School Science Lessons
4. Scientific method, graphs, pulse rate, seat belts, electromagnet, magnetic
fields, daily temperature
2012-05-05 SPw
Please send comments to: J.Elfick@uq.edu.au
Table of contents
4.0.0 Scientific method
4.1.1 Graphs
4.1.0 Scientific method
4.1.1 Graphs
4.1.1 Graphs
4.1.2 Qualitative analysis of graphs, distance /
time graph
4.1.3 Use of graphs
4.1.4 Linear graphs
4.1.5 Gradient k of the line
4.1.6 Intercept of the line b
4.1.7 The area under the velocity / time graph
4.1.0 Scientific method
4.1.0.1 Measurements
4.2.0 Scientific method applications
4.1.0.2 Scientific terminology
4.1.0.3 Standard form
4.2.0 Scientific method applications
4.2.1 Human pulse rate, recording and averaging
4.2.5 Necessity of seat belts in a motor car
4.2.3 Study an electromagnet
4.2.4 Substances magnetic fields can pass through
4.2.2 Heat one litre of water from room temperature
to 100oC
4.1.0.1 Measurements
Observations should be as accurate as possible, unaffected by preconceived
ideas. Measurements are more precise if several measurements agree closely.
The accuracy of measurement is limited by the smallest unit on the measuring
instrument, e.g. using a ruler marked in millimetres (mm), if the average
of several measurements is 174.5 mm. The reading is between 174 mm and 175
mm and the absolute error is +- 0.5 mm.
4.1.0.2 Scientific terminology
Prediction of a relationship between measured quantities is called a hypothesis.
Further experiments can be carried out to either confirm or reject the hypothesis.
A scientific law is a statement about the state of nature, e.g. the law
of conservation of energy. A principle is a generally accepted statement
deducted or proved from the law, e.g. Pascal's principle. A theory is a
generally accepted set of principles and rules which can account for a wide
range of observations, and can predict behaviour with mathematical
precision,
e.g. Einstein's Special Theory of Relativity. A model is used to give a mental
image of how something you cannot see is behaving, e.g. light as a wave
and consisting of particles.
4.1.0.3 Standard form
Express decimal fractions in standard form, e.g.
0.1 = 1 × 10-1
0.2 = 1 × 10-2
0.019 = 1.9 × 10-2
0.00087 = 8.7 × 10-4
4.1.1 Graphs
See diagram 2.0.10
Plot a graph of the measurements of one quantity, y, against the measurements
of the other quantity, x. If the graph is a straight line passing through
the origin there is a simple relationship between two sets of measured
quantities. If a straight line passes through the origin (0, 0), the constant
gradient k = y / x, so y = kx.
If the graphs plotted have the shape as in diagram 4.1.1A then by changing
the quantity on the horizontal axis the graphs have the straight line form
as in 4.1.1 B below, the quantity on the vertical axis is proportion to
Xn, X1 / n, X-1 / n.
4.1.2 Qualitative analysis of graphs,
distance / time graph
See diagram 2.0.11
The graphs of distance against time in diagram 4.1.2 describes the distance
travelled and time taken by two swimmers in a race of two laps of a 50 metre
pool. From qualitative analysis of the graphs you can say:
1. Swimmer A preceded swimmer B during one period only and Swimmer B preceded
swimmer A during one period only.
2. Swimmer A preceded swimmer B for a longer period but finally Swimmer
B won.
3. Swimmer B outstripped swimmer A just near to the finish.
4. At the first lap, Swimmer A outstripped swimmer B. During the front
25m at the second lap, they kept the same distance apart (the graph lines
are parallel.).
5. The shape of the curve shows why swimmer A failed to win. Swimmer A
swam at the second lap more slowly than that at the first lap. By contrast
swimmer B swam at the second lap faster than that at the first lap and especially
during the final 1 / 4 distance of the second lap swimmer B swam very fast.
4.1.3 Use of graphs
Much information may be obtained from graphs so they have many uses:
1. Determine the relationship between two variables and shows the possibility
of applying mathematics functions.
2. Get the data at any point of the graphs, called interpolation. It provides
the possibility to getting some data not get measured at the experiment.
For example, from graph 4.1.2 you may know how far swimmer A swam in the
first 30 seconds.
3. Get the data at some point outside the graphs, called extrapolation.
By extending the graphs lines you can get an estimate of data that was not
measured. For example, applying diagram 4.1.2, it may be estimated how far
swimmer A would swim after 130 seconds if the swimmer could keep going at
the same speed. However, this would have to be proved by further experiment!
4. Get the information about measuring error. For any graphs drawn carefully,
the distribution of separate points at the graphs shows the accidental error
of measuring. The denser the points distribute, the less the accidental
error.
5. Get other useful information, e.g. maximum and minimum values, the
points of intersection between curves and co-ordinate axes, the angles of
curves with axes, the area under a curve.
4.1.4 Linear graphs
See diagram 2.0.12
The simplest relationship between two variables is shown as a straight
line graph. For example, the distance/ time graph of swimmer B in Diagram
4.1.2 is a straight line. A timer with a stopwatch stands 5m far from the
pool side where swimmers A and B set out and starts to record the time from
zero when the swimmers pass in front of the timer at nearly the same time.
