Physics is the study of how things work in terms of matter and energymatterenergy at the most basic level. Physics is everywhere! Some areas of physics.

Introduction to Physics

What is Physics?

  Physics is the study of how things work in terms of matter and

energy at the most basic level. Physics is everywhere! Some areas of physics include: ThermodynamicsMechanicsVibrations and wave phenomenaOpticsElectromagnetismRelativityQuantum mechanics 

Scientific Method

 1. Make an observation and collect data

that leads to a question2. Formulate and objectively test

hypotheses through experimentation3. Interpret the results and revise the

hypotheses if necessary.4. State a conclusion in a form that can

be evaluated by others.

Physicists use models to help build hypotheses , guide experimental design and help make predictions in new situations .

Sometimes the experiments don’t support the hypothesis. In this case the experiment is repeated over and over to be sure the results aren’t in error. If the unexpected results are confirmed, then hypothesis must be revised or abandoned. As a result the conclusion is very important. A conclusion is only valid if it can be verified by other people.

Keep in mind in that any theory, no matter how firmly it becomes entrenched within the scientific community, has limitations and at any point may be improved.

ie. There is always a possibility that a new or better explanation can come along.

Problem Solving in Physics In physics there is an organized approach that breaks down the

task of obtaining information to solve a problem.  List all the possible solutions Look for patterns Make a table, graph or figure Make a model Guess and check Work backwards Make a drawing Solve a simpler or similar related problem Often, the more problems you work on the better you get at

solving them. 

The Measure of Science

Physics usually involves the measurement of quantities.

In Physics, numerical measurements are different from numbers used in math class.

In math, a number like 7 can stand alone and be used in equations.

In science, measurements are more than just a number.

For example, if you were to measure your desk and report the measurement to be 150.

This leads to several questions:

What quantity is being measured? What units was it being measured

in? What did you used to measure it? How exact is the measurement?

SI Units – Base Units

The system of measurement in the scientific community is the SI (Système International) is used.

There are three fundamental units we will be using: seconds [s] to describe time kilograms [kg] to describe mass metres [m] to describe length

SI Units – Base Units

SI Units – Derived Units

Other units are found by combining these fundamental units:

Example:

volume = length x length x length = m3

speed = length ÷ time = m/s

Scientific Notation

Often, the numbers we use are very large or very small so to make things easier, we use scientific notation

The numerical part of the measurement must be between 1 and 10 and multiplied by a power of 10.

Eg. A softball’s mass is about 180 g or 1.8 x 10-1g.

Prefixes

We also use prefixes to accommodate these extreme numbers. Each prefix represents a power of 10.

Prefixes

Often we need to convert between units to solve a problem.

To convert between units we need to multiply by a factor of one.

We know that 1Mm = 106 m so:

1Mm = 1 and 106 m = 1

106 m 1Mm

So how far is 652 Mm in m? (Pick the ratio that will cancel out the units)

Solution

652Mm x 106 m 1Mm

=652 x 106 m

=6.52 x 108 m

 Sometimes you have to convert two units at once. What is 200 km/h in m/s?

Solution:

* don’t forget that if you are adding two measurements, they must have the same units.

Accuracy and Precision

Accuracy is how close the measured value is to the true or accepted value.

 For example, when you read the

volume of a liquid you will get a different measurement if you look at the meniscus from different angles. This phenomenon is called parallaxParalax

Problems with accuracy are due to error. Experimental work is never free of error but it needs to be minimized.

To minimize human error, parallax  should be minimized by taking the reading directly in front of the device being measured. Another way is to take several measurements to be made to be sure they are consistent.

 Ex. Gas gauge, speedometer

Instrument error can also occur. This occurs when a device is not in good working  order. When lab equipment isn’t handled properly problems with accuracy arise.

  Ex. Balances damaged, tare, wooden

meter stick got wet etc…

Precision

Precision  is due to the limitation of the measuring device.

  A microscope will give you a more

precise picture of something small than a magnifying glass will. A ruler with mm on it will give you a more precise measurement than a ruler with only cm marks

When we are taking a measurement the last digit that we measure is estimated to a degree. In this course we will assume that you can make a fair estimate to about ½ of the smallest increment.

