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Pendulum Coursework.

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Introduction

PENDULUM COURSEWORK

PLANNING

INTRODUCTION- Pendulumis an apparatus consistingof an objectsuspended by a fixed point so that it swings freely back and forth under the influence of gravity. Repeated motion of pendulum (to and fro) is called an oscillation. And the time taken for one full oscillation is called period. In this experiment the pendulum gains Gravitational Potential Energy or GPE, as the bob is being raised from its original hanging position. When the pendulum is at the top of its swing it is momentarily stationary. It has zero Kinetic Energy (KE) and maximum Gravitational Potential Energy (GPE) because it’s the highest point.

As the pendulum falls thus moving downwards towards its original hanging point the gravitational potential energy is transferred to kinetic energy. The speed increases as the pendulum falls and reaches a maximum at the bottom of the swing. Here the speed and kinetic energy are a maximum and the gravitational potential energy is a minimum. As the pendulum rises the kinetic energy is transferred back to potential energy. The speed of the pendulum decreases and falls to zero as it reaches the top of its swing. Small amount of energy is lost due to air resistance as the pendulum swings.

     Pendulums are also beneficial in our day to day life for example its used in several kinds of mechanical devices such as grandfather clocks.

image00.png

AIM- investigating how to determine the value of acceleration due to gravity using simple pendulum in the laboratory

APPARATUS –

  • Stand
  • Metre ruler
  • Stop watch
  • Thread
  • One small ball
  • Two small pieces of wood – to hold thread in between them

PREDICTION- I predict that the length of the thread will affect the period of the pendulum. I believe that there is positive correlation between time and length of the pendulum. The longer the length of the thread the longer the time period of the pendulum. I can say this because if the string is longer, it will have to travel a greater distance, so the time period will be longer, but the gravitational acceleration will remain the same. I also predict that the value of acceleration due to gravity must be between 9.8m/s² to 10m/s².

METHOD-I set up my simple pendulum like the one shown in the diagram. Firstly I took a piece of string 50cm long and attached securely a small bob at the end of the string.                

image01.png

The thread is secured between the two halves of a split cork held securely in a clamp mounted on a stand. The length of the pendulum is carefully measured from the place where the thread emerges from the cork to the middle of the pendulum bob. This would ensure that the bob swings from a single fixed point.

Time period of a pendulum is the time taken to complete one full oscillation. I need to record the time period but it is too short, so I will time 20 periods and then divide the final time by 20 to give me the time period of the pendulum.

Timings for twenty complete oscillations are started and stopped as the pendulum passes through the mid point. As the thread passes the mid point the stopwatch is started and counting is started. The pendulum will swing to one side, then back through the centre and to the other side. When it passes the centre again ‘1’ is counted for the first complete swing. This is repeated until 20 oscillations and the time is stopped as the thread passes the 20th oscillation.

Then to find the time of one oscillation divide the time taken for all 20 oscillations by 20. The angle of amplitude must not be very big because then the gravitational potential energy will increase tremendously. Each time I increase the thread length by 10cm and measure another reading.

Formula for time period of a pendulum is:

T=2 Π√l/g                            

T²=4Π² l/g

g=4Π² l/ T²   …………..(1)

Where

Π = 3.14

● l = length of the thread

● g = acceleration due to gravity

● T = time for one oscillation or the period of the pendulum

  • G= ΔT²                                                   G stands for gradient

Δl

  • 1  =    l
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Middle

if the experiment were not carried out safely there would have been possibilities of accidents occurring. In order to prevent such accidents occurring I had to keep a few simple guidelines into consideration: -
  • Keep my table clean and tidy before starting.
  • Care will be taken not to let the bob come into contact with anything whilst swinging.
  • When the bob is swinging take care that it does not hit someone.
  • The stand should be kept clearly and firmly secured to the table otherwise it could fall over and hit someone.
  • Excessively large swings should be avoided.

OBTAINING EVIDENCE

I used the method proposed in my plan, taking two readings of each value and measuring the time taken for 20 oscillations rather than for one. I was careful to use

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Conclusion

After drawing my graph I found the gradient of my graph. I got G= 0.04 where is the gradient. And then I found the acceleration due to gravity (g) using the formula T=2 Π√l/g. then I got g= 9.85m/s²  which again proves my prediction to be correct.

EVALUATION        

From looking at my results on the table, graphs and comparing them to the formula I concede that the investigation was successful.

There is a possibility for an inaccuracy in my project and that is when I left the bob from my hand, there is no surety as to whether the stopwatch was started at exactly the same time when the bob was left.

Also it was not entirely possible to get completely accurate results, as there was not an easy way to recognize where to stop the clock.

If I was to repeat the experiment I would make sure there were two people doing the experiment so that when one leaves the bob the other person starts the stopwatch exactly at the same time so that there were no inaccuracies.

Secondly I would prefer for there to be some indication of one oscillation, if I were to repeat this investigation so that I know when to stop the stopwatch.

But overall according to me the experiment was successful as it matched with my prediction and it gave me evidence that could be said to be reliable as it matches with the information found in physics textbooks about the formula and the shape of graph. I also got g= 9.85m/s² which is nearly equal to Newton’s result.

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