AP PHYSICS 1 SUMMER PACKET

Table of Contents 1.What is Physics? 2.Scientific Method 3.Mathematics and Physics 4.Standards of Measurement 5.Metric System 6.Conversion Factors 7.Scientific Notation 8.Significant Digits 9.Graphing Linear Relationships 10.Problem Solving 11.Using Algebra to Rearrange Equations

What is Physics? Physics studies the nature of Matter and Energy in the Physical World.

Scientific Method Tool for developing possible explanations to problems.

Scientific Method 1.Identify the problem 2.Make a hypothesis Educated Guess 3.Experimentation Test your Hypothesis 4.Analysis of results Reject Hypothesis or Continue Testing

Mathematics and Physics ■Mathematics is the language of Physics and all sciences. ■Mathematics is used to strengthen theories that are difficult to test. ■Theoretical Physicists make mathematical predictions to explain evidence or direct their research.

Standards of Measurement S.I. System  In 1960 an international committee of scientists agreed on a system of Standards for Physical Quantities called the S.I. System (Système International).  Standard Unit for length – Meter (m)  Standard Unit for time – Second (s)  Standard Unit for mass – Kilogram (kg)

Metric System ■The SI System also includes the metric system. ■The Metric System uses prefixes to represent large and small measurements. ■The Metric System is divided into prefixes larger than 1 and smaller than 1 ■These Prefixes are based on powers of 10!

Conversion Factors ■Conversion Factors are used to change the unit without changing the measurement. ■Conversions Factors are fractions that always equal 1!! ■You may use as many conversion factors as you need to. (You can multiply by 1 anytime). ■Any equality can be a Conversion Factor!

RULES FOR USING CONVERSION FACTORS

1 st and 2 nd Steps ■Write Down the Measurement 12.3cm ■Write out Fraction Bar (---) 12.3cm x { __ } { }

3 rd Step ■Put Unit to Cancel on the Bottom. ■ Unit you are Changing to goes on the top. ■{12.3cm} x {1m} ■ {100cm}

4 th Step ■If number is on top, Multiply. ■If number is on bottom, Divide. ■{12.3cm} x {1m} = 0.123m {100cm}

DON’T FORGET YOUR UNITS!!!

SCIENTIFIC NOTATION

What is Scientific Notation? Scientific notation is a way of writing extremely large or small measurements. The number is written as a product.

What are the steps? 1.Write number such that it is between 1 and Write next factor as an exponent of 10 and count decimal places moved. 3.Large Measurements will have a positive exponent. (Move decimal to the left) 4.Small Measurements (Decimals) will have a negative exponent. (Move decimal to the right.)

Rules for Changing Exponents ■If you increase the exponent, decrease the number (move decimal to the left) ■If you decrease the exponent, increase the number (move the decimal to the right)

Adding and Subtracting Using Scientific Notation If the exponents are the same it’s easy. Add or subtract the numbers Keep the exponent and the unit the same. If the exponents are not the same we have to make the exponents the same. Then add or subtract. See rules for changing exponents (previous slide) If the units are not the same, make the units the same before making the exponents the same. Then proceed with addition or subtraction.

Multiplying and Dividing Using Scientific Notation Rule for multiplying: Multiply numbers then add exponents and then multiply the units. Rule for Dividing: Divide numbers and then subtract the exponents and then divide the units. Make sure your answer is in Correct Scientific Notation.

SIGNIFICANT DIGITS

Rules For Significant Digits ■Non zero digits are significant ■ Final zeros after the decimal point are significant ■ Zeros between significant digits are significant ■ Zeros used only for spacing are not significant

What If You Want to Make a Zero Significant? –You can draw a line over a zero if it is significant. OR –Write the measurement in scientific notation.

Adding and Subtracting with Significant Digits Rule: Round your answer to the least precise measurement. Example: g g g = g (unrounded answer) (Since 2.6 g is the least precise measurement and ends at the tenths decimal place. You must round your answer to the tenths decimal place to have the correct number of significant digits.) g is rounded to 12.5 g g g g = 12.5 g (answer with correct significant digits)

Multiplying and Dividing with Significant Digits Rule: Your answer should have the least number of significant digits. Example: (4.168 m) * (5.7 m) = m 2 (unrounded answer) m (4 significant digits) 5.7 m (2 significant digits) You must round your answer to have the least number of significant digits. In this case, your answer must be rounded to have 2 significant digits m 2 rounds to 24 m 2 (4.168 m) * (5.7 m) = 24 m 2 (answer with correct significant digits) (4 SD) * (2 SD) = (2 SD)

Conversion Factors and Significant Digits When using a conversion factor, you do not gain or lose significant digits, unless it is defined by an equality! answer with correct significant digits)

RULES FOR GRAPHING

Rules for Graphing 1.Identify the Independent and Dependent Variables. ■Independent Variable – the variable that the experimenter controls ■Dependent Variable – the variable that changes as the independent variable changes

Rules for Graphing 2.Determine the range of the independent variable to be plotted. 3.Decide whether the origin (0,0) is a valid data point. 4.Spread the data out as much as possible. Let each division on the graph paper stand for a convenient unit. 5.Number and Label the Horizontal Axis.

Rules for Graphing 6.Repeat steps 2-5 for the Dependent Variable. 7.Plot the Data Points on the Graph. 8.Draw the “best fit” straight line or smooth curve that passes through as many data points as possible (Do not have to connect the dots). 9.Give the graph a title that clearly tells what the graph represents.

Graphing a Linear Relationship (Direct Proportion) ■Look for a constant rate of increase or decrease in both variables. ■ y = mx + b (slope intercept form of a linear relationship) ■m = slope = rise/run = (y 2 – y 1 ) / (x 2 – x 1 ) ■b = y – intercept (the “y” coordinate where x = 0) 1.Find the slope (m) with two points from your data (x 1,y 1 ) and x 2, y 2 ). 2.Substitute the value of the slope (m) into y = mx+ b along with an (x, y) coordinate and solve for the y-intercept (b).

PROBLEM SOLVING

Problem Solving 1. Read problem carefully (more than once). 2. Draw a suitable Diagram (whenever possible). 3.Identify Given Information and What you are solving for. 4. Select equation(s) that can be used to find the unknown. 5.Substitute given values with appropriate units into the equation. 6. Obtain value for unknown. Check Units? Is Answer Reasonable? Is Plus or Minus sign meaningful?

Example Problem ■Assuming the Earth is a perfect sphere and has a mass of 5.96 x kg. Calculate the Volume of the Earth in km 3 and the radius of the earth in km, if it has an approximate Density of 5.52 x 10 3 kg/m 3. ■Answer: –V Earth = 1.08 x km 3 –R Earth = 6.37 x 10 3 km

USING ALGEBRA TO REARRANGE EQUATIONS

Using Algebra to Rearrange Equations Goal: For a given equation you need to be able to rearrange the equation to solve for what you want. When you rearrange an equation, you want the variable you are solving for: 1.To be in the numerator (On top). 2.To be isolated (by itself). 3.To be positive (+). 4.To have an exponent of 1.

Using Algebra to Rearrange Equations Use opposite mathematical operations to isolate a variable in an equation. ■Use Multiplication to remove Division ■Use Addition to remove Subtraction ■Use the Square Root to remove the Square Exponent (x 2 ) Note: The reverse of the above is also true! Always remember!! ■What ever you do on one side of an equation you must do on the other! ■Check the units to make sure you rearranged the equation correctly!