For example, use a ruler to measure the length of your desk. What did you measure?

Was it exactly ?

Might it have been closer to ?

or perhaps been as small as ?

Because of the uncertainty in the last digit of your measuring device, we indicate that we are estimating our value to within ± ½ of the smallest increment.

So your desk measurement would be

We call this the measurement’s uncertainty.

Percent Error

When you are taking measurements, the percent error is also important. To find the percent error in your measurements:

|accepted value – measured value| x 100%

accepted value

Significant Figures

  Numerically 3.0, 3.00, 3.000 are of the

same value, but 3.000 shows that it was measured with the more precise instrument. The zeroes in all three numbers are considered "significant figures". They are shown to indicate the precision of the measurements. If we take away the zeroes, the value does not change. The measurement is still "three".

On the other hand, the zero in ".03" is not a significant figure. It is important though, because if we leave it out and write .3 then the value is completely different from .03 (it is 10 times bigger). Thus, such zeroes are said to "place the decimal", and not considered "significant".

Sometimes .03 is written as 0.03. The first zero also does not change the value of the number, but neither does it indicate more precision. It is generally included to stress the location of the decimal point, and its inclusion is never essential.

General Rules

All digits are significant with the exception that:

1. leading zeroes are NOT significant (0.0005 has only one sig. fig.)

2. tailing zeroes in numbers without decimal points are ambiguous. (zeroes in 700 are not, but the zeroes in 700.0 are)

Such tailing zeroes are assumed not significant. They must be expressed in scientific notation to

remove the ambiguity.

Example:

5200 as stated is assumed to have 2 sig. fig.

If it were to have 3 sig. fig., it should have been expressed as 5.20 x 10 3.

If it were to have 4 sig. fig., it should have been expressed as 5.200 x 103,

Example:

30 is assumed to have one sig.fig. If you have to report such a number, you MUST express it in scientific notation.

30. has sig. fig.

(The number has a decimal point, so all tailing zeroes are significant.) This is NOT appropriate notation. It also MUST be expressed in scientific notation.

30.0 has sig. fig.

(Again, the number has a decimal point, so all tailing zeroes are significant.)

0.0050200 has sig. fig.

(Leading zeroes are not significant, but the tailing zeroes are significant, because the number has a decimal point.)

12.00 has sig. fig.

32.0 x 102 has sig. fig.

Counting numbers and conversion numbers are

always infinitely significant

Calculating with Significant Figures

 When adding and subtracting with

significant figures, the answer should have the same number of digits to the right of the decimal as the measurement with the smallest number of digits to the right of the decimal.

Example:  97.3 +5.85

round off to 103.2 

When multiplying or dividing the final answer must have the same number of significant figures as the measurement having the smallest number of significant figures.

 Example: 123x 5.35658.05 round off to 658

When adding or subtracting AND multiplying or dividing, you must keep track of your significant figures but save your rounding until the end.

Example 1:  (10.2 + 2.45) x 6.9=12.65 x 6.9=87.285=87

Example 2: (4.2 – 4.18) x 19= .02 x 19= .38= 0.4

Example 3: (32.01 + 12.2) x 623= 44.21X623=27542.83=2.75X104

Example 4 =(.02 +.612) x 3.12=(.02 + .3721) x 3.12=(.3921) x 3.12=1.22 3352=1.2

Displaying Data

Displaying Data and Graphing

The best way to represent a set of data is by drawing a graph. We need to determine which variables are the independent variables and the dependent variables.

Independent variables are the ones we can manipulate (x axis)

Dependent variables are the ones that respond to the manipulation (y axis)

We title the graph “y vs x”

Example:

A car drives at a certain speed, brakes and travels a certain distance before it comes to a full stop.

What are the two variables? distance and time Which is the independent and which is

the dependent?  Independent: time Dependent:

distance What would the title of this graph be?

Distance vs Time

Rules for graphing:

a) Independent variable goes on the x axis and the dependent goes on the y axis.

b) Determine the range of both variables and label both axes accordingly. Use a ruler and use the whole space.

c) Is the origin (0,0) a valid data point?d) Draw a best fit straight line or smooth

curve** do not do dot to dot**

e) Give the graph a clear title that tells what it represents (dependent vs independent)

Let’s make a graph!