The relationship of S-T is linear, i.e. y = kx +b, where k is gradient of
the line, b is intercept of the line with y-axis.
4.1.5 Gradient k of the line
See diagram 2.0.12
The straight line from measuring data is produced by joining points apart
from each other. In reality, measuring data may be not on the actual line
so do not put measuring data into the linear equation directly. Gradient
k may be found by following graphic method. Suppose A and B are two any points
at the line, C is the point of intersection of a level line through A and
a vertical line through B. The length of AC is equal to the change in x-axis,
i.e. (x2 - x1). The length of BC is equal to the change
in y-axis, i.e. (y2 - y1), negative perhaps. Hence
the gradient of the line k = (y2 - y1) / (x2-
x1). Measure the lengths of AC and BC at the graph. Gradient
k may be calculate by: k = (47 - 19) m / (30 - 10) second, approximately
= 1.4 m / s
When calculating a gradient:
1. Get a triangle from the graph as large as possible, i.e. choose two
points farther from each other so that the gradient calculated is more exact.
2. Use the values of two points at the line. Do not use the two readings
at recording unless the two readings coincide to the line very much.
3. Measure the lengths of relative lines, e.g. AC and BC, through the
scale of the axes but not with a ruler.
4.A gradient usually has its own unit determined by the units of two variables,
such as m / s as in the above example. The unit of a gradient usually shows
its meaning in physics.
4.1.6 Intercept of the line b
See diagram 2.0.12
The distance between the point of intersection of a line with an axis
and the origin is called the intercept of the line. As long as you find gradient
k of a line and intercept b of the line with y-axis, the equation of the line
may be written. The equation of the line at diagram 4.1.4.1 is: S = 1.4 t
+ 5
Intercept of the line with the x-axis is useful too. For example, extend
the line describing the movement of swimmer A at the first lap in the reverse
direction. It intersects x-axis at the point (-12, 0). Intercept of the
line with x-axis a = -12 (s). It shows how long swimmer A took from starting
to swim at some side of the pool to starting to record the time. The interval
is 4 seconds. Intercept of the line with x-axis is usually expressed as
(a = - b / k), i.e. intercept of the line with x-axis is equal to negative
ratio of intercept of the line with y-axis to gradient of the line.
4.1.7 The area under the velocity / time
graph
See diagram 2.0.12
Sometimes the area surrounded by a line and axes also has meaning. Usually
it shows another dependent quantity related to either the independent variables
or dependent variables. Select the best fit curve and axis when calculating
the area. For example, the distance a traveller gone is the area of the
line with time axis, not velocity axis, at a v-t graph.
At diagram 4.1.4.4,
the distance covered by a car in uniformly variable motion in 8 seconds is
the area of shaded section:
Distance gone (m) = average speed (m / s) × time taken (s) = the
average height of the shaded section × the length of the bottom side
= (½) × (10 + 20) (m / s) × 8 (s) = 120 m. Similarly the
force acting on the spring and the distance i.e. length of the spring contracted
form a curve. The work done is the area of the curve with distance axis,
not force axis, at the force distance graph.
4.2.1 Human pulse rate, recording and
averaging
See 5.18 Feel your pulse
Pules rate is the artery beat due to the
blood rush when the heart contracts. The number of the times every minute
that heart contracts is expressed by the pulse rate, the beat of blood vessel
felt when your fingers press on your wrist. The pulse rate of a healthy adult
resting quietly is about 60 to 80 times per minute. Pules rate may accelerate
after taking part in sport or having a fever. Measure your pules rate by
counting for a minute, take it three times and calculate the average. Use
a table to record the data. If the table is for a group of students or the
whole class's pules rates, the table should either record the numbers of
each student in each measuring or record the numbers of all students. Should
you calculate the average of each student's pules rate or calculate average
those of all students? Have both the two averages meanings?
4.2.2 Heat one litre of water from room
temperature to 100oC
Before the experiment, set up a tripod, a heating mat, and place the beaker
on the mat. Design a table of results. Hold the thermometer vertically and
slowly put it into the water until the liquid bulb of the thermometer immerses
into the water completely. Do not stir water with the thermometer. The thermometer
must remain in the water while observing and should not touch the bottom
and wall of the beaker. Then read the value of the temperature of water with
eyes being the same level of the liquid column. The temperature of the water
should the same as the room temperature. Light the Bunsen burner and turn
the sleeve around to get a non-luminous flame. Slide the burner under the
beaker to heat the beaker evenly. Keep stirring and steadily heat the water
while recording the temperature every 30 seconds. Draw a graph of variation
of temperature in water with the time. Plot temperature on the vertical
axis and time on the horizontal axis. Connect each data point to get a smooth
graph. Reach a conclusion according to the shape of the graph.
Repeat the experiment with a fan blowing slowly on the apparatus. The temperature
rises rapidly at first heating because the rate of evaporation is slow at
that temperature and loss of heat to the surroundings is slows a long as
the temperature difference between the water and room temperature is small.
