We must make sure that when we time the period that we do so by marking the swings from the centre of its swing, and that one period is equal to the pendulum bob having passed the central point twice as demonstrated in the diagram below.
We think this a good way of obtaining results because it is accurate as we have looked at all the possible problems such as making sure the constants stay the same every time and making sure that our stand holding the pendulum is secured to the table.
Equipment
- Stand
- String (required amount)
- 5 x 100g weights
- Protractor
- Clamp
- 2 x metal rods
- Stop watch
- Pen and Paper (to record results)
The brief set out by my teacher put me on track to establish a plan.
Prediction
I predict that the length of string will affect the period of time taken for 10 swings because:
Speed, s = Distance, d
Time, t
This shows that the length of string should affect the period of time because the longer the string the bigger the distance the weight has to travel and so it should therefore take longer for it to swing 10 times. As a pendulum with a length of 5cm has a lot less distance to travel than a pendulum with a length of 25cm
Changing the angle should also affect the period of time taken for 10 swings because the bigger the angle it is released from the larger the distance it has to go. E.g. if it is a small angle (1° - 5°) the speed will be a lot faster and therefore take less time to complete 10 swings
The change of weight should also affect it because
Force, F (Newton’s) = mass, m (g/kg) x gravity, g
Which shows that an increase of mass will result in an increase of force, as the force of gravity is stronger. The force of gravity is constant close to the earth’s surface.
Evidence
Changing mass – length of string 30cm, angle 45°
Changing angle – length of string 30cm, mass 500g
Changing length of string – mass 500g, angle 45°
Analysis of Evidence
To make my results a lot more accurate we have recorded the time taken for 10 swings and divided this time by 10, to obtain a more accurate result for the period for one swing. This gave a much more precise reading, giving us better results.
From the results and the graphs produced from the results, we found that the weight and angle did not affect the period of the pendulum; this was made clear by the best-fit line equalling a constant value on the y-axis (period). My prediction for these variables was incorrect as shown by my results.
However the results of the period against length of pendulum, produced results were as we predicted in my plan. We predicted that the length of string would affect the period; the results clearly showed that as the length of string was increased the time period also increased with it. This shows that the length of string is proportional to the period. I plotted my results onto both a graph and a table to show any patterns and trends; from the graph we only saw one trend, which was as the length of string went up the period time also went up.
We researched this result further in the Nelson Advanced Science: Waves and Our Universe, and found that T was directly proportional to the square root of the length with the constant proportionality as 2π divided by the square root of g (acceleration due to gravity)
T = 2π √ (ℓ / g)
I then decided to add another column to my table of results and plot a graph of T against √ ℓ to prove that it was a straight line through the origin with the gradient equal to 2π / √ g; my results complying with the relationship given above.
Evaluation of Evidence
More swings
Timed more accurately e.g. light gate multiplying result by 2 to give the period
The evidence obtained from my experiment, supported part of my prediction as two of my predictions were incorrect which I could improve by looking further into explanations and equations. The prediction that it did support was that when the length of string is increased then the period is also increased. This is also shown in the graph T = 2π √ ℓ / g, which displays a straight line through the origin with a positive gradient. This discovered that T is directly proportionate to ℓ, as long as all other values remain constant. Thos led me to believe that my method was sufficient for the experiment.
Factors, which may have affected the accuracy of my results, include:
- Error in measurement of angle. This proved difficult to measure as the protractor attached to the clamp was not fixed in place correctly and may have give inaccurate results
- Error in measurement of string. To improve the accuracy of this I could have off the points off the points with a pen to make sure they were as accurately measured as possible.
- Human reaction time. Depending on human reaction time, the measurement of the period time could have been measured inaccurately, when setting the stopwatch.
- Recording of more swings. I could have recorded more swings of the pendulum as it would have been much more accurate and give more results
This procedure is relatively reliable, not including human error, and so I can strongly conclude from these results that, the only factor, which affects the period of a simple pendulum, is its length. As the length increases, so does the period.
