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Title: Module: Science Skills and Safety Time allocation: 8 hours


1
Module Science Skills and Safety Time
allocation 8 hours
IJSO Training Course Phase III
2
Objectives
  • Describe, distinguish between random
    uncertainties and systematic errors.
  • Define and apply the concept of significant
    figures.
  • Identify and determine the uncertainties in
    results calculated from quantities and in a
    straight-line graph.
  • Introduce general procedures of writing
    experimental reports
  • Laboratory safety and rules.

3
1. Significant Digits
  • Suppose you want to find the volume of a lead
    cube. You could measure the length l of the side
    of a lead cube to be 1.76 cm and the volume 13
    from your calculator reads 5.451776. The
    measurement 1.76 cm was to three significant
    figures so the answer can only be three
    significant figures. So that the volume 5.45
    cm3. The following rules are applied generally

4
  • All non-zero digits are significant. (e.g., 22.2
    has 3 sf)
  • All zeros between two non-zero digits are
    significant. (e.g., 1007 has 4 sf)
  • For numbers less than one, zeros directly after
    the decimal point are not significant. (e.g.,
    0.0024 has 2 sf)
  • A zero to the right of a decimal and following a
    non-zero digit is significant. (e.g., 0.0500 has
    3 sf)

5
  • All other zeros are not significant. (e.g., 500
    has 1 sf, 17000 has 2 sf)
  • When multiplying and dividing a series of
    measurements, the number of significant figures
    in the answer should be equal to the least number
    of significant figures in any data of the series.

6
  • For example, if you multiply 3.22 cm by 12.34 cm
    by 1.8 cm to find the volume of a piece of wood,
    you get an initial answer 71.52264 cm3 from your
    calculator. However, the least significant
    measurement is 1.8 cm with 2 sf. Therefore, the
    correct answer is only 72 cm3.
  • When adding and subtracting a series of
    measurements, the answer has decimal places with
    the least accurate place value in the series of
    measurements.

7
  • For example, what is your answer by adding 24.2 g
    and 0.51 g and 7.134 g? You get an initial answer
    31.844 g from your calculator. However, the least
    accurate place measurement is 24.2g with only one
    decimal point. So the answer is 31.8 g.

8
  • Exercises
  • 1. How many significant figures are indicated by
    each of the following?
  • (a). 1247 (b). 1007 (c). 0.0345
  • (d). 2.20 x 107 (e). 62.00 (f). 0.00025
  • (g). 0.00250 (h). sin 45.2o
  • (i). tan-10.24 (j). 3.20 x 10-16
  • (a). 4 (b). 4 (c). 3 (d). 3
    (e). 4
  • (f). 2 (g). 3 (h). 3 (i). 2
    (j). 3

9
  • 2. (a) Add the following lengths of 3.15 mm and
    7.32 cm and 19.2 m.
  • (b) A rectangular box has lengths of 2.34 cm,
    90.66 cm and 3.7 cm. Calculate the volume of the
    box cm3.
  • (a) 0.00315 0.0732 19.3 19.27635. Thus the
    answer is 19.3 m.
  • (b) 2.34 x 90.66 x 3.7 784.93428. Thus the
    answer is 780cm3.

10
2. Making Measurements
  • A measurement should always be regarded as an
    estimate. The precision of the final result of an
    experiment cannot be better than the precision of
    the measurements made during the experiment, so
    the aim of the experimenter should be to make the
    estimates as good as possible.

11
  • There are many factors which contribute to the
    accuracy of a measurement. Perhaps the most
    obvious of these is the level of attention paid
    by the person making the measurements a careless
    experimenter gets bad results! However, if the
    experiment is well designed, one careless
    measurement will usually be obvious and can
    therefore be ignored in the final analysis.

12
  • Systematic Errors
  • If a voltmeter is not connected to anything else
    it should, of course, read zero. If it does not,
    the "zero error" is said to be a systematic
    error all the readings of this meter are too
    high or too low. The same problem can occur with
    stop-watches, thermometers etc.

13
  • Even if the instrument can not easily be reset to
    zero, we can usually take the zero error into
    account by simply adding it to or subtracting it
    from all the readings. (However, other types of
    systematic error might be less easy to deal
    with.)
  • For this reason, note that a precise reading is
    not necessarily an accurate reading. A precise
    reading taken from an instrument with a
    systematic error will give an inaccurate result.

