Physics M1 Graphs I

OBJECTIVESOBJECTIVES What is a graph?What is a graph? Different types of graphsDifferent types of graphs Line of best fitLine of best fit QUIZQUIZINTRODUCTIONINTRODUCTION

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GRAPHS

Physics Module 1 Unit 1 Lesson 13-14BEGINBEGIN


XXIntroduction

http://www.nationsonline.org/maps/jamaica-administrative-map.jpg

FEEDBACK3

1. What is the purpose of a map?

2. Are vertical and horizontal lines on the map?

3. What is the purpose of the vertical and horizontal lines?

4. Do you think that a map is like a graph? Why?


XXIntroduction

http://www.nationsonline.org/maps/jamaica-administrative-map.jpg

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1. What is the purpose of a map?

2. Are vertical and horizontal lines on the map?

3. What is the purpose of the vertical and horizontal lines?

4. Do you think that a map is like a graph? Why?

To locate places

Yes

They are used to state the location of a place on the map

Yes. The lines on a map are used to write coordinates of places in the same way the lines on a graph are used to write coordinates of points on the graph


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Objectives

At the end of this lesson, you will be able to the following:

1. State what is a coordinate grid (Cartesian plane) and a graph.

2. Explain what is an experimental graph.

3. Distinguish between independent and dependent variables.

4. Apply the required rules for plotting experimental graphs.

5. Identify different types of experimental graphs that are commonly found in physics.

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1. What is a Cartesian plane? What is a graph?

Cartesian plane is formed by intersecting two real number lines at right angles. It is also called the x-y plane or the rectangular coordinate system.

Horizontal axis isusually called the

x-axis

Vertical axis isusually called

the y-axis

The intersectionof the two axes is called the origin

6Cont’d


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1. What is a Cartesian plane? What is a graph?

A graph is a best possible line drawn through points on a cartesian plane

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graph


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What is an experimental graph?

An experimental graph is a graph that is plotted using data from an experiment.

An experimental graph gives a pictorial view of the relationship between two variables in an experiment.

The illustration shows an experimental graph of the relationship between the velocity of an object and the time of its motion

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XX1. What is an experimental graph? Independent and dependent variables

1. An experimental graph shows the relationship between two variables in an experiment.

2. In an experiment the magnitude of one variable is measured and the magnitude of another variable that depends on it is measured whenever the magnitude of the first variable changes. The magnitude of the first variable is most times varied by the experimenter

3. The variable that is varied by the experimenter in the experiment is called the independent variable.

4. The variable that depends on the independent variable is called the dependent variable

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XX1. What is an experimental graph? Independent and dependent variables

The values of the independent variable form the x-coordinates of the points on an experimental graph

The values of the dependent variable form the y-coordinates of the points on an experimental graph

In the experimental graph shown, velocity is the dependent variable and time is the independent variable

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Dep

ende

nt v

aria

ble:

y-a

xis

The independent variable: x-axis


XX1. What is an experimental graph? Elements of a Proper Graph

A proper graph must display the following: A title The dependent variable on the y-axis and independent variable on the x-axis. Axes labeled with the names of the variable quantities and their units. Properly calibrated axes. An axis is calibrated when the numbers representing the

magnitudes of the quantity are written along the axis at evenly spaced intervals Calibrations must be such that the ranges of values on each axis must take up

more than half the length of the axis. Numbering can begin at a non-zero value to accommodate this requirement , however this cannot be broken if intercept values are required from the graph.

DO NOT use 1 cm to represent 3 or 7 units or any multiple or fraction of 3 or 7 units. Similarly DO NOT use 3 or 7 cm to represent 1 unit.

Use or × to plot points on the graph.

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TITLE Clearly states the purpose of the graph Should be located on a clear space near the top of the graph A possible title for a graph would be: Graph showing the variation of the

period of a Simple Pendulum with its length. The title should uniquely identify the graph

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EXAMPLES OF POOR CHOICES OF TITLESExample 1. “v vs t"

The title should be in words and should not just repeat the symbols of the quantities plotted on the axes!

Example 2. “Velocity versus time“

This title is in words, but just repeats the names of the quantities plotted on the axes.

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The axes should be labeled with words and with units clearly indicated. The units: are generally in parentheses, e.g., Displacement, y, of ball (cm) Avoid saying Diameter in meters (x 10-4) since this confuses the reader.

Instead state Diameter (x 10-4 meters) or use standard prefixes like kilo or micro so that the exponent is not needed: "Diameter (mm)".

Time of fall (s)

Displacement of ball (cm)

LABELLING AXES

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1. What is a graph? Elements of a Proper Graph

1. The scales should be chosen so that the graph spreads over as much of the graph sheet as is possible. This is done by spreading the range of magnitudes of the quantities on both the axes over more than half of the respective axis

2. The first graph is a good graph because the range of values on both axes are spread over more than half the length of the axis while it is not so in the second.

Good

Poor

CALIBRATING SCALES

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XX1. What is an experimental graph? Elements of a proper graph. Summary

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Clearly stated title

Axis labeled with quantity and its SI units

Points plotted using or ×

Axis calibrated using 4 cm (NOT 3 cm or 7 cm) to represent 1 unit

Range of values spread over more than half the length of the axis


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2. Types of experimental graphs

Two types of experimental graph that are most commonly used in Physics are:

You will use mostly linear graphs in physics.

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LinearLinear ExponentialExponential


XX 2. Types of experimental graphs: Linear graphs

Linear graphs can be

1. Directly proportional: The line passes through the origin of the axes

2. Linear with positive slope: The line slopes upwards to (or from) the x-axis

3. Linear with negative slope: The line slopes downwards to (or from) the x-axis.

4. NOTE: Proportional graphs can also have negative slopes.

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2. Making linear graphs

If the displacement (s) of an object that is traveling with constant acceleration (a) from rest is plotted against the time (t) the object travels the graph obtained would be as in the Figure 1.

