Graphing

General Physics Lab.

Dr. Said Azar

Experiments Outline
➲

Exp. 1: Measurements in Physics

➲

Exp. 2: Errors and Uncertainty

➲

Exp. 3: Simple Pendulum

➲

Exp. 4: Force Table

➲

Exp. 5: Hook’s Law

➲

Exp. 6:Ohm’s Law

➲

Exp. 7: Viscosity

➲

Exp. 8: Prism and Refraction

Report
➲

Experiment Title (‫)عنوان التجربة‬

➲

Experiment Purposes (Goals) (‫)اهداف التجربة‬

➲

Experiment Procedure (‫)اجراءات التجربة‬

➲

Experiment Theory (‫)نظرية التجربة‬

➲

Data Analysis and Interpretation (‫)تحليل و تفسير النتائج‬

➲

Conclusion (‫)التستنتاج‬



Most people at one time or another during
their careers will have to interpret data
presented in graphical form.



This means of presenting data allows one
to discover trends, make predictions, etc.



To take seemingly unrelated sets of
numbers (data) and make sense out of
them is important to a host of disciplines.



An example of graphing techniques used in
physics follows.

➲

When weight is added to a spring
hanging from the ceiling, the spring
stretches.

➲

How much it stretches depends on how
much weight is added.

➲

The following slide depicts this
experiment.

Stretch mass mass
Add a isis now here
another
Stretch now
Starting level here

We control the mass that is added.
It is the independent variable.
The stretch is dependent on what mass is added.
It is the dependent variable.

➲

The following data were obtained by
adding several different amounts of
weight to a spring and measuring the
corresponding stretch.

Stretch
(meters)

Weight
(Newtons)

0.1240

6.0

0.1475

14.0

0.1775

22.0

0.1950

30.0

0.2195

38.0

0.2300

40.0

0.2525

47.0

0.2675

54.0

0.2875

58.0

The Newton
is a unit of
force or
weight

➲

There are two variables or parameters that
can change during the experiment, weight
and stretch.

➲

As mentioned earlier the experimenter
controls the amount of weight to be added.

➲

The weight is therefore called the
independent variable.

➲

Again as mentioned before the amount that
the spring stretches depends on how much
weight is added. Hence the stretch is called
the dependent variable.

➲

The dependent variable is the quantity that
depends on the independent variable.

➲

A graph of this experimental data is
shown on the next slide.

➲

The independent variable is always
plotted on the horizontal axis, the
abscissa.

➲

The dependent variable is plotted on the
vertical axis, the ordinate.

➲

Notice that each axis is not only labeled
as to what is plotted on it, but also, the
units in which the variable is displayed.

➲

Units are important.

Stretch Versus Weight - Mohmmad

ght, the independent variable, will be plotted along the horizontal axis (the abscissa).
0.30
Each graph should be identified with a title and the experimenter's name.
retch, the dependent variable, will be plotted along the vertical axis (the ordinate).
0.26

Stretch (meters)

0.22
The graph should be made so that the data fills as much of the page
as possible. To do this, sometimes it is better not to start numbering
an axis at zero, but rather a value near the first data point.

0.18

0.14

0.10
0

10

20

30
Weight (Newtons)

40

50

60


0.30

(58.0, 0.2875)
(54.0, 0.2675)

0.26

(47.0, 0.2525)

Stretch (meters)

(40.0, 0.2300)
(38.0, 0.2195)
Let’s plot the data.

0.22

(30.0, 0.1950)
0.18

This is
(22.0, 0.1775) not a connect-the-dot exercise.
Each data point should be circled, so that it can be easily
(14.0, 0.1475)
found and distinguished from other dots on the paper.

0.14

(6.0, 0.1240)
The data appears to fit a straight line somewhat like this one.

0.10
0

10

20

30
Weight (Newtons)

40

50

60

Stretch Versus Weight - Susie Que

0.30

If there is a general trend to the data, then a best-fit
curve describing this trend can be drawn.
In this example the data points approximately fall
along a straight line.
This implies a linear relationship between the stretch
and the weight.
A wealth of information can be obtained if the
equation that describes the data is known.
With an equation one is able to predict what values
the variables will have well beyond the scope or
boundaries of the graph.
A timid mathematician should not be scared away,
since finding the equation is not hard and requires
very little knowledge of math.