Time (s) Volume (L)

0 7

1.0 28

2.0 60

3.0 86

4.0 114

5.0 138

6.0 175

7.0 200

Scaling your Axes:

Scaling your Axes: On your graph paper you have a set number of division s for each axis. You proceed as follows to assign the value for each division:

Division value = largest data - smallest data

Number of divisions

Example:

For time (x axis) we have _____ divisions and a range of 0s to 7.0s

 div. value = = s/div

You have some leeway to round this value up to a convenient value, say, __________ s/div, but you cannot round it down (your data will not fit on the graph if you do). This method allows us to use the maximum spread of the graph paper, giving us a longer line and more accurate slope calculations.

For the volume data we have div value =    

Do not use an awkward scale. The scale should be in easy counting numbers.

Good numbers for scaling are 1, 2, 3 or multiples like 10, 20, 30 etc

Plotting the line

Straight lines: set your ruler on the page a pass it through the line the data suggests, keeping equal numbers of dots above and below the line.

Let the y intercept take care of itself.

Curved lines: Use your elbow as a pivot and ghost your pencil over the points, fine tuning your curve with your hand.

When you have it right, put your pencil down and draw in the curve in one pass

Make sure your graph has all the required parts as listed above.

Volume vs Distance

0 1 2 3 4 5 6 7 80

50

100

150

200

250

Volu

me [

L]

Time [s]

Types of graphs: 

Linear Relationships The dependent variable varies linearly with the

independent variable in the formy = mx + b

 whereb = y intercept or where the line crosses the y axis m = rise = Δy = yf - yi

run Δx xf - xi

Δy

Δx

b

 Quadratic Relationships

(Parabolic) Smooth line curves upwards in the form

y = kx2

where k = some constant

Inverse relationships (hyperbolic) Smooth line curves downwards in the form:

y = k ( ) = kx-1

1x

Frequency and Period

Time is an important measure of events in physics.

 There are two quantities that we can

record that will give us a sense of time.

Frequency

Period

Frequency

Frequency is the number of events that occur within a given amount of time (usually represented by f )

Example: The number of times a guitar string

vibrates back and forth might be 300 times /second or 300 s-1. We measure frequency in Hertz [Hz]. So, instead we would say that the guitar string has a frequency of 300Hz.

Period

Period is the time it takes for an event to complete one cycle (usually represented by T).

Example: The time it takes for one complete vibration of the string would be 1/300th of a second or

1 second. 300 As you can see, period and frequency are inversely

related so:  Period = 1 or T = 1

Frequency f

Writing a Lab Report

Lab ReportsName:Partners’ Name:Due Date:Lab Date:

 Objective: (or Purpose): In your words, not just copied from the lab handout. Materials: Rewritten from lab handout. Add or delete items as needed. Procedure: “As on lab handout”. Then note any changes you made.    

Data: (or Observations): Data should be in a table with lines and appropriate units. Make sure all data is taken with the same precision.*don’t forget your uncertainty

Observations must be in full sentences.

 Graphs:

Should be on one WHOLE sheet of graph paperShould have the correct unitsLine of best fit (for linear data)Title/labelsCorrect labeling of data points USE A RULER

Questions: All questions should be answered in full sentences. Always give your reasoning or an

explanation. Conclusion: Give 3 or 4 full sentences that

respond to the objective of the lab and summarize your work. You should include 2 or 3 sources of error.

Staple all rough work, especially your original data collection to your lab

YOUR LAB SHOULD BE NEAT.

NEAT I SAY!

An aside….

 Galileo’s thought experiment on objects

at the same speed:

Two objects fall at the same speed. If you tie them together (doubling the mass) they should fall at a faster speed.

They don’t.

falling

Experimental Design

He used experimental design. He used controlled experiments and observed objects falling from the same height. Because air resistance was always a factor he used balls rolling down an incline. The steeper the incline, the closer the model represented free fall.

His theories were used to predict the motion of many things in free fall such as raindrops or boulders.