# The Rate of Pendulum

ntroduction In this piece of Coursework I shall being trying to determine whether or not the variables length (l) and Mass affect the rate of the pendulum. Other variables which effect the rate of a pendulum or time (T) (that I shall keep at a constant) are angle of amplitude and gravitational fields strength. I predict that when the length increases the time length of [image]a period also will increase. This is because the distance travelled in the period would have also increased (see diagram on the right). I [image][image]believe that the greater the mass the quicker it takes. I believe this because greater masses have greater a gravitational field. Background Knowledge ==== Gravitation Force If you hang an object from a spring balance, you measure a downward pull from the earth. This pull is called a gravitational force. No one is sure what causes gravitational force, but here are some of its main features: Â? All masses attract each other. Â? The greater the masses, the stronger the force. Â? The closer the masses, the stronger the force. The pull between small masses is extremely weak. It is less than 10-7 N. But the Earth is so massive in comparison that its gravitational pull is strong enough to hold most things firmly on the ground. Weight Weight is another name for the Earth?s gravitational force on an object. Like other forces, it is measured in newtons (N). Near the Earth?s surface , an object of mass 1kg has a weight of 9.8N, though 10N newtons is accurate for many calculators and will be used in this Coursework. Greater masses have greater weights. Here are some examples: G= gravitational field strength =10N/kg [image]Mass 1Kg 2Kg 50Kg m [image] [image] [image] [image] [image] [image] [image] [image]Weight 10N 20N 500n mg (gravitational force) Gravitational strength (g) The Earth has a gravitational field which exerts a force on any mass in it. Near the Earth?s surface, there is a gravitational force of 10 newtons on each kilogram of mass: the Earth?s gravitational field strength is 10 newtons per kilogram (N/kg). Gravitational field strength is represented by the symbol g. So : Weight = Mass x g (g = 10N/kg) In symbols: W = mg In everyday language, we often used the word ?weight? when it should be ?mass?. Even balances, which detect, which weight, are normally marked in mass units. But the person in the diagram above doesn?t ?weigh? 50 kg he/she has a massof 50kg and a weight of 500N [image] Centre Of Gravity [image]Like other objects, the beam on the right is [image]made up of lots of tiny particles, each with a small gravitational force on it the beam balances when suspended at one particular point, G, because the gravitational forces have turning points about G which cancel out. Together, the small gravitational forces act like a single force at G in other words, they have a resultant force at G. this resultant is the beam?s weight. G is the centre of gravity (or centre of mass). A pendulum can be used to find the direction of the gravitational field. It is a length either flexible or ridged (it makes no difference) and has a mass on the end. The mass will go straight towards gravity until it stops central to the force of gravity: [image] Finding a centre of gravity In diagram a (below) the card can swing freely from the pin. When the card is released, the forces on it turn the card until its centre of gravity is vertically below the pin as in diagram b. what ever point the card is hung from its centre of gravity will always be vertically under the pin. This fact can be used to find the centre of gravity. [image] [image] [image] [image] In diagram c, the centre of gravity lies somewhere along the plum line, whose position is marked by the line AB. If the card is hung at a different point the line CD can be drawn. The point where these lines cross is its centre of gravity. [image] Fair Test The following variables will be considered whilst providing a fair test: Â? The masses will be changed only after all the different lengths are completed for that particular mass Â? The angle of amplitude shall be a constant 30 degrees through out. This is to ensure there is no variation of the forces acting on the pendulum. Â? The test will be repeated 3 times for each length/mass so that there is a higher accuracy, then an average result shall be worked out using the formula for the mean which in this case will be test 1+2+3=nÃ?3(number of results)=average. Â? I will ensure that there is no obstacles in the path of the swing which could effect the rate of the pendulum or even damage it. Â? The gravitation force will effect the experiment but this should remain a constant. However this may vary very slightly due to the outer core beneath the Earth?s solid lithosphere (crust and mantle) moving. it moves because it is a molten liquid made up of mainly Iron (Fe) and Nickel (Ni). As this moves the denseness or mass of the earth at that particular point will vary. Thus causing the gravity to be effect as we no that mass effects the rate of gravitation force. After completing the experiment I shall rearrange the equation of a pendulum (T=2Ï?