0.26

Stretch (meters)

0.22

0.18

0.14

0.10
0

10

20

30
Weight (Newtons)

40

50

60


0.30

If data points follow a linear relationship (straight line),
the equation describing this line is of the form

0.26

Stretch (meters)

0.22

A very important
equation.

y = mx + b

0.18

where y represents the dependent variable
(in this case, stretch), and
x represents the independent variable (weight).

0.14

0.10
0

10

20

30
Weight (Newtons)

40

50

60


0.30

The value of the dependent variable when x = 0 is given
by b and is known as the y-intercept.

0.26

The y-intercept is found graphically by finding the

Stretch (meters)

intersection of the y-axis (x = 0) and the smooth curve

0.22

through the data points.
(From the equation y = mx + b, if we set x = 0

0.18

then y = b.)

y = mx + b

In this case b = 0.11 meters.

0.14

0.10
0

10

20

30
Weight (Newtons)

40

50

60

The quantity m is the slope of the best-fit line.

0.30

It is found by taking any two points,

0.26

for instance (x2, y2) and (x1, y1), on the straight line and
subtracting their respective x and y values.

Stretch (meters)

0.22

y = mx + b

Note
y2 = mx2 + b

0.18

We’ll call this

y1 = mx1 + b

Subtracting one equation from the other yields
0.14

y2 - y1 = mx2 - mx1
y2 - y1 = m(x2 -x1)

Therefore

rise
y2 − y1
m=
=
x2 − x1
run

0.10
0

10

20

30
Weight (Newtons)

40

50

60


0.30

slope

0.26

0.05 meters
rise
=
=
run 17.0 Newtons

= 0.00294 meters / Newton

rise = (0.21 – 0.16) meters = 0.05 meters
Stretch (meters)

0.22
Y2 = 0.21

Point 2

0.18
To find the slope of this line pick a
Point 1 couple of points on the line that are
somewhat separated from each other.
run = (34.0 – 17.0) Newtons = 17.0 Newtons

Y1 = 0.16
0.14

X2 = 34.0

X1 = 17.0

0.10
0

10

20

30
Weight (Newtons)

y-intercept = 0.11 meters
40

50

60

Stretch Versus Weight - Mohammad

0.30

slope

0.26

0.05 meters
rise
=
=
run 17.0 Newtons

= 0.00294 meters / Newton

At this point everything needed to write the equation
Stretch (meters)

describing the data has been found.

0.22

Recall that this equation is of the form
0.18

y y = m x ++ b
= mx b

0.14

Stretch

= ( 0 . 00294 meters / Newton ) ¿ Weight + ( 0 . 11 meters )
y-intercept = 0.11 meters
0.11 meters

0.10
0

10

20

30
Weight (Newtons)

40

50

60

Stretch Versus Weight - Mohammad

0.30

Here are two ways we can gain useful information
from the graph and from the equation of the line.

0.26

If we wanted to know how much weight would give
Stretch (meters)

us a 0.14 m stretch, we could read it from the plot

0.22

thusly.
This would be about 10.2 Newtons.

0.18

Solving the equation for x when y=0.14 m gives
x=10.2 Newtons.

0.14

Stretch

y = mx + b

= ( 0 . 00294 meters / Newton ) ¿ Weight + ( 0 . 11 meters )

0.10
0

10

20

30
Weight (Newtons)

40

50

60

6

This relationship would be
Suppose you have some x and y data
related to each other in the following way.

5

2

y = mx + b

4

y2

A curve through this data is not
straight and x and y are not linearly
related. Their relationship could be
complicated.

3

2

A replot 2 this data
Let’s try yofversus x. might
straighten this line some to
give a linear relationship.

1

0
0

10

20

30

x

40

50

60

In the earlier example of stretch vs. weight
one over the slope of this curve is called
the spring constant of the spring.
This method of determining the spring constant
of a spring is better than alternate methods
such as
calculating the spring constants of individual
measurements and taking an average or
taking an average of weights and dividing by an
average of the stretches.
Graphing is a powerful analytical tool.
The information on this slide will most likely be
on the lab final exam.

Graphing

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