14
  • Random Errors
  • Try asking 10 people to read the level of liquid
    in the same measuring cylinder. There will almost
    certainly be small differences in their estimates
    of the level. Connect a voltmeter into a circuit,
    take a reading, disconnect the meter, reconnect
    it and measure the same voltage again. There
    might be a slight difference between the
    readings.

15
  • These are random (unpredictable) errors. Random
    errors can never be eliminated completely but we
    can usually be sure that the correct reading lies
    within certain limits.
  • To indicate this to the reader of the experiment
    report, the results of measurements should be
    written as

Result Uncertainty
16
  • For example, suppose we measure a length, l to
    be 25 cm with an uncertainty of 0.1 cm. We write
    the result as
  • By this, we mean that all we are sure about is
    that is somewhere in the range 24.9 cm to 25.1
    cm.

l 25.0 0.1cm
17
A. Quantifying the Uncertainty
  • The number we write as the uncertainty tells the
    reader about the instrument used to make the
    measurement. (As stated above, we assume that the
    instrument has been used correctly.) Consider the
    following examples.

18
  • Example 1 Using a ruler
  • The length of the object being measured is
    obviously somewhere near 4.3 cm (but it is
    certainly not exactly 4.35 cm). The result could
    therefore be stated as
  • 4.3 cm Half the smallest division on the ruler

19
  • In choosing an uncertainty equal to half the
    smallest division on the ruler, we are accepting
    a range of possible results equal to the size of
    the smallest division on the ruler.
  • However, do you notice something which has not
    been taken into account? A measurement of length
    is, in fact, a measure of two positions and then
    a subtraction.

20
  • Was the end of the object exactly opposite the
    zero of the ruler? This becomes more obvious if
    we consider the measurement again, as shown
    below.

21
  • Notice that the left-hand end of the object is
    not exactly opposite the 2 cm mark of the ruler.
    It is nearer to 2 cm than to 2.05 cm, but this
    measurement is subject to the same level of
    uncertainty.
  • Therefore the length of the object is
  • (6.30 0.05)cm - (2.00 0.05)cm

22
  • so, the length can be between
  • (6.30 0.05) - (2.00 - 0.05) and (6.30 - 0.05)
    - (2.00 0.05)
  • that is, between 4.40 cm and 4.20 cm
  • We now see that the range of possible results is
    0.2 cm, so we write
  • Length 4.30 cm 0.10 cm
  • In general, we state a result as

Reading The smallest division on the measuring instrument
23
  • One may record the length of the following red
    stick to be 5.9 0.1 cm.

24
  • Example 2 Using a Stop-Watch
  • Consider using a stop-watch which measures to
    1/100 of a second to find the time for a pendulum
    to oscillate once. Suppose that this time is
    about 1s. Then, the smallest division on the
    watch is only about 1 of the time being
    measured. We could write the result as
  • T 1.00 0.01s
  • which is equivalent to saying that the time T is
    between 0.99s and 1.01s.

25
  • This sounds quite good until you remember that
    the reaction-time of the person using the watch
    might be about 0.1s. Let us be pessimistic and
    say that the person's reaction-time is 0.15s. Now
    considering the measurement again, with a
    possible 0.15s at the starting and stopping time
    of the watch, we should now state the result as
  • T 1.00 s (0.01 0.3) s

26
  • In other words, T is between about 0.7s and
    1.3s. We could probably have guessed the answer
    to this degree of precision even without a
    stop-watch!

27
  • Conclusions from the preceding discussion
  • If we accept that an uncertainty (sometimes
    called an indeterminacy) of about 1 of the
    measurement being made is reasonable, then

(a) a ruler, marked in mm, is useful for making measurements of distances of about 100mm (or 10 cm) or greater.
(b) a manually operated stop-watch is useful for measuring times of about 30 s or more (for precise measurements of shorter times, an electronically operated watch should be used)
28
B. How many Decimal Places?
  • Suppose you have a timer which measures to a
    precision of 0.01s and it gives a reading of 4.58
    s. The actual time being measured could have been
    4.576 s or 4.585 s etc. However, we have no way
    of knowing this, so we can only write
  • t 4.58s 0.01s

29
  • We now repeat the experiment using a better timer
    which measures to a precision of 0.0001 s. The
    timer might still give us a time of 4.58s but now
    we would indicate the greater precision of the
    instrument being used by stating the result as
  • t 4.5800 s 0.0001 s
  • So, as a general rule, look at the precision of
    the instrument being used and state the result to
    that number of decimal places.

