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# Scientific Investigations by tambe87

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```									LESSON 4 - SCIENTIFIC                                         Hypothesis
INVESTIGATIONS                                                A general statement about the relationship
between a manipulated variable and a
When physicists observe a particular physical                responding variable.
phenomenon they will as questions as to how
or why it happens . A hypothesis will be put                 The hypothesis should be written as :
forth and experiments or scientific                          The greater the………, the greater the…….
investigations will be carried out to prove or               Or
disprove the hypothesis. If the experiments                  The bigger the…………., the smaller the…..
bear out the hypothesis, the hypothesis may
come to regarded as theory or law of nature. If        Manipulated variable
the don’t the hypothesis will be rejected or
modified.                                              The quantity whose values we deliberately choose
In any experiment , the report on the                  to change or a primary variable which causes other
experiment will be based on these guidelines           secondary variable to change.
and follows a sequence as shown in the
following flow chart:                                  Responding variable

The quantity whose value depend on the
manipulated variable or a secondry variable
which changes in response to the change in the
manipulated variable.

Fixed variable

The quantity whose value is kept constant
throughout the experiment.

Aim

A statement to show the investigation of the
variables involve.

The aim of the experiment should be written as:
To investigate the relationship between
………..and ………………

Apparatus
Inference
List the apparatus and materials used so that at
Early assessment that is carried out to answer         least a set of data for manipulated and responding
the questions raised.                                  variables can be determined.

The inference should be written as :                   State the arrangement of the apparatus that can
…………………depend on…………………….                              function by drawing a labeling diagram .
Or
The ……………..changes as the                              Procedure
…………...changes
State the method of controlling the manipulated
variables
State the method of measuring the responding
variables
Repeat the experiments at least four times.

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Tabulating the data                                        If the data too small or too big use the standard
form number.
Record the data in the following table
For example
Manipulated variable         Responding variable            Temperature  /oC     10     20     30    40       50
Density,  / kgm-3    9.7    8.5    7.3   6.6      5.1
x 104

How to plot the graph ?

The title of the graph must be shown.
The axes of the graph must be labelled with the
Analysing the data                                         unit used.
For example:
Plot a graph of ( Responding variable) against
(Manupulated variable)

How to tabulate the data ?

The table muast be neatly drawn and the data
arranged in either and rows.
The names and symbols of the manipulated and               The scale choosen must be easy to use.
responding variables must be written together with         Scales such 1:1 , 1:2 , 1:5 ,1:10 ,1:100 are
the units.                                                 preffered in plotting a graph.
For example,                                               Odd scales such as 1:3 , 1:4 , 1: 6 , 1:7 , 1: 30
should be avoided in plotting a graph.
Velocity,v / s
Time , t / s                                       Make sure the area covered by the plotted points
must not be less than 50% of the area of the graph
Volume , V / m3        Pressure , P / Pa        paper.

For example:

The data shown in the table must be consistent in
the number of decimal places in accordance with
the respective measuring instruments.                      The scale on the axes must be uniform and clearly
For example,                                               marked with value.
Length, l / cm     Time , t /s                For example:
0                12.8
2                25.6
4                39.4
6                52.2
8                75.0

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All the points are marked with a symbol such as a            y is directly proportional to x.
cross or circle and the centre of the cross must             or y  x
accurately positioned.                                             or y = kx k = constant
or y = mx m = gradient
or y1 = y2
The best straight line or the best curve graph must                       x1       x2
be drawn.
The best straight line or the best curve graph is the
line that passes through most of the points plotted
such that it is balanced by the number of points
above and below the line.The line also must be
smooth.
y increases linearly with x
or y = mx + c
c = intercept on axis-y

y decreases linearly with x
or y = -mx + c
It is not advisable to plot graph by joining point to              m = gradient
point because the graph obtained is not smooth.                    c = intercept on axis-y

y is inversely proportional to x
atau y  1
x
atau y = k
x
k = constant

atau y1 x1 = y2 x2
How to analyse the data ?

(a) Determine the relationship between two
variables.
Example :

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(b) Determine the gradient of the graph
Example

Draw a suffiecienly large triangle to calculate
State value of the gradient with correct unit.
The gradient of the graph is

m = y2 - y1
x2 - x1
= QR
QR

(c)   Determine the certain values from the graph.

Certain important values can be obtained from
the graph plotted by drawing a horizontal line
or by extrapolating the graph.

(d) State the precautions should be taken
For example:
The circuit connentions must be taken
Off the switch when taking the raeding of the
meters.
Make sure the amplitude of oscillation is small.

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TUTORIAL 4                                                4   Which of the following graphs show that y
increases linearly with x?

