Determination of Gravitational Acceleration

Introduction

Pendulums can be defined as a body suspended from a fixed support so that it swings freely back and forth under the influence of gravity, commonly used to regulate various devices, especially clocks.

Worth (2008) states that pendulums have been used for thousands of years. The ancient Chinese used the pendulum principle to try and help predict earthquakes. Hundreds years ago the famous Italian scientist Galileo was the first European to really study pendulums and he discovered that their regularity could be used for keeping time, leading to the first clocks. Worth (2008) goes on to explain that in 1656, the Dutch inventor and mathematician, Huygens, was the first man to successfully build an accurate clock. It was the first time pendulums were used for human’s everyday life.

There are four basic laws of a pendulum: Van & Albert (1995) explain that firstly the time it takes for a pendulum to complete a swing is related to the square root of the length of string of the pendulum. Secondly the time it takes for the pendulum to swing is related to the square root of the gravitational acceleration. Gravitational acceleration can be defined as the force that attracts objects in space towards each other, and that on the earth pulls them towards the centre of the planet, so that things fall to the ground when they are dropped (Wikipedia 2010). Thirdly the time it takes for the pendulum to swing is not related to the mass and material of the small ball at the end of the pendulum. Finally the time is independent of the greatest distance that a wave provided the greatest distance that a wave is small.

The principles of a pendulum can be proven. This experiment is going to show the effect changing gravitational acceleration has on a pendulum, and will determine gravitational acceleration using a simple pendulum

Methods

Equipment of determination of gravitational acceleration using a simple pendulum

• A long piece of string
• A wooden block
• A small ball
• A one meter long ruler
• A protractor
• Vernier caliper
• A stop-watch

This experiment is talking about determination of gravitational acceleration using a simple pendulum fig 1 was showed that the simple pendulum was used in this experiment.

Procedure

1. The long piece of string and the small ball were connected.
2. The small ball was suspended from the wooden block with the long piece of string，such as in figure 1
3. The length of the long piece of string L was measured using the ruler. Then the diameter of the small ball was measured using the vernier caliper. The long piece of string was not stretched. It was measured to the centre of the small ball.
4. The small ball was raised up about 15 degrees using the protractor, and then released so that oscillations were executed.
5. The time it took for the pendulum to complete a swing T was measured using the stop-watch to time 50 oscillations.
6. Steps 1 to 5 were repeated for five more values of L, and each part was done twice to verify the correct answer.

Experiment 1 the length of the long piece of string was measured to 0.4 m

Experiment 2 the length of the long piece of string was measured to 0.6 m

Experiment 3 the length of the long piece of string was measured to 0.8 m

Experiment 4 the length of the long piece of string was measured to 1.0 m

Experiment 5 the length of the long piece of string was measured to 1.2 m.

Result & Calculation

Below is a table to show the results recorded from trails 1 to 5.

The average time was calculated using the formula

The square of period T was calculated using T times T.

The information in this table can be plotted in a line graph see graph 1. The vertical axis shows that the time takenthe square of period T for 50 oscillation. The horizontal axis shows that the different lengths of the piece of string. The gradient of the line shows the gravitational acceleration.

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Discussion

In this experiment there were controlled variables. Controlled variable can be defined as one which is not allowed to change unpredictably during an experiment Answers Corporation (2010). The first controlled variable was the number of swings. Second was the angle of the swing. The last one is mass of the bob, we all kept their same. In addition, there was one experimental variable. The experimental variable can be defined as some values in experiment we change on purpose. In my experiment, the experimental variable was the length of swings.

Error is an experiment word means that mistake, especially one that causes problems or affects the result of some thing. The error can be caused when the small ball was not raised up about 15 degrees, location, the total number of oscillation are not 50.

I compared with the data of my classmate, the square period T was proportional to the length of string s. All the points of the graph lie on a straight line so the conclusion is very reliable over this range. It seems likely that the same trend would continue if the string was made longer. I solve the equation and get the acceleration of gravity is 9.78m/s, it’s not really correct. I think the biggest problem was that the small ball was not raised up about 15 degrees; location and the total number of oscillation are not 50

Conclusion

This experiment is talking about determination of gravitational acceleration using a simple pendulum.

Firstly I used five steps to finish this experiment first I connected the long piece of string and the small ball. Second I Suspended The small ball from the wooden block with the long piece of string，such as in figure 1. Third I measured the length of the long piece of string L using the ruler and measured the diameter of the small ball using the vernier caliper. Forth I raised up the small ball about 15 degrees using the protractor. Fifth I unclasped the small and using the stop-watch to measure the time it took for the pendulum to complete a swing T.

Secondly I made a graph to show my data about this experiment.

Thirdly I used these data to calculate the value of gravitational acceleration.

Finally I compared my result with my classmate to find mistake

In my results, the first two purposes were proving. I measured that the gravitational acceleration is 9.78m/s, it smaller than 9.8m/s. I think one of the most important problem is the total number of oscillation are not 50. Measuring the total number of oscillation about 1.20m is easier than short lengths. Because of the speed of the length is 1.2m is lower than the speed of the length is 0.4m

In addition, I think my experiment is good even have some mistake. I will carefully to measure total number of oscillation I am going to try my best to let my data much exact.