The reason for this is the time taken varies with distance in the following way s = ½a t2

If however a graph of s against t2 is plotted the graph in the illustration will be obtained as in Figure 2.

Other examples are acceleration against mass will give a curved graph but acceleration against 1/mass will give a proportional graph because acceleration = force/ mass for constant force.

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XX3. Line of best fit. What is it?

What is meant by straight line of best fit?

x

xx

x

x

x

‘line of best fit

’‘lin

e of best

fit’

This is a line that should pass as close as possible to each of the points but should not be connected point-to-point. If the relationship appears to be linear, the line of best fit should be a straight line.

EXAMPLE 1EXAMPLE 1 EXAMPLE 2EXAMPLE 2

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3. Line of best fit. What is it?

Is the line best fit linear? Click YES or NO.

x

x

xx

x x It is not linear.

This is a line that should pass as close as possible to each of the points but should not be connected point-to-point. But the relationship appears to be non linear.

NOYES Try again

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XX3. Line of best fit. Steps to follow to draw a line of best fit

Draw a line of best fit using a ruler for a straight line graph, or draw free-hand for a curved graph. The line should be drawn so that there are roughly the same number of points above and below.

too hightoo low

too steep

too shallow

correct

This is called an inconsistent point.

Use your apparatus to check this measurement again

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Choose good scales, with the dependent variable on the y-axis and the independent variable on the x-axis

Plot the points carefully.

Inconsistent points should be rechecked. If this is not possible they should be ignored when drawing the best-fit line


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QUIZ

Are you ready to test yourself? There are five multiple choice questions For each question, click on the correct response and then click on the

feedback for explanations of the answers being correct or incorrect.

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BEGIN QUIZ!BEGIN QUIZ!


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QUIZ: Question 1

Which is the independent variable on the graph in the diagram?

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A. Potential difference A. Potential difference

B. AmpsB. Amps

C. VoltsC. Volts

D. CurrentD. Current

FEEDBACKFEEDBACKFEEDBACKFEEDBACK


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Quiz: Feedback to Question 1

Which is the independent variable on the graph in the diagram?

27 NEXT QUESTIONNEXT QUESTIONNEXT QUESTIONNEXT QUESTION

A is incorrect: Potential difference is the dependent quantity. It is on the y-axis.

B is incorrect: Amps is a unit and not a quantity.

C is incorrect: Volts is a unit and not a quantity.

D is correct: Current is the independent quantity. It is on the x-axis.


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QUIZ: Question 2

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B. I and III only B. I and III only

D. I, II and III D. I, II and III

C. I and II only C. I and II only

A. NoneA. None


Which of the graphs in the diagrams could be considered to be proper graphs?

I II III


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A is correct: None of the graphs have the range of quantities on both axes spread over more than half the length of the axes

B is incorrect: Neither of the two graphs have the range of quantities on both axes spread over more than half the length of the axes.

C is incorrect: Neither of the two graphs have the range of quantities on both axes spread over more than half the length of the axes.

D is incorrect: Neither of the two graphs have the range of quantities on both axes spread over more than half the length of the axes.

Which of the graphs in the diagrams could be considered to be proper graphs? I II III


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QUIZ: Question 3

Which is a good criticism of the graph shown?

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A. Axes are not properly labeled.A. Axes are not properly labeled.

D. The line of best fit is not correctly drawn. D. The line of best fit is not correctly drawn.

B. Spread of values on the axes not large enough.B. Spread of values on the axes not large enough.

C. The plotted points are not represented correctly.C. The plotted points are not represented correctly.


Current (A)

Vol

tage

(V

)


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A is incorrect: Both axes are labeled with the quantities and their units.

B is incorrect: The range of values on both axes is spread over more than half the length of the axes.

C is correct: The accepted or × for plotting points is not used.

D is incorrect: There is a balance of points about the graph line.

Which is a good criticism of the graph shown?

Current (A)

Vol

tage

(V

)


XX

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Based on the information on the graph in the diagram which of the following is the most likely equation relating the two variables?

Quiz: Question 4

A. I = k × 1/r A. I = k × 1/r

D. I = k × r2D. I = k × r2

C. I = k × rC. I = k × r

B. I = k × 1/r2 B. I = k × 1/r2


1/r2 (m-2)

I (Wm-2)


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A is incorrect: For that equation, a graph of I against 1/r would be a straight line.

B is correct: For that equation, a graph of I against 1/r2 would be a straight line.

C is incorrect: For that equation a graph of I against r would be a straight line.

D is incorrect: For that equation a graph of I against r2 would be a straight line.

Based on the information on the graph in the diagram which of the following is the most likely equation relating the two variables?

1/r2 (m-2)

I (Wm-2)


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QUIZ: Question 5

Which is the best reason for the line of best fit in the diagram being incorrect?

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B. The points are on a curve and not a straight line B. The points are on a curve and not a straight line

D. The question is not necessary because the line of best fit is correct

D. The question is not necessary because the line of best fit is correct

C. The line should be sloping upwards from the x-axis C. The line should be sloping upwards from the x-axis

A. There is an imbalance of points above the lineA. There is an imbalance of points above the line



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A is correct: There are more points above the best fit line than below.

B is incorrect: The points do lie on an approximate straight line.

C is incorrect: If the line sloped upwards from the x-axis the points would not be clustered around the line.

D is incorrect: The line of best fit is NOT correct.

Which is the best reason for the line of best fit in the diagram being incorrect?


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Physics M1 Graphs I