30
C. How does an uncertainty in a measurement
affect the FINAL result?
  • The measurements we make during an experiment are
    usually not the final result they are used to
    calculate the final result. When considering how
    an uncertainty in a measurement will affect the
    final result, it will be helpful to express
    uncertainties in a slightly different way.
    Remember, the uncertainty in a given measurement
    should be much smaller than the measurement
    itself.

31
  • For example, if you write, "I measured the time
    to a precision of 0.01s", it sounds good unless
    you then inform your reader that the time
    measured was 0.02s! The uncertainty is 50 of the
    measured time so, in reality, the measurement is
    useless.

32
  • We will define the quantity Relative Uncertainty
    (sometimes called fractional uncertainty) as
    follows
  • (To emphasize the difference, we use the term
    "absolute uncertainty" where previously we simply
    said "uncertainty").

Relative Uncertainty (Absolute Uncertainty) / (Measured Value)
33
  • Exercises
  • 1. If we use the formula xy/z3 and the
    percentage uncertainty (relative uncertainty
    100) in y is 3 and in z is 4, what is it
    percentage uncertainty in x?
  • 2. Same as above, but the formula is xy2/vz ?
  • 1). 15 2). 8

34
  • We will now see how to answer the question in the
    title. It is always possible, in simple
    situations, to find the effect on the final
    result by straightforward calculations but the
    following rules can help to reduce the number of
    calculations needed in more complicated
    situations.

35
Rule 1 If a measured quantity is multiplied or divided by a constant, then the relative uncertainty stays the same. See Example 1.
Rule 2 If two measured quantities are added or subtracted then their absolute uncertainties are added. See Example 2.
Rule 3 If two (or more) measured quantities are multiplied or divided then their relative uncertainties are added. See Example 3.
Rule 4 If a measured quantity is raised to a power then the relative uncertainty is multiplied by that power. (If you think about this rule, you will realise that it is just a special case of rule 3.) See Example 4.
36
  • A few simple examples might help to illustrate
    the use of these rules. (Rule 2 has, in fact,
    already been used in the section "Using a Ruler"
    on page 3.)

37
  • Example 1
  • Suppose that you want to find the average
    thickness of a page of a book. We might find that
    100 pages of the book have a total thickness of T
    9.0 mm. If this measurement is made using an
    instrument having a precision of 0.1 mm, then the
    relative uncertainty is e 0.1/9.0. Hence, the
    average thickness of one page, t, is given by t
    T/100 0.09 mm with an absolute uncertainty 0.09
    x e 0.001mm, or t 0.090 mm 0.001mm. Note
    both T and t have only 2 sf.

38
  • Example 2
  • (a) To find a change in temperature T T2-T1 ,
    in which the initial temperature T1 is found to
    be 20C 1C and the final temperature T2 is
    found to be 45C 1C. Then T 25 2C.
  • (b) Now, the initial temperature T1 is found to
    be 20.2C 0.1C and the final temperature T2 is
    found to be 45.23C 0.01C. Then the calculated
    value is 25.03 0.11. However, the least decimal
    place measurement is 20.2 with only one decimal
    point. So the answer is T 25.0 0.1C.

39
  • Exercise
  • 3. The first part of the trip took 27 ? 3 (s),
    the second part 14 ? 2 (s). How long time did the
    whole trip take? How much longer did the first
    part take compared to the second part?
  • 41 ? 5s , 13 ? 5s

40
  • Example 3
  • To measure a surface area, S, we measure two
    dimensions, say, x and y, and then use
  • S xy. Using a ruler marked in mm, we measure x
    54 1 mm and y 83 1 mm. This means the
    relative uncertainties of x and y are,
    respectively, 1/54 and 1/83. The relative
    uncertainty of S is then e 1/54 1/83 0.03.
    The calculated value of the surface area is 4482
    with uncertainty 134.46. Thus, the surface area
    S is 4500 100mm². (2 significant figures)

41
  • Exercises
  • 4. An object covers 433.07 ? 1.05 (m) in 23.09 ?
    1.10 (s). What was the speed?
  • 5. If using the formula v u at we insert u
    6.0 ? 0.4 ms-1, a 0.200 ? 0.002 ms-2 and time t
    2.00 ? 0.10 s, what will v be?

