Pendulum Investigation

Pendulum Investigation

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Pendulum Investigation

Plan

Aim

To investigate how the length of a simple pendulum will affect the
time for a full swing.

Variables

Length

The length of the pendulum has a large effect on the time for a
complete swing. As the pendulum gets longer the time increases. As the
pendulum gets shorter the time decreases.

Air resistance

A big and light pendulum bobble would be affected by a major amount of
air resistance. This might cause the pendulum to move in a different
way.

With a little pendulum bobble there is very small air resistance. This
can easily be observed because it takes an extended time for the
pendulum to stop swinging, so only a small amount of energy is lost on
each swing.

Gravity

The pendulum is motivated by the force of gravity acting on it.

The more gravity the shorter time it will take for a complete swing.

The less gravity the longer it would take for a complete swing

Size of swing

The size of the swing does not have large effect on the time.

Mass

The mass of the pendulum does not affect the time at all.

Prediction
The diagram shows the arcs through which two pendulums swing. The red
one is twice the length of the black one. The black arc is always at a
steeper angle than the red arc, and always above it.

The black pendulum has the most gravitational potential energy at the
top of the swing because it is higher. This means the kinetic energy
and speed through the centre will also be greater.

The steeper the arc the greater the acceleration of the pendulum will
be. A greater acceleration means a shorter time for each swing. The
blue arc has the steepest gradient at the top and is flat when it
reaches the middle. The acceleration of the bobble will decrease from
a maximum at the top of the swing to zero at the centre.

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For these reasons, I predict as the string gets longer the time per
swing will get longer.
Equipment List
string, blue-tack, long pin, stopwatch, measuring tape, electronic
scale

Risks and precautions

There are no risks or precautions involved in this experiment

Method

[IMAGE]

The string is secured between two small blocks of wood. This ensures
that the cotton swings from a single fixed point. A small ball of
blue-tack is attached to the bottom end of the cotton and the length
is adjusted by pulling the cotton through the two blocks. Gravity may
be considered to act through the centre of gravity of the bobble. For
this reason the length of the cotton is measured from the wooden
blocks to the centre of the bobble.

Timings for twenty complete swings are started and stopped as the
pendulum passes through the mid-point. A long pin is set up at the
mid-point, at right angles to the plane of swing, to provide an
accurate reference point. This is achieved by positioning yourself so
that you are looking directly along the line of the pin. As the cotton
passes the point the stopwatch is started and counting is started at
"0". The pendulum will swing to one side, and then back through the
centre and to the other side. When it passes the centre again "1" is
counted for the first complete swing. In the same manner this process
is repeated twenty complete swings.

Each process is repeated three times. It is important to ensure that
the pendulum is swinging in a single plane before measurements are
started. The size of swing must be kept small and accurate.

Variable table

Dependent Variable

value

how measured

Time for one complete swing
(Period)

Time for 20 swings.
3 repeats for each length

digital stopwatch

Independent Variable

length

5,10,20- 180cm in 20cm steps

ruler

Control Variables

size of swing

small (10° or less)

protractor

mass

10g

electronic balance

air resistance

very small

n/a

gravity

10 N/kg

Trial data

1. Altering the length
the length was altered by a measurement of 20 cm. The time increased
as the length increased but by a factor of 1.4 approximately.

length
(cm)

mass
(g)

displacement
(cm)

time (20 swings)
(seconds)

20

10

10

18.10

40

10

10

25.41

2. Altering the mass of the bob

The mass was altered by a measurement of 20 grams. This had a small
effect on the time.

length
(cm)

mass
(g)

displacement
(cm)

time (20 swings)
(seconds)

60

5

10

31.02

60

25

10

31.16

3. Altering the displacement of swing
the size of the swing was changed by a measurement of 20 cm and this
had little effect on the time.

length
(cm)

mass
(g)

displacement
(cm)

time (20 swings)
(seconds)

60

10

10

31.05

60

10

20

31.39

From the trial data I found the only variable that made a major
difference was the length of the pendulum.


