How this will be a fair test:
Because every time we do the experiment, we will only change one variable at a time and keep everything else the same i.e. the angle at 90 degrees from the floor, the weight ball of weight of 40g etc…The only variable we will change is the length of the string.
Safety Precautions:
We will always keep to strict safety precautions by which we will stand back from the pendulum as it swings so it doesn’t hit us. We will tie our hair back so not to get caught in the pendulum and wear safety goggles to protect our eyes.
Background Research
Pendulum clocks have been used to keep time since 1656, and they have not changed dramatically since then. Pendulum clocks were the first clocks made to have any sort of accuracy.
A pendulum clock is made from these parts:
- There is the face of the clock, with its hour and minute hand (and sometimes even a "moon phase" dial).
- There are one or more weights (or, if the clock is more modern, a keyhole used to wind a spring inside the clock -- we will stick with weight-driven clocks in this article).
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And, of course, there is the pendulum itself.
The Weight:
The weight is used so that the pendulum can run for a longer amount of time, without having to be tampered with. It acts as an energy storage device so you can leave it unattended. If you pull on the string or cord that attaches the weight upwards, you automatically give the weight potential energy. It then uses this potential energy in a moment, as the weight falls to drive the clock's mechanism. However the weight of the weight does not effect the period of the pendulum.
The pendulum consists of either a light rod or piece of string. St the end o this rod o string there is a weight attached. We know that, so long the angle of the piece of string is less than 20 degrees, the period will remain constant however, it is still not a precise measurement even then. When you have it over the angle of 20 degrees, the pendulum has to go further but at a greater velocity due to the fact that it falls from a greater height, meaning it is at a more acute angle than normal. Overall, this means that the pendulum traverses a longer distance in a shorter amount of time.
The pendulum demonstrates an almost continuous perpetual motion, until it finally sops, dues to friction. The pendulum has a falling motion. The pendulum keeps a very regular beat, which is why for many years it was used in clocks.
The period of a pendulum can be affected or not affected by three variables:
- The weight of the pendulum.
- The length of the pendulum.
- The angle of which the pendulum departs.
These are the main factors which people commonly presume to have an effect on the period of the pendulum; however, the weight of the pendulum has little or no effect at all, neither does the angle of which the pendulum departs. On the other hand, length of the pendulum is correct, due to the fact it has to traverse a further distance. The pendulum period is related only to the length of the pendulum and the force of gravity. However due to the fact that gravity remains constant at any particular point anywhere in the planet, this means the length of the pendulum is the only thing that effects the period of a pendulum.
Preliminary Trial
These results aren’t very accurate and don’t really follow a certain pattern. Also, I don’t think they cover a big enough range so we don’t really get a chance to see how length effects the pendulum later on when the string is longer. Therefore, We are going to change the difference between each length from 5cm –10cm.
This is the new Method:
1) Firstly, we have to determine, how many lengths we ant to compare, and also (in cm) how long each piece of string is.
We have decided to go up in tens i.e. 5, 15, 25 etc…
2) Then we have to draw up a table o record all f our results.
3) Next we have to collect all our apparatus.
4) Firstly, we will measure a piece of string to the length required, plus a bit for excess to tie around the weight ball etc…
5) We then will set up our clamp and attach the string to the clamp attachment and in turn, attach the weight ball to the string.
6) After all is set up, we will need to wind up the string around the clamp to the lowest measurement ready to begin the experiment. (we will measure it with a ruler)
7) We will then pull back the string ready to begin at about 90d degrees ready to time the period. This will be our preliminary experiment.
8) Whilst one person holds he string and lets go, another person times it in seconds (using a stop watch) how long it takes for the string to swing once, forward and back ant then stop the watch at the time it reaches the end of the period.
9) We will then record the first result in the table.
10) Because this is the preliminary experiment, we will only trial each measurement once.
11) We will then continue this over and over until we’ve done it once for every measurement.
