A simple Pendulum.

PREDICTION

I predict that the longer the length of string the longer it will take the pendulum to complete one period. This is because the length of the arc, the pendulum is travelling along is greater (x = 2?L = circumference) but the gravitational acceleration will remain the same. This prediction is also proved by the formula

Here if the length of the string is increased (L) then that side of the equation becomes larger because the size of the fraction is increasing and because one side of the equation is increasing so must the other to remain equal so T will also increase.

SAFETY

There are many accidents that could happen if this experiment was not carried out safely; below I have outlined a few simple guidelines to prevent such accidents occurring.

Danger

Risk

Precaution

Bob swinging

Could hit someone

Do not swing the bob from large angles.

Heavy mass

Could fall off table and hit someone

Make sure the mass isn't on the edge of the table and is away securely held.

Clamp stand

Could fall over and hit someone

Make sure a large mass is holding it down

FAIR TESTING

To make sure our results are accurate we need to keep everything but the variable constant. Below are some simple guidelines to ensure that our testing is fair.

Procedure/Object

Problem

Solution

Clamp Stand

Could rock

Place a heavy mass on the base to prevent this.

Mass of the bob (see note below)

If we use different bobs there mass could be different

Make sure we use the same bob

Angle

Angle could be different

Make sure we measure the angle accurately

Gravity

If we move to another area of the world, the effects of gravity will be slightly different

Stay in the same area of the earth as much as possible.

Human error

Human error between releasing the bob and starting the stopwatch.

Make sure the same person does each task every time, use a standard pre-release method, i.e. 3,2,1, go. We should also let the pendulum swing for ten periods and then divide by 10 to reduce the effect of human error.

Note: Although during my research I ascertained that the mass of the bob does not effect the period of the pendulum, I should still keep this constant, as I should only have one variable in my experiment.

METHOD

APPARATUS

For our experiment we needed:

* A length of String at 60 cm long

* A bob

* A boss, clamp, and stand

* A heavy mass

* A large protractor

* A Stopwatch

* A meter ruler

* A cork split in two

Firstly we set up the equipment as shown below:

. We measured the string to 10 cm. from the bottom of the corks to the middle of the mass.

2. We then pulled the string back to 40?:

3. We then released the bob and started the stopwatch at the same time.

4. We let the bob swing backwards and forwards 10 times

5. We then stopped the pendulum swinging and recorded the times.

6. We repeated the experiment with the same length 3 times

7. We then repeated steps 1-6 for string lengths 10cm, 15cm, 20cm 25cm, 30cm, 35cm, 40cm, 45cm, 50cm and 55cm.

RESULTS

Length of string

Attempt 1 (sec)

Attempt 2 (sec)

Attempt 3 (sec)

Average for 10 oscillations (sec)

Average for 1 oscillation (sec)

0

7.06

7.31

7.20

7.19

0.719

5

8.5

8.52

8.65

8.56

0.856

20

9.76

9.59

9.67

9.67

0.967

25

0.80

0.62

0.86

0.76

.076

30

1.48

1.42

1.39

1.43

.143

35

2.45

2.48

2.32

2.42

.242

40

2.72

2.89

2.77

2.79

.279

45

3.95

4.03

3.81

3.93

.393

50

4.42

4.65

4.56

4.54

.454

55

5.84

5.85

5.44

5.71

.571

ANALASIS

By looking at my results, I can immediately tell that the longer the length of string the longer it takes the pendulum to complete one period. This increase in time is always between 30 second and 90 seconds. I have drawn a graph, which shows the period for each oscillation. My line of best fit shows that the time taken increases in a linear fashion and does not go through the point of origin. This shows me that the period does increase relative to the length of string, this supports my prediction that because of the length of the arc increasing with the length of the string that the period would increase.

EVALUATION

I believe that my experiment went reasonably well, the results we collected would seem to be very good and we had no accidents. I also believe that the method we used to obtain these results was an accurate one, but it could have been improved with the use of light gates and a computer because this would have removed the element of human error. I would like to take this investigation further by continuing to increase the lengths of the string until about one-meter. I would also like to try this experiment with different angles to see what effect that has on the results and then compare the results to these ones. The evidence I have here is only just enough to support a firm conclusion, but does show a trend appearing.

Kenny Larsen Page 1 01/05/2007