42
  • Example 4
  • To find the volume of a sphere, we first find its
    radius, r (usually by measuring its diameter).
    We then use the formula V 4/3 (p r3) . Suppose
    that the diameter of a sphere is measured (using
    an instrument having a precision of 0.2mm) and
    found to be 50.0mm, so r 25.0mm with relative
    uncertainty 0.2/50 0.004, so r 25.0 0.1mm.
    The relative uncertainty of V is 3 x 0.004
    0.012. The volume of the sphere is V 65500
    800mm3.
  • (3 significant figures)

43
  • Exercises
  • 6. The dimensions of piece of paper are measured
    using a ruler marked in mm. The results were x
    60mm and y 45mm.
  • (a) Rewrite the results of these measurements
    "correctly".
  • (b) Calculate the maximum and minimum values of
    the area of the sheet of paper which these
    measurements give.
  • (c) Express the result of the calculation of
    area of the sheet of paper in the form area A
    A.
  • (a) 60 1mm, 45 1mm. (b) 2806mm2, 2596mm2.
  • (c) 2701 105mm2.

44
  • 7. A body is observed to move a distance s 10m
    in a time t 4 s. The distance was measured
    using a ruler marked in cm and the time was
    measured using a watch giving readings to 0.1 s
  • a) Express these results "correctly" (that is,
    giving the right number of significant figures
    and the appropriate indeterminacy).
  • b) Use the measurements to calculate the speed
    of the body, including the uncertainty in the
    value of the speed.
  • Distance 10 0.01 m, time 4 0.1s.
  • Since, v 2.5m/s. The uncertainty 0.065m/s.
    Therefore, v 2.5 0.1 m/s.

45
  • 8. A body which is initially at rest, starts to
    move with acceleration a. It moves a distance s
    12.00 0.12m in a time t 4.5 0.1s. Calculate
    the acceleration.
  • 1.2 0.1 m/s

46
  • 9. The diameter of a cylindrical piece of metal
    is measured to a precision of 0.02mm. The
    diameter is measured at five different points
    along the length of the cylinder. The results are
    shown below. Units are mm.
  • (i) 7, (ii) 9.4, (iii) 5.6, (iv) 5 and (v)
    4.8
  • (a) Rewrite the list of results "correctly".
  • (b) Calculate the average value of the diameter.
  • (c) State the average value of the diameter in a
    way which gives an indication of the precision of
    the manufacturing process used to make the
    cylinder.
  • (d) Calculate the average value of the area of
    cross section of the cylinder. State the result
    as area A A(mm2).
  • (a) (i)7.00 0.02, (ii) 9.40 0.02, (iii) 5.60
    0.02, (iv) 5.00 0.02, and (v) 4.80 0.02
  • (b) 6.36 mm.
  • (c) 0.02mm, 6.36 0.02mm.
  • (d) 31.77 0.20mm2.

47
3. Graphs
  • The results of an experiment are often used to
    plot a graph. A graph can be used to verify the
    relation between two variables and, at the same
    time, give an immediate impression of the
    precision of the results. When we plot a graph,
    the independent variable is plotted on the
    horizontal axis. (The independent variable is the
    cause and the dependent variable is the effect.)

48
A. Straight Line Graphs
  • If one variable is directly proportional to
    another variable, then a graph of these two
    variables will be a straight line passing through
    the origin of the axes. So, for example, Ohm's
    Law has been verified if a graph of voltage
    against current (for a metal conductor at
    constant temperature) is a straight line passing
    through (0,0). Similarly, when current flows
    through a given resistor, the power dissipated is
    directly proportional to the current squared. If
    we wanted to verify this fact we could plot a
    graph of power (vertical) against current squared
    (horizontal). This graph should also be a
    straight line passing through (0,0).