12) Next we will completely redo the whole experiment, starting at 5cm up to about 95cm at about 90 degrees.
13) Finally we will find out the averages for each length and record the results on to a graph.
Obtaining
The Table of results for altering the lengths of a pendulum and the effect it has on the period
Evaluation
My overall prediction is correct; the longer the piece of string, the longer it will take the pendulum to complete one period, however on average, it doesn’t increase by 0.15 seconds, but it increases by 0.1 seconds. But still this is not accurate. I have quite a few anomalies.
However, like in what I discussed in my analysis, I did make some mistakes with accuracy etc… If I were to redo this experiment, then I would consider making sure I got the timings absolutely perfect. Which although would take a lot of time which I didn’t have this time around, so maybe this shows to get excellent results you need a lot of time and it takes a lot of effort.
One anomaly that in particular stands out is when the string is of length 75 cm and the result is 1.55 seconds. Whereas the result just before it is 65cm and 1.68; before this result, the trend line goes up consistently, however, when it hits this point, it goes down by 14 seconds, which is a pretty large jump and the result after it is at 85 cm and 2.07. There is then a massive jump to the next point. It goes up by 0.51 seconds, which is a massive increase. It is the biggest increase in the whole experiment. This again shows another flaw in my experiment, or maybe just reinforces the anomaly before hand.
It is very low compared to 85cm but is also lower than 65 cm which cannot be right because, as we discovered, as the length of the string increases, so to does the length of the period. Therefore this is incorrect. Looking back at the table, the first trial for 75 cm is 1.81 cm, which seems pretty accurate but then for trial 2 and 3, it slips to 1.43 and 1.42 seconds. This could have happened because, the unbeknown to us the string slipped or tightened in this case, or it bashed the table or we timed it wrong by stopping the stopwatch too early or starting it too late. This is an easy mistake to make however, on the other hand, I could have measured the results before of after inaccurately in the same way, timing inaccurately. This is quite unlikely though. Again if I were to do the experiment again I would have to be more accurate.
I don’t think my results are that reliable, and don’t always fit the formula. And there a lot of anomalies in the separate trials. If I were to do it again, I would do it in more time with more accuracy. I would maybe even do an even bigger range and perhaps another trial.
I would also check the length of the sting hadn’t slipped or adjusted itself between each trial.
Analysis
If I pick two points on the line of best fit, near the end and the beginning:
0.80 and 2.20
The co-ordinates are
0.80 = (3,8)
2.20 = (17,22)
22-8=14
17-3=14
14/14=1
44π² = 39.5
39.5/1=39.5
(39.5-9.8)/9.8 = 3.0306
=3
3 is the percentage error so this shows my results aren’t completely accurate. Therefore if I were to do it again, I would need to be more accurate.
Between point’s 25, 35,45 and 55 it goes up almost identically, very, very consistently. It goes from 1.11 (1.1) to 1.30 (1.3) to 1.59 (1.6) to 1.67 (1.7). The third goes slightly out, but they are the most accurate ones.
This shows good and accurate timings, which is very good n the fact we’re trying to compare the length of string and the how it affects the time it takes the pendulum to complete one period.
The rule for this graph is, as the length of string increases, the time it takes the pendulum to complete period increases at the same time. My graph clearly shows this as the line of best fit goes up diagonally right.
t² = (4π²/g)L.
39.5/39.5=1
1 times 5 = 5
Therefore should be at point 5 (0.5) on the graph.
Therefore our result is inaccurate.
However, it does relate to my background research because it said that length would be the only variable able to change the length of the period. Also that the longer the string the longer it would take to complete a period. This means it does link closely to the background research, just not extremely accurately. The main theory does.
Conclusion
The rule for this graph is, as the length of string increases, the time it takes the pendulum to complete period increases at the same time. My graph clearly shows this as the line of best fit goes up diagonally right. In my prediction I said that it goes up by roughly 0.15 in every 10cm but I think its now more closer to 0.1 seconds in every 10 cm.
