# Physics Tools

## The toolbox-math, algebra and units

#### Overriding Objectives

This course has two overriding objectives, to provide instruction in problem solving techniques while helping you become comfortable using mathematical equations to model physical actions and predict the results of these events.

### What is “Physics?”

Our authors define physics as “…the branch of science that describes the motion and energy of all matter throughout the universe…” and they continue stating, “Physics is often considered to be the most fundamental of all the sciences.” (p. 3)

In order to begin investigating something, we often start with some self-evident truths. These truths, often assumed without proof, become the assumptions, something to build on, a way to interpret the world…. For example, to investigate motion we must assume time exists. That time measurements are meaningful and quantifiable. “…that an ordered sequence of events can be measured on a uniform absolute scale.” (time’s arrow)

Could Laws be constructed on the foundation of Hot and Cold or for that matter long and short? Water does freeze when it is cold but, I get cold long before water freezes. Does developing better laws require more specific or less specific input data?

#### Quantifying Data

Measurement is merely a standardized way to compare quantities. The size of a mug of coffee, tea (or other beverage) is not a standard quantity. Any mug can hold a “cup” of coffee to get you going in the morning but it may not work when measuring flour to make a cake.

There are two ways to look at measurement Qualitative and Quantitative. General techniques for describing the relative largeness or smallness of something or the amount of something result in a — Qualitative measurement. A specific measurement of a quantity of something is a — Quantitative measurement. Our interest lies in the quantitative realm. The only way to get to repeatable solutions for any problem is through accurate measurement. (Ewen, 2012, p. 13, Lost in Space)

In physics people sometimes run into problems with pre- conceived notions and misconceptions.

For example, can you measure distance with time?

Selections from “Minute Physics” at; https://www.youtube.com/user/minutephysics

This is an algebra based Physics course. This limits our discussion of dynamics, objects in motion, but you will be using basic mathematical rules, basic trigonometric identities and basic algebra to answer questions from the textbook and supplemental worksheets. In addition, we will spend some time comparing actual measured values with the mathematical models introduced in the book. Though models of reality can take other forms, the basic elementary models for this class use the rules introduced in algebra and trigonometry.

Unfortunately, the units of the input values complicate solution process because the right numerical answer depends on the units associated with the solution. Indeed, the process of translating the input units into the standard (required) output can provide hints to the solution.

The equation;

$F=ma=\frac&space;{mv}{t}\\$

Should be interpenetrated as, force equals mass times the speed of light squared. It continues, suggesting that mass times acceleration is equal to mass times velocity divided by time. By the way, it is a good idea to show your work because it helps to highlight the areas that are giving you the trouble. Documenting the solution steps will also help you as you review the material before a test. In the past it has been a requirement on tests, quizzes and other collected assignments. Should it be again?

For example; (Note how the units are transformed as the equation is solved.)

If, how much time does it take a 1.02-kg mass starting from rest to reach a final velocity of 10.0-m/s under the influence of a continuously applied force of 10.0 N (10.0kgm/s2)?

$F=ma=\frac&space;{mv}{t}\\\\&space;t=\frac{mv}{F}=\frac{(1.02&space;kg)(10&space;m/s)}{(10&space;N)}=\frac{(10.2&space;kg&space;m/s}{(10&space;N)}=1.02\frac{kg&space;m}{kgm/s^2}&space;=1.02&space;sec$

Would the answer be completely right without the units?

Ewen, D. S. (2012). Applied physics (10th ed.). Upper Saddle River, NJ: Pearson Prentice Hall.