49
B. The "Best-Fit" Line
  • The best-fit line is the straight line which
    passes as near to as many of the points as
    possible. By drawing such a line, we are
    attempting to minimize the effects of random
    errors in the measurements. For example, if our
    points look like this ?

50
  • The best-fit line should then be ?
  • Notice that the best-fit line does not
    necessarily pass through any of the points
    plotted.

51
C. To Measure the Slope of a Graph
  • The slope of a graph tells us how a change in one
    variable affects the value of another variable.
    The slope of the graph is defined as an must, of
    course, be stated in the appropriate UNITS.

Slope vertical change / horizontal change
52
  • (x1, y1) and (x2, y2) can be the co-ordinates of
    any two points on the line but for best
    precision, they should be as far apart as
    possible as shown in the two examples below.

53
  • In the second graph, it is clear that y decreases
    as x increases so in this case, the slope is
    negative.

54
D. Error Bars
  • Instead of plotting points on a graph we
    sometimes plot lines representing the uncertainty
    in the measurements. These lines are called error
    bars and if we plot both vertical and horizontal
    bars we have what might be called error
    rectangles, as shown on next slide

55
  • x was measured to 0.5s, y was measured to 0.3m

56
  • The best-fit line could be any line which passes
    through all of the rectangles. Assume that the
    line passes through zero, use the example above
    to estimate the maximum and minimum slopes of
    lines which are consistent with these data. (The
    diagram is too small to expect accurate answers
    but you should find about 1.06ms-1 maximum and
    about 0.92ms-1 minimum.)

57
E. Measuring the slope at a Point on a Curved
Graph
  • Usually we will plot results which we expect to
    give us a straight line. If we plot a graph
    which we expect to give us a smooth curve, we
    might want to find the slope of the curve at a
    given point for example, the slope of a
    displacement against time graph tells us the
    (instantaneous) velocity of the object.

58
  • To find the slope at a given point, draw a
    tangent to the curve at that point and then find
    the slope of the tangent in the usual way. As
    shown, a tangent to the curve has been drawn at x
    4.5s. The slope of the graph at this point is
    given by ?y/?x (approximately) 5ms-1.

59
  • Exercises
  • 1. The diameter of a metal ball is measured to be
    28.0mm 0.2mm. The mass of the ball is measured
    to be 120g 2g. Use these results to find a value
    for the density r, of the metal of which the ball
    is made.
  • Density is defined as mass per unit volume so to
    calculate the density of a substance we use the
    equation 
  • 0.0104 0.0004g/mm3

?m/V
60
  • 2. An investigation was undertaken to determine
    the relationship between the length of a pendulum
    l and the time taken for the pendulum to
    oscillate twenty times. The time it takes to
    complete one swing back and forth is called the
    period T. It can be shown that T 2p v(l /g)
    where g is the acceleration due to gravity. The
    following data was obtained.

61
Length of pendulum 0.05m Time for 20 oscillations 0.2s Period T T2 Absolute error of T2
0.20 17.5
0.42 24.8
0.59 32.0
0.81 35.9
1.02 41.0
62
  • (a) Complete the period column for the
    measurements. Be sure to give the uncertainty and
    the units of T.
  • (b) Calculate the various values for T2 including
    its units.
  • (c) Determine the absolute error of T2 for each
    value.
  • (d) Draw a graph of T2 against l. Make sure that
    you choose an appropriate scale to use as much of
    a piece of graph paper as possible. Label the
    axes, put a heading on the graph, and use error
    bars. Draw the curve of best fit.
  • (e) What is the relationship that exists between
    T2 and l?
  • (f) Are there any outliers?
  • (g) From the graph determine a value of g.

63
  • 3 Suppose the relationship between the semi-major
    axis a and the sidereal period P of a planet in
    the solar system is given by ,
    where k and a are constants. From the table
    below, plot a suitable graph to find k and a.

Planet Mercury Venus Earth Mars Jupiter Saturn Uranus Neptune
Semi-majorAxis a (AU) 0.3871 0.7233 1.0000 1.5237 5.2028 9.5388 19.1914 30.0611
SiderealPeriod P (year) 0.2408 0.6152 1.0000 1.8809 11.862 29.458 84.01 164.79
63
64
4. Writing Experimental Reports
  • You will perform a number of experiments in the
    future. You must keep a record of ALL the
    experiments which you perform. For a few of the
    experiments you will be required to present a
    full, detailed report, which will be graded. The
    grades will form part of your final result
    (remember, a significant percentage of your final
    result will be based on your practical
    abilities). Usually, a report is set out as
    follows.

