# Pendulum Investigation

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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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### Related Searches

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 (10Â° 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

(âˆšcm)

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 Â‘XÂ’ measured

The gradient 'm' measured = 2.5Ã·13.5 = 0.19

If Â‘TÂ’ is the time for one swing in seconds, and Â‘LÂ’ is the length in

centimeters, the equation for the line is written as:

T = 0.19âˆšL

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