Using the angle from which the pendulum is dropped as a variable would affect the height and therefore the gravitational energy as demonstrated above. However, the ideal angle to get the best results is 10°. This is because above this value x (as illustrated by the diagram below, is much greater than value d. We can’t measure the value of x, but we can easily find out the value of d using trigonometry. Because the actual distance travelled is x not d, d needs to as close to x as possible, therefore the angle has to be around 10°.
Acceleration due to Gravity:
If we refer back to the equation to find out the gravitational potential energy of the pendulum, another variable is acceleration due to gravity.
We can see that varying the acceleration due to gravity will affect the gravitational potential energy of the pendulum. We already know acceleration due to gravity to be 9.8m/s2, and we will need this figure later on in the experiment. However, it is quite hard to vary gravity, without the aid a spaceship so we can’t investigate this as a variable.
Air resistance:
If there was no other force acting on it, the pendulum would keep swinging until it hit something. However, it slows down quite quickly so we know that there must be another force acting on it. This force is friction caused by air resistance. If we could vary the amount of air resistance acting on the pendulum then we would vary its speed. However, without a vacuum, it is impossible to vary the air resistance and so we can’t use this as a variable. It will also remain the same and therefore act on our results evenly so we do not need to worry about it affecting our results.
Weight of the Pendulum:
If we look once more at the gravitational potential energy equation, there is one more variable that we have not looked at: Mass.
If we vary the mass, it will affect the gravitational potential energy as shown in the above equation. With more energy, the pendulum will swing faster, and therefore the time period will be shorter. However, it will be very difficult to change the mass of a pendulum several times.
Variable I will be changing:
The variable I will be changing will be the length of the string. I will be doing this because it is the easiest variable to change and has a clear relationship with the time period of the pendulum.
Equipment/Diagram.
Hypothesis
I think that as the string gets longer, the time period of the pendulum will increase.
This will occur because the string is like the radius of the circle and so changing the length of string will change the circumference of the circle according to the relationship C=2πr, so the longer the piece of string; the bigger the circle, and the bigger the distance that the pendulum will travel. Since 2 and π are constants, the only thing that will affect the circumference (arc length) is r, i.e. the length of the string.
I will then use the following formula to gain predicted results for my experiment:
T = 2π (l/g)
T =Time period of the pendulum
l = length
g = Acceleration due to gravity (9.81m/s2)
In this formula, 2, π and g are all constants. Acceleration due to gravity is the same for any weight at 9.8m/s2. This shows that length must be my variable.
Using the above formula, I have produced a table of predicted results.
If I plot these points onto a graph, I would expect it to be a straight line as T is proportional to l, as l is the only factor in my experiment that is variable.
As you can see, this line is not straight, I must now refer back to my formula to obtain a straight line. If we ignore all of the constants, we can see that T is proportional to l, and therefore a graph portraying T2/l should give us a straight line:
This is a straight line, which proves that Tsq. Is proportional to l.
Method:
- Set up equipment as shown in diagram
- Pull the string through the pieces of wood until there are 10 cm of string between the wood and the pendulum
- Pull the pendulum out so that the string is at 10°.
- Let the pendulum go and let it swing
- Once the pendulum gets to the top of its swing, in either position A, or position C, start the stopwatch.
- Count each time the pendulum returns to that position.
- Once you get to 10, stop the stopwatch
- Repeat steps 3-7 3 times.
- Keep changing the length of the string in 10 cm steps and repeat steps 3-8 until you get to 1 meter.
Fair test:
To make this experiment a fair test we need to keep all of the fixed variables fixed, and to carefully control how we vary the length of the string. This means measuring as accurately as possible for all lengths and angles; making sure that there is no wind affecting the swing of the pendulum; and making sure that we drop rather than throw the pendulum. In addition we will measure the reaction times of each person in our small groups and use the person with the quickest. We do not have to worry about delayed reactions too much though as they will be nearly the same throughout the experiment and therefore will cancel each other out.
Safety:
This experiment has very few hazards. The only way to make this experiment dangerous would be for pupils to abuse the equipment by swinging the pendulums or heavy clamp stands around. Obviously we took care not do this.
Results:
The following table shows the results that I obtained from my experiment.
Using the above table I will produce a table of the average time period.
I will now calculate the percentage error from my predicted results to my actual results.
I can check the accuracy of my experiment again by plotting a graph of Tsq. against length and calculate the gradient.
The gradient = change in y / change in x
The gradient = 4
Tsq./l=4
If I rearrange the formula, I can see that:
Tsq/l=4πsq./g
4πsq./4=g
4πsq./4=9.87. This is an error margin of 0.6%, this shows that my experiment was quite accurate
Conclusion:
From this experiment I was able to prove that Tsq. Is proportional to l: i.e. when Tsq. Doubles, so does l. From this I can conclude that l, is the key factor which directly affects T.
Evaluation:
The experiment was quite accurate as it produced an error margin of only 0.6%. However, comparing predicted results to my results I found a 13% error margin in some cases. This was when the pendulum was at its shortest length and therefore had its shortest difference to travel, which meant that the time periods were very quick, and therefore harder to calculate. This may have led to my inaccuracies.
