Section 1–3:The Language of Physics

Coach KelsoePhysics

Pages 21–25

Objectives• Interpret data in tables and graphs, and

recognize equations that summarize data.

• Distinguish between conventions for abbreviating units and quantities.

• Use dimensional analysis to check the validity of equations.

• Perform order-of-magnitude calculations.

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.

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.

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.

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.

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.”

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.

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

Quantity Symbol Units Unit Abbrev.

Change in vertical position

Δy meters m

Time interval Δt Seconds s

Mass m kilograms kg

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.

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.

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?

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.

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.