Transcript How Science works : Graphs

How Science works:
Graphs
Learning Objectives
You should learn :
• About different types of graphs,
• How to draw them when you
are doing your practical work,
• How to interpret the different shapes.
Drawing a graph
When
should
…and
when
I draw
a
should
I draw
a
bar-chart
…? ?
line-graph
Drawing a graph
Look at the table of your results:
If this column has
• only certain fixed values,
use a bar-chart:
• a continuous range of values,
use a line-graph:
Drawing a graph
What is the best
way to draw a
line-graph?
5 steps in drawing a graph
1. Choose simple scales.
For example:
1 large square = 1 newton (1 N)
or
1 large square = 2 N, or 5 N, or 10 N
But never choose an awkward scale,
like 1 square = 3 N or 7 N
Choose a scale that will make your graph
use most of the sheet of paper.
5 steps in drawing a graph
1. Choose simple scales.
Put the dependent variable
on the ‘y-axis’
and
the independent variable on the ‘x-axis’
5 steps in drawing a graph
2. Plot the points neatly.
To mark the points we usually use an X
x
x
x
Usually you need
5 or more points
for the graph.
x
x
x
Re-check each one before your next step.
5 steps in drawing a graph
3. If the points form a straight line…
…draw the best straight line through them
x
x
x
x
x
x
Check that it looks the best straight line.
5 steps in drawing a graph
4. If the points form a curve…
…draw a free-hand curve of best fit
Do not join the points like a ‘dot-to-dot’.
5 steps in drawing a graph
5. If a point is not on the line…
…use your apparatus to check this
measurement again
x
x
x
x
This is called an
anomalous point.
x
x
You can decide to ignore anomalous points.
5 steps in drawing a graph
In summary:
1. Choose good scales,
with the dependent variable on the y-axis
2. Plot the points carefully
3. Draw a line of best fit
using a ruler for a straight line graph,
4. or draw free-hand for a curved graph
5. Check anomalous points.
Types of graphs
Let’s look at some examples of graphs
Types of graphs
1
length
length
A straight line graph:
weight
An example would be
the length of a spring
against the weight on it.
weight
Types of graphs
2
A special case is when the
straight line goes through the origin :
In this case the
two quantities are
directly proportional.
origin
If one doubles,
then the other one
also doubles.
Types of graphs
2
If you think your graph should go through the
origin, then draw it exactly through the origin.
Types of graphs
2
extension
Example 1: the extension of a spring
against the weight on it.
weight
Types of graphs
2
current
Example 2: the current in a resistor
against the p.d. across it.
voltage
This illustrates Ohm’s Law.
Types of graphs
3
A curved graph, rising :
The dependent
variable rises
quickly at first
and then more slowly
Here are some examples:
Types of graphs
3
velocity
Example 1: the velocity of a falling object
against the time.
time
Eventually the object will reach its terminal velocity.
Types of graphs
3
current
Example 2: the current in a filament lamp
against the p.d.
voltage
Types of graphs
4
A curved graph, falling :
The dependent
variable falls
quickly at first
and then more slowly
Here are some examples:
Types of graphs
4
activity
Example 1: the activity of a radioactive source
against the time.
time
The time to fall to half is called the half-life.
Types of graphs
4
acceleration
Example 2: the rate of change is shown by
the gradient of the graph.
time
Learning Outcomes
You should now:
• Know how to draw a line-graph correctly,
• Be able to give examples of graphs
with different shapes,
• Be able to interpret graphs with
different shapes.
DISTANCE-TIME GRAPHS
Plotting distance against time can tell you a lot about
motion. Let's look at the axes:
Time is always plotted on the X-axis
(bottom of the graph). The further to
the right on the axis, the longer the
time from the start.
Distance is plotted on the Y-axis (side
of the graph). The higher up the
graph, the further from the start.
If an object is not moving, a horizontal line is shown on
a distance-time graph.
Time is increasing to the right,
but its
distance does not change. It is
not
moving. We say it is At Rest.
If an object is moving at a constant speed, it
means it has the same increase in
distance in a given time:
Time is increasing to the right,
and distance is increasing
constantly with time. The object
moves at a constant speed.
Constant speed is shown by
straight lines on a graph.
Let’s look at two moving objects:
Both of the lines in the graph show that each
object moved the same distance, but the
steeper dashed line got there before the other
one:
A steeper line indicates a larger
distance moved in a given time.
In other words, higher speed.
Both lines are straight, so both
speeds are constant.
Graphs that show acceleration look different
from those that show constant speed.
Time is increasing to the right, and distance
The line on this graph is curving
upwards. This shows an
increase in speed, since the
line is getting steeper:
In other words, in a given time,
the distance the object moves is
change (getting larger). It is
accelerating.
Summary:
A distance-time graph tells us how far an object has
moved with time.
• The steeper the graph, the faster the motion.
• A horizontal line means the object is not changing its
position - it is not moving, it is at rest.
• A downward sloping line means the object is returning
to the start.
SPEED-TIME GRAPHS
Speed-Time graphs are also called Velocity Time graphs.
Speed-Time graphs look much like Distance-Time
graphs. Be sure to read the labels!! Time is plotted on
the X-axis. Speed or velocity is plotted on the Y-axis.
A straight horizontal line on a speed-time graph means
that speed is constant. It is not changing over time. A
straight line does not mean that the object is not
moving!
This graph shows increasing
speed.
The moving object is
accelerating.
This graph shows decreasing speed.
The moving object is decelerating.
What about comparing two
moving objects at the same
time?
Both the dashed and solid line
show increasing speed.
Both lines reach the same top
speed, but the solid one takes
longer.
The dashed line shows a
greater
acceleration.
Summary:
A speed - time graph shows us how the speed
of a moving object changes with time.
• The steeper the graph, the greater the
acceleration.
• A horizontal line means the object is moving
at a constant speed.
• A downward sloping line means the object is
slowing down.
Graph
Slope
Area under
the graph
Position vs.
time
velocity
---------
Velocity vs.
time
acceleration
displacement
Acceleration
vs. time
----------
Change in
velocity