Lesson 1.3 The Language of Physics Essential Question: What do physicists use to analyze and summarize their observations?

Math and Physics Physicists use the tools of mathematics to analyze and summarize their observations. These mathematical relationships help them make predictions in new situations.

How do physicists organize their data? Tables Graphs Equations These all make the data easier to understand.

Galileo’s “Thought Experiment” Modeled the behavior of falling objects Galileo hypothesized all objects fall at the same rate in the absence of air resistance. Dropped a table tennis ball and a golf ball in a vacuum and recorded the data.

Data from Dropped-Ball Experiment Time(s) Distance golf ball falls (cm) Distance table tennis ball falls (cm) 0.067 2.20 0.133 8.67 0.200 19.60 19.59 0.267 34.93 34.92 0.333 54.34 54.33 0.400 78.40 78.39

The table shows a clear trend in the data. The more time that passes after each ball is dropped, the farther the ball falls.

Graph the Data

Since the graph shows an obvious pattern, a smooth curve can be drawn through the data points so estimations can be made for times we don’t have data for. The shape of the graph also provides information about the relationship between time and distance.

Write an equation for the data change in position in meters=4.9× time of fall in seconds 2 This equation allows you to reproduce the graph and make predictions about the change in position for any arbitrary time during the fall.

Why use equations in physics? Physics equations describe relationships between physical quantities. The physical equation is a compact statement based on a model of the situation.

To make expressions as simple as possible, physicists often use letters to describe specific quantities in an equation.

Equation for Dropped-Ball Experiment ∆𝑦=4.9 ∆𝑡 2 ∆𝑦 is the vertical change in a ball’s position from its starting point ∆𝑡 indicates the time elapsed

Is it a variable or a unit? Variables and other specific quantities are abbreviated with letters that are boldfaced or italicized. Units are abbreviated with regular letters.

Abbreviations for Variables and Units Quantity Symbol Units Unit abbreviations Change in vertical position ∆𝑦 Meters m Time interval ∆𝑡 Seconds s Mass Kilograms kg

Are all equations valid? Physics equations are valid only if they can be used to make correct predictions about situations. Conducting an experiment is the best way to check an equation but there are other techniques.

Dimensional Analysis Dimensional analysis can weed out invalid equations. Dimensional analysis makes use of the fact that dimensions can be treated as algebraic quantities.

Order of Magnitude Order-of-magnitude estimations check answers. An order-of-magnitude calculation means determining the power of 10 that is closest to the actual numerical value of the quantity.

Order-of-magnitude estimates can also be used to estimate numbers in situations in which little information is given.

What do physicists use to analyze and summarize their observations?