the air between the boat and the pier waiting to experience the acceleration of gravity and fall into the water.

In order to understand the full importance of these laws, it is necessary to understand the concepts of and relationships among mass, momentum, force, and acceleration.

Mass, momentum, force, and acceleration

Newton introduced the term mass as being distinct from weight . Mass is not easy to define in its own right. Mass can be thought of as being a "quantity of matter" or a "measure of inertia."

One of the properties of mass in a gravitational field is weight. Newton showed that weight is proportional to mass.

(In earlier modules, we have said that the weight of a body is a measure of the force required to cause that body to accelerate toward the surface of the earth at a rate of approximately 32.2 ft/s^2 or 9.81 m/s^2.)

Newton also worked with the concept of momentum , which is the product of the mass and the velocity of an object. Momentum is a vector quantity, having the same direction as the velocity to which it applies. Therefore, momenta are always added or subtracted as vectors.

The rate of change of momentum

As indicated in the second law , the force required to bring about a change in momentum is proportional to the rate of change of the momentum:

F $ (m*v2 - m*v1)/t

where the momentum is changed from a value of m*v1 to a value of m*v2 in a time interval t .

(Note that I elected to use the $ character to indicate "is proportional to." Textbooks typically use a Greek letter for this purpose, which is not compatible with many Braille displays and some audio screen readers.)

Given that the mass is constant (for the scenarios addressed in this collection of modules), and acceleration is given by the rate of change of velocity, factoring mass out of the above equation gives us

F $ m*(v2 - v1)/t, or

F $ m*a

where a is acceleration. Thus, force is proportional to the product of mass and acceleration. For a given mass, a specific force is required to cause that mass to accelerate by a given amount.

Resources

I will publish a module containing consolidated links to resources on my Connexions web page and will update and add to the list as additional modules in this collection are published.

Miscellaneous

This section contains a variety of miscellaneous information.

Note:

Housekeeping material
  • Module name: Force and Motion -- Introduction
  • File: Phy1140.htm
  • Revised: 07/27/2011
  • Keywords:
    • physics
    • accessible
    • accessibility
    • blind
    • graph board
    • protractor
    • screen reader
    • refreshable Braille display
    • JavaScript
    • trigonometry
    • Galileo
    • Newton
    • inertia
    • mass
    • momentum
    • force
    • acceleration

Note:

Disclaimers:

Financial : Although the Connexions site makes it possible for you to download a PDF file for this module at no charge, and also makes it possible for you to purchase a pre-printed version of the PDF file, you should be aware that some of the HTML elements in this module may not translate well into PDF.

I also want you to know that I receive no financial compensation from the Connexions website even if you purchase the PDF version of the module.

Affiliation : I am a professor of Computer Information Technology at Austin Community College in Austin, TX.

-end-

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