School Science Lessons
Scientific method
2009-10-10
Please send comments to: J.Elfick@uq.edu.au
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Table of contents
4.0 Scientific method
4.1.0 The basic contents of scientific method
4.1.1 Graphs
4.2.0 Examples of scientific method application
4.2.1 Human pulse rate, recording and averaging
4.2.2 Variation of temperature in water with the time and drawing a graph of the data
4.2.3 Study an electromagnet
4.2.4 Substances magnetic fields can pass through
4.2.5 Seat belts in a motor car, problems of daily life and application of physics
4.1.0 The basic contents of scientific method
4.1.0.1 Measurements
4.1.0.2 Scientific terminology
4.1.0.3 Standard form
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
4.1.0.1 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 X 10-1
0.2 = 1 X 10-2
0.019 = 1.9 X 10-2
0.00087 = 8.7 X 10-4
4.1.1 Graphs
See diagram 4.1.1
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 4.1.2
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 4.1.4.1
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 4.1.4.2
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 4.1.4.2
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 4.1.4.3
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) x time taken (s) = the average height of the shaded section x the length of the bottom side = (½) x (10 + 20) (m / s) x 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 our 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 Variation of temperature in water with the time processing experimental data by drawing a graph
To learn to process the data in an experiment by drawing a graph of the variation of temperature in water with the time, heat the water in the beaker over a burner. Measure the temperature of water once every minute. Before the experiment set up a tripod, a mat, and place the beaker on the mat. Light burner and turn the sleeve around to get a non-luminous flame. Slide the burner under the beaker to heat the beaker evenly. Stir the water with a stirring rod. Hold the thermometer vertically and slowly put it into the water until the liquid bulb of the thermometer immerses into the water completely. Then read the value of the temperature of water with eyes being the same level of the liquid column. Measure the temperature once a minute and eight times at least. Design a table being used to record the data of the experiment as the one given in the figure. Record the data of temperature and time into one table. Then 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. If a few data points deviate from the overall trend, do not consider it again as it probably has been observed or recorded incorrectly. Finally, reach a conclusion according to the shape of the graph. Note: Do not stir water with the thermometer, and the thermometer must remain in the water while observing and should not touch the bottom and wall of the beaker.
4.2.3 Study an electromagnet
See diagram 4.2.3
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
See diagram 4.2.4
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 Seat belts in a motor car, problems of daily life and application of physics
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 you should 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.