Title Introduction Diagram Method Results Theory Conclusion
65
1. Title (Aim)
  • The title must state clearly the aim of the
    experiment. It must tell the reader what you are
    trying to prove or measure. For example, Ohms
    Law is not a suitable title for an experiment
    report, whereas, Experiment to verify Ohms Law
    is a suitable title. Similarly, Relative
    Density is not a suitable title but Experiment
    to measure the Relative Density of some common
    substances is a more suitable title.

66
2. Introduction
  • If the experiment is designed to verify a law,
    state the law in the introduction. The
    introduction can also include such ideas as why
    the results/conclusions of the experiment are
    important in every-day life, in industry etc. (It
    might even include a little historical
    background, but not too much). 

67
3. Hypothesis
  • Before starting your investigation you usually
    have some idea of what you expect the results
    will show. The hypothesis is basically a
    statement of what you are expecting. If you are
    trying, for example, to show how two variables
    are related, state the expected relation and try
    to give and explanation of you choice.

68
  • For example, when Newton was thinking about
    gravitation, he assumed that the strength of the
    force of gravity would become weaker as one moved
    further from the body causing the field. He
    suggested that the relation between force and
    distance might involve the inverse of the
    distance squared and to defend this choice he
    pointed out that the surface area of a sphere
    depends on the square of its radius. Various
    observations then confirmed this suggestion.

69
4. Diagram
  • In most cases a labelled diagram is useful. Every
    electrical experiment report must include a
    circuit diagram. If diagrams are drawn by hand,
    use a sharp pencil and a ruler. (If you use a
    computer, learn how to make the best use of your
    drawing program.) 

70
5. Method
  • The method section should give enough detail to
    enable another experimenter to repeat the
    experiment to see if he/she agrees with your
    results/conclusions. The method should include
  • - a description of the apparatus used
  • - what measurements you made (if possible, in
    the order you made them)
  • - what precautions you took to ensure the best
    accuracy possible
  • - a mention of any unexpected difficulties (and
    how you overcame them)

71
6. Results
  • You should record all the measurements made
    during the experiment along with some indication
    of the uncertainty of each measurement. Whenever
    possible, present the results in the form of a
    table. 

72
7. Theory
  • This section should include any information which
    might help the reader to understand how you used
    your measurements to reach the aim mentioned in
    the title. For example, in one experiment,
    designed to measure the relative density of a
    substance, the actual measurements made are two
    distances. The theory section of a report on such
    an experiment must include a clear explanation of
    how these two distances are related to the
    relative density of the substance being
    measured. 

73
8. Conclusion/Evaluation
  • Every experiment report must have a conclusion.
    If your aim was to verify a law, state whether
    you have verified the law or not. If the aim was
    to measure a particular quantity (e.g. relative
    density), give the final measured value of the
    quantity in the conclusion.
  • In the case of an experiment designed to measure
    some well known physical constant you should
    attempt to explain any difference between your
    result and the accepted result.

74
  • For example, if you find g 9.5ms-2, you should
    try to think of the most likely cause of this
    obvious error.
  • If the experiment results were in some way
    unsatisfactory, try to suggest how the
    investigation might be improved in order to
    improve accuracy of measurements or range of data
    obtained. This evaluation section should include
    comments on the apparatus used and the method
    employed.

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5. General Laboratory Rules
  • Do not enter the laboratory unless the laboratory
    superintendent is present.
  • When you come into the laboratory, you should
    walk to your place calmly. If you run you are
    sure to bump into someone - and if he is carrying
    equipment there could be an accident.
  • At your place, take out your writing materials,
    file and text book. Put your bag under the bench
    and put your coat out of the way in a clean area.
    Do not leave anything lying beside your bench
    someone is sure to fall over it.

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  • Wear a white laboratory jacket. This is important
    as the laboratory jacket will stop your clothes
    from getting dirty or burnt.
  • If you have long hair make sure that you have an
    elastic band or a hair clip to tie it back. This
    will help to keep it out of the way which is much
    safer.
  • Wear safety spectacles to protect your eyes when
    you are using chemicals such as acids and when
    you are boiling liquids or heating solids.

