Section 1–3: The Language of Physics

1. Section 1–3:The Language of Physics Coach Kelsoe Physics Pages 21–25

2. Objectives • Interpretdata in tables and graphs, and recognize equations that summarize data. • Distinguishbetween conventions for abbreviating units and quantities. • Usedimensional analysis to check the validity of equations. • Performorder-of-magnitude calculations.

3. Mathematics and Physics • Tables, graphs, and equations can make data easier to understand. • For example, consider an experiment to test Galileo’s hypothesis that all objects fall at the same rate in the absence of air resistance. • In this experiment, a table-tennis ball and a golf ball are dropped in a vacuum. • The results are recorded as a set of numbers corresponding to the times of the fall and the distance each ball falls. • A convenient way to organize the data is to form a table, as you see on page 22 of your textbook.

4. Data from Dropped-Ball Experiment • A clear trend can be seen in the data. The more time that passes after each ball is dropped, the farther the ball falls.

5. Graph from Dropped-Ball Experiment • One method for analyzing the data is to construct a graph of the distance the balls have fallen versus the elapsed time since they were released. • The shape of the graph provides information about the relationship between time and distance.

6. Equation from Dropped-Ball Experiment • We can use the following equation to describe the relationship between the variables in the dropped-ball experiment:(change in position in meters) = 4.9 x (time in seconds)2 • With symbols, the word equation above can be written as follows:Δy = 4.9(Δt)2 • The Greek letter Δ (delta) means “change in.” The abbreviation Δy indicates the vertical change in a ball’s position from its starting point, and Δt indicates the time elapsed. • The equation allows you to reproduce the graph and make predictions about the change in position for any time.

7. Physics Equations • Physicists use equations to describe measured or predicted relationships between physical quantities. • To make expressions as simple as possible, physicists often use letters to describe specific quantities in an equation. • For example: • The Greek letter Δ (delta) is often used to mean “difference” or “change in.” • The Greek letter Σ (sigma) is used to mean “sum” or “total.”

8. Physics Equations Describe Relationships • Using these abbreviations and conventions, the word equation we saw a few slides back can be written as follows: Δy = 4.9(Δt)2 • The abbreviation “Δy” indicates the vertical change in a ball’s position from its starting point and “Δt” indicates the time elapsed.

9. Physics Equations Describe Relationships • The units in which some quantities are measured are often abbreviated with one or two letters. • Italicized letters represent quantities. Notice the m’s • The table on page 23 gives examples of symbols for quantities and their respective unit abbreviations

10. Evaluating Physics Equations • Physics equations are valid only if they can be used to make correct predictions about situations. • Even though an experiment is the ultimate way to check the validity of a physics equation, several techniques can be used to evaluate whether an equation or result can possibly be valid.

11. Using Dimensional Analysis • Dimensional analysis is a technique we teach in order to make sure we have chosen the appropriate equation for our situation. • Dimensional analysis is also something I teach because it is something you will hear over and over in your college science classes, much like sig figs.

12. Using Dimensional Analysis • So how do we do dimensional analysis? • Good news! You already know how! • Dimensional analysis is all about treating dimensions as algebraic quantities. • That means FORGET THE NUMBERS! • For instance, let’s say that a car is moving at a speed of 90 km/h and we need to know how much time it will take to travel 800 km. How can we decide how to solve this?

13. Using Dimensional Analysis • We know the speed of our car (90 km/h) and how far the car has traveled (800 km). What we need to know is how much time it took. • Forgetting about the numbers and using only the units: • We see that if we multiply the two units, our resulting unit is km2/h. Makes NO sense. • If we divide km by km/h, our unit is hours. • Setting up conversion factors is a form of dimensional analysis.

14. Order-of-Magnitude • In physics, it is possible to have calculations with answers that are astronomically large or microscopically small. • As a way to estimate an answer, you can use an order-of-magnitude calculation. • We could do this with the previous example: • Car travels 90 km/h for 800 km. • 90 is close to 100 (102) and 800 is close to 1000 (103) • Dividing 103 by 102, we get 101, which is close to the correct answer of 8.88.