âˆšL/g) so that g is the subject (g=4Ï?Â²L/TÂ²). I will then add an extra column to my results and work out the strength of the gravitational pull to see if It could have changed the out come of the experiment. Safety -?- Here is a list of safety precautions I will need to follow: Â? When moving around the laboratory, always walk, don?t run. Â? Keep bags, coats and stools under the desks so that they don?t obstruct. Â? Never eat or drink in the laboratory?s (this also applies to teachers at break times) Equipment List -?????- The equipment I shall be using a what each pieces purpose is, is listed below: Â? Clamp Stand- to hold the pendulum, Â? String- to be the length of the pendulum, Â? Weights- to be the mass on the end of the pendulum (the weights have kg marked on them.) Â? Protractor- to measure the 30 degree angle of amplitude, Â? Ruler- to measure the length of the string. Â? Stopwatch- to time ten periods [image]Diagram Plan The experiment will be set up like the diagram below. I shall do the experiment by following these simple steps: Step 1- measure out a length of 10, 15, 20, 25 or 30 cm. Step 2- Secure a mass of 50, 100 and 200 grams to it. Step 3- Have a stopwatch reset and ready to time. Step 4- Bring the pendulum back to a 30Ëšangle (measured by the protractor) and release. Step 5- At the same time the pendulum is released start timing on the stopwatch. Step6- Use the stopwatch to time when ten periods are completed and record the time in a table of results. Results [image] Graphs Looking at the variables I can see little if any change in the time taken for ten swings whilst holding different masses, therefore the graphs that shall be plotted will plot string length against the time for ten swings. As there would be 3 results for each test and 9 results for each string length before the average is worked out my graphs will all be from the mass of 100g only. All the graphs show positive correlations as expected. This is because when the string gets longer so does the distance between the angles. Take these two circles for instance: Oval: 2 Oval: 1 Both these circles are 360 degrees but have different radius?s this is why there is a positive correlation. Analyses First of all I need to know whether I have proven my prediction. My prediction was "I predict that when the length increases the time of a period also will increase. This is because the distance travelled in the period would have also increased. I believe that the greater the mass the quicker it takes. I believe this because greater masses have greater a gravitational field. " I now need to know whether I have proven, partly proved or disproved my theory. String lengths- the time taken as the string gets longer does increase like I thought; I can conclude that this is because the size of the gap travelled will also increase. Therefore giving the pendulum further to go. Masses- looking at my results I can see that the mass on each length doesn?t effect the time taken in any way. Therefore my theory of greater masses being quicker was wrong. Gravity- I decided to test the gravitational strength as well, by re-arranging the formula T=2Ï?âˆšL/g so that g would be the subject. Giving me the formula g=4Ï?Â²L/TÂ². This should have the answer 10 as this is the standard force of gravity on earth, but the highest I had was 9.8 only and more significantly the lowest I had was 8.2 and the average was 8.3! This means that the experiment I did was an unfair test and that the results aren?t completely accurate as I had a varying rate of gravity acting on the pendulum. Evaluation During this experiment there are things that maybe weren?t done to the standard required. When the experiment was done it was done on two different days and with convection currents effecting gravity this will of cause an inaccuracy in my results. Also the experiment was conducted in two different classrooms one on the lower floor and one upstairs. This will have changed the distance from the ground as on the first day we could have been 100 meters above sea level and on the second in the other room it may have only been 80 meters. If I did the experiment again it would be necessary to complete in one sitting and to do it I exactly the same spot. Even so I am pleased with the experiment and my results are very pleasing as I have proven half my theory.

The Rate of Pendulum
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