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  • On your bench you find a water tap and a sink.
    The laboratory is not as clean as a cafeteria, so
    do not drink from the taps in the laboratory.
    Also do not eat in the laboratory. After you have
    been doing practical work, especially if you have
    been handling animals or chemicals, wash your
    hands carefully.
  • You will also find a gas tap on your bench. This
    is for use with the Bunsen burner. Sometimes you
    will need to heat things and that is what the
    Bunsen burner is used for. Your teacher will show
    you how to use one properly. When you are not
    using a Bunsen burner the gas tap should be
    turned off all the time.

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  • The third thing that you will find on your bench
    is an electricity socket.  If you use the
    electricity on your bench, for example when you
    use a lamp, make sure that the bench is dry.
  • Some practical investigations are wet, so drops
    of water can spread all over the bench and your
    papers. It is a good idea to remove everything
    that you do not need from your bench during
    practical work. You will only need a pencil or a
    pen to write with, a piece of paper for your
    results and the instructions. The instructions
    can be kept safe in a plastic folder.

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  • When you do a practical investigation you will
    need to collect equipment and materials. Never
    carry too much equipment each time.
  • When you have finished a practical investigation
    always leave your bench clean and dry. You can
    rinse and clean your test tubes in the sink but
    do not put solid objects down the sink, they will
    block it.
  • When you leave the laboratory take all your
    belongings with you and make sure that everything
    is turned off (gas tap, water tap)
  • If you should have an accident always tell the
    laboratory superintendent.

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  • Exercises
  • Filling in the missing words.
  • 1. Put all coats in a ...........................
    .........
  • 2. Your bags should be put under
    .........................
  • 3. Never .................................... or
    shout in a laboratory. 
  • 4. Do not use the services (gas, water or
    ....................................) unless you
    are told to.

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  • 5. Never .................................... or
    drink in a laboratory 
  • 6. ..................................  long hair
    during practical work.
  • 7. Protect your eyes with  ......................
    .............. when you boil liquids
  • 8. Put all solid waste in the 
    ................................. not in the
    .................................

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  • 9. Put broken glass in the ......................
    ..............
  • 10. Report all ..................................
    .. immediately to the laboratory superintendent.
  • 11. Wash your hands after handling ..............
    ........ and .................................
  • clean, out of the way area, the bench, run,
    electricity, eat, tie back, safety spectacles,
    plastic waste bin, sink, metal waste bin,
    accidents, chemicals, animals.
  • End

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Supplementary Notes
  • Indices and Logarithm
  • Scientists investigate the dependence of two or
    more physical or chemical or biological
    quantities. For example, the relationship between
    a current I flowing through a light bulb with
    resistance R and the potential difference V
    across the light bulb is simply VIR. However,
    physical situations are usually not simple,
    mathematical tools, like indices and logarithms,
    are required.

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(a) am?an amn
(b) am/an am-n
(c) (am)n amn
(d) am ?bm (ab)m
(e) (a/b)m am/bm
(f) a0 1, where a ? 0
(g) a-m 1/ am, where a ? 0
(h) v(a2) a
  • Laws for Indices
  • If a, b are real numbers and m, n are positive
    integers, we have the following laws

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(a) loga 1 0
(b) loga a 1
(c) loga (MN) loga M loga N
(d) loga(M/N) loga M - loga N
(e) loga Mp p loga M
(f) loga N logb N/ logb a, where a ? 0 , N gt 0
  • Properties of Logarithm
  • Definition If ax N , then x loga N.

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  • In physics, engineering and economics, the
    natural logarithms are most often used. Natural
    logarithms use the base e 2.71828, so that
    given a number ex , its natural logarithm is x .
    For example, e3.6888 is approximately equal to
    40, so that the natural logarithm of 40 is about
    3.6888. The usual notation for the natural
    logarithm of x is ln(x) and for logarithms to the
    base 10 is log(x).

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  • Example 1.1
  • It is known that Y kXn . From the graph given,
    find k and n.
  • n -3/7 and k 1000

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  • Example 1.2
  • Solve
  • ln(x2 3x 2) 2 ln(2x - 1) ½ ln(4)
  • x 5/7
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