As the temperature of the water rises, the rate of rise of temperature diminishes
at an increasingly rapid rate.
4.2.3 Study an electromagnet
See diagram 32.2.3
To study the magnetism and polarity of an electromagnet, wrap about 20
turns of wire around a large nail. Use the connecting wires to connect the
nail to a power supply via a touch bulb. Here the role of the bulb is to
show if the circuit is on or off. Set the power supply to 2, 4, 6 volts DC,
and turn it on in turn. Each time, use a pocket compass to test which is
the north pole and south pole of the electromagnet. Reverse the connections
to the power supply under the condition of the same voltages. Observe what
will happens. Finally, use the head of the nail attracted pins and observe
the number of the pins being attracted roughly. Record the phenomenon under
each voltage. Increase the number of the wire turns of the nail to 40 turns.
Repeat the steps of the above experiment and take a detail record. Let every
student observe and analyse the record seriously and independently. Think
how to conclude the record into several aspects, each one can be described
only by one or two sentences.
4.2.4 Substances magnetic fields can
pass through
Collect some thin and small things in different materials such as pieces
of wood, pieces of metal, slice of plastic, paper, glass, iron sheet, piece
of cloth and sponge. Can they stop the magnetic field? Or can magnetic
field go through them?
Hypothesis: They all allow the magnetic field go through. Design a experiment
to verify the hypothesis. Set up the magnet and paper clip tied to the thread and stone in a proper
place on the table. The clip attracted by the magnet maintains a distance
from the magnet due to tying to the thread so there is a magnetic field
between the magnet and clip. Insert the materials you have prepared between
the magnet and clip in turn. If the clip falls, the material there stops the
magnetic field. Record the results of the
experiment. Consider how to describe
the conclusion you have got from the experiment? Apparently, the simplest
method of describing is classify. One is the materials which can stop the
magnetic field, the other is those which cannot stop the magnetic field.
You can describe this by means of table. There are two methods of designing
table, one is shown as figure A which has three columns in horizontal, the
other is shown as B which has two parts. If you use figure A, the names of
the materials may be filled in advance and use the signals like + or -, or
"yes" or "no" as recording. If you use figure B, you must fill the names of
the materials during the experiment. Burn the thread tied to the clip with
a match. Think what will happen about the clip?
4.2.5 Necessity of seat belts in a motor
car
The Volvo car company had investigated for the effect of seat belt in Sweden.
They analyse 50 thousand car accidents, half of them involved the use of
a seat belt. The data analysis shows that among 25 thousand of no seat belt
37 persons died, 263 persons had severe injuries, but among the people who
used seat belts in same numbers with the above, only 6 died, 161 had severe
injuries. The results of the analysis shows that the seat belt can effectively
decrease the degree of the hurt in car accidents. For a fixed change in momentum,
if the time during which the change takes place is increased the impulsive
force will be decreased. If the opposite happens and the time is decreased,
the impulsive force will be increased. Equipment A 1.5 m long, 30 cm wide
wooden board used for ramp, a small piece of wood used for a barrier, a
toy car, a piece of Plasticine (modelling clay), a piece of chalk, a metre
ruler, masking
tape and sheets of graph
paper. Mark 20 cm intervals on the ramp, starting from the bottom 0, 20, 40
. . . Support one end of wooden board by some books about 40 cm in height,
the end of 0 marked is downward to construct a ramp. Put the small piece of
wood on bottom of the ramp about 30~40 cm from 0, tape it firmly on the table
or ground. Form the Plasticine (modelling clay) into a cube with side 1 cm,
put it on the cover of the engine (in front of driver). Put the car on the
place of 20 cm of the ramp, release it,
it moves along the ramp. As the car
crashes into the wooden block, observe what happens to the Plasticine cube.
Mark with a piece of chalk where it hits on the table and measure the distance
between the marked point and impact point, accurately to cm. Record the data
in a table. Repeat the above experiment twice, each time operate
as consistently as possible. Then calculate the
average of the distances
that the Plasticine was compressed for the three times. Put the car on
a higher place in ramp, e.g. 60 cm, repeat the above experiment, three times
in one height, calculate the average. Do the experiment at 3 heights. Graph
by using the data from the experiment on graph paper, the horizontal axis
is the height of the car's original place, the vertical axis is the distance
of Plasticine compressed. Analyse according to the graph what is the relation
between the distance of Plasticine compressed and the speed of the car when
it crashes. You can see through your analysis that as the mass of the Plasticine
is fixed, the more the car's speed is, the more the impact violently, and
so the variation of the momentum of the Plasticine is greater, the distance
it is compressed is greater. As the car crashes with the barrier in certain
speed, it is acted on by a large impact force to stop it in a very short
time. This rapid change in momentum means the Plasticine is acted on by a
very strong push in a very short time intervals. If the Plasticine was replaced
by a car driver the driver would be seriously hurt. The seat belt not only
stops the crash with the barrier in front of him, but also as the body of
the car crumples lengthens the time interval for the change in momentum
and so decreases the impact force.