1   Which of the following is the best way to
tabulate the data ?

A Voltage,V      0        5       10     15      20
Current,I      0        1.7     2.5    3.4     4.2

B Time,t /s      2        4       6      8       10
Density, /    2000     5000    8000   11000   14000
kgm-3                                                       5   Hooke’s law states that applied force F is
directly proportional to the extension x of
C Period,T       10.5     15.3    19.8   27.9    36.0             spring if its elastic limit is not exceeded. Which
/s                                                              of the following graphs shows the Hooke’s
Distance,d     2.5      3.3     4.6    5.8     6.9              Law?
/m

D Object         5.1      8.7     11.6   16.5    18.6
distance
,u / cm
Image          2.3      5       6.9    9       11.6
distance,
v / cm

2   Which of the following scales is the most
suitable to plot a graph?                                 6   The acceleration,a of an object is inversely
proportional to the mass,m of the object
A     1 cm : 3 unit       B    1 cm : 5 unit                  under constant force.
C     1 cm : 6 unit       D    1 cm : 8.8 unit                Which of the following graphs describes the
relationship between a and m .

3   Which of the following is the best graph ?

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7    An experiment is carried out to find the                12   The resistance R and temperature T for an
relationship between mass and acceleration of                electric conductor is given as R = r + aT with
a trolley on a wooden runway.                                r as the resistance at 0oC dan a as a
The experiment is repeated by adding the                     constant.
number of trolleys.                                          A graph of R against T is shown .
The responding variable in this experiment is

A    the length of the wooden runway.
B    acceleration
C    mass
What is the resistance ,R of the conductor at a
8    In a simple pendulum experiment, the length
temperature 60oC ?
of the pendulum and time for 20 oscillations
are recorded.
A     35                    B     47
The length of the pendulum is a
C     86                    D     93
E    180
A    manipulated variable
B    responding variable
15   The pressure ,P of the gas is directly
C    fixed variable
proportional to the absolute temperature, T of
the gas.
When P = 100 ,T = 50. What is the value of P
when T = 400.

A    0.8A                   B    125
C     200                   D     800
9    Based on the graph above, what is the
E     2000
16   A student carries out an experiment to find
A     - 1.5           B     - 0.7
out the relationship between the change in
C     0.7             D     1.0
length , y , of a spring and mass, m , of the
E    1.5
load on the spring. The arrangement of the
apparatus for the experiment is shown in
Figure 1 . The length of the spring when a
load is placed on the piston is l .

10   What is the unit of the gradient of the graph
above?

A     m                     B       m2 s
C     ms2                   D       ms- 2

11   A student plot a graph for a physical quantity ,
Q on axis-y against a physical quantity ,R on
axis –x
The relationship between Q and R is given by
as Q - aR = b , where a and b are constants.
The gradient of vthe graph is

A     a                     B       R
b                             Q
C     b                     D       a

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At the beginning of the experiment there is no           Figure 6 and Figure 7.
load. The length of the spring is lo . The actual
length of lo is shown in Figure 2.
The experiment is repeated by using load with
mass , m , equal to 0.5 kg , 1.0 kg , 1.5 kg ,
2.0 kg and 2.5 kg. The actual lengths of the
spring when the different masses are used are
shown in Figure 3, Figure 4 , Figure 5 ,

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27
(a) Based on the aim and the procedure of
the experiment state the:
(i)   manipulated variable

________________________________

(ii)    responding variable

_________________________________

(iii)   constant variable

________________________________                   (c) On the graph paper , plot a graph of y
against m.
(b) Measure the length of the spring in
Figure 2.                                           (d) Based on your graph, state the
lo = ___________________                          relationship between y and m .

Measure the lengths l of the spring in                 _________________________________
Figure 3 , Figure 4 , Figure 5 , Figure 6
and Figure 7 when different load are                   _________________________________
used.

In each case, calculate the change in
length, y , of the spring where;
y = ( lo – l )

Tabulate your results for m ,l and y in the
space below.

28
29
Graph T2 against l
T2 / s2

5

4

3

2

1

l / cm

0   20   40           60           80   100

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17         A student carries out an experiment to
investigate the relationship between the
length of a simple oscillating pendulum ,l ,
with its period, T.
The experiment is repeated using different
lengths,l, and their corresponding periods, T,
are recorded. A graph of T2 against l , is
then plotted as shown above.
(a) Based on the graph,
(i) State the relationship between T2
with l.

…………………………………………..

…………………………………………..
(ii) Calculate period,T, when the length
l = 45 cm.
(Show your working)                                 18    The graph above represents graph W
against V , where W and V are the distances
on a wooden rod.

(a)     Based on the graph state the:

(i)      manipulated variable

________________________________
(iii) Calculate the gradient of the graph.
(ii)     responding variable

_________________________________

(b) Calculate the gradient of the graph.
(b)      Using the value of the gradient obtained
from (a)(iii) and the equation,
l
T 2  4 2
g
calculate the acceleration due to
gravity , g.                                             (c)    Determine the intercept on
(i) axis- W

....................................................

(ii)          axis-V

.....................................................
(c)     State one precaution for this experiment.
(d) State the equation of the line
………………………………………………
...............................................................
………………………………………………

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