Results
-------

Pendulum

length
(cm)

length
(√cm)

Number
of swings

Timings

1st 2nd 3rd

Average time

average time
1 swing
(sec)

5

2.24

20

9.10

8.77

9.36

9.07

0.45

10

3.16

20

12.86

12.79

12.82

12.82

0.64

20

4.47

20

18.15

18.13

18.20

18.16

0.91

40

6.32

20

25.60

25.32

25.87

25.29

1.26

60

7.75

20

31.17

31.21

31.12

31.16

1.58

80

8.94

20

35.90

35.88

35.95

35.91

1.79

100

10.00

20

40.12

40.15

40.07

40.11

2.00

120

10.95

20

43.82

43.90

43.86

43.86

2.19

140

11.83

20

47.92

47.97

47.98

47.95

2.39

160

12.65

20

50.15

50.10

50.10

50.11

2.50

180

13.41

20

53.39

50.44

50.45

52.42

2.62

Control variables
mass of bobble = 10g
size of each swing kept small and accurate (max displacement
approximately 10cm.

Analysis and Conclusions

Graph1 shows that the time for each swing increases as the length
increases and the gradient of the graph decreases as the length
increases.

Graph2 shows each swing plotted against the square-root of the length.
This gives a straight line graph through the origin.

Using the equation: Y=mx (used for straight line graphs through the
origin) the gradient ‘X’ measured

The gradient 'm' measured = 2.5÷13.5 = 0.19

If ‘T’ is the time for one swing in seconds, and ‘L’ is the length in
centimeters, the equation for the line is written as:

T = 0.19√L

Conclusions

The time for one complete swing is proportional to the square root of
the length. All the points for Graph2 lie on a straight line so the
conclusion is very reliable over this range.

It seems likely that the same trend would continue if the length was
extended. Shorter lengths look like they would also follow the same
pattern despite the fact that it gets more difficult to take the
measurements as the time gets shorter. For very short lengths the
trend might not continue and would be extremely difficult to measure.

Evaluation

Measuring the length
A difficult part of measuring the length is make your mind up where
the centre of the bobble is. The uncertainty in determining this
measurement is probably about 1-2 mm. . The total error in measuring
the longest and shortest length is not likely to be more than a
millimeter.

Adjusting the length of the pendulum was time consuming but was not a
problem in the path of accuracy. The string could be accurately pulled
through the wooden blocks to the required lengths.

Measuring the time

The stopwatch I used, measures to one hundredth of a second even
though the overall accuracy of the time measurements are so accurate.
The human reaction time to start and stop the watch roughly cancel
each other out as the same event is being observed, and reacted to in
the same way, each time. Errors are produced by any variability in the
reaction time of the individual which could be affected by various
things.

The even trend in the graph specifies that the results are accurate
and dependable. There are no irregular results to be seen in the trend
of the graph.

Reliability

No significant problems or difficulties were met when performing this
investigation. The accuracy and reliability of the results and
conclusions are incredibly good. From the accuracy method applied and
for the range of values tested, it is quite understandable that the
time for a simple pendulum takes for a complete swing is proportional
to the square-root of the length.


Improvements

The procedure used was simple and straightforward and no difficulties
were encountered. A small improvement could be made regarding the
measuring of the length pendulum. A piece of wood, could be placed
level with the point of suspension, and a set square could be placed
along the flat side and just touching the bottom of the pendulum. This
distance could then be measured extra accurately than trying to guess
where the middle of the bobble is.

More attempts could be taken but I do not think it is necessary or
would make a significant difference to the morals of the conclusion.

Longer lengths could be tried, up to whatever lengths desired. If the
pendulum gets very long a stronger string will be needed and a bobble
in ratio.

Extending the investigation

Extending the investigation would mean extend the range of lengths
tested and observing if the same trend continues. Add more to the
extension
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