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# Objectives: To determine the center of gravity of a body of irregular shapes

Extracts from this document...

Introduction

Experiment 2A: Centre of gravity of a body(irregular shape only)

Objectives:

To determine the center of gravity of a body of irregular shapes

## Experimental Design

Apparatus:

 Name of apparatus Number Remarks Irregular shape board 3 pic Optical pin of cork 1 pc Cellulose tape 1 roll Scissors 1 pair A4 sheet 3 pic Meter -rule 1 pic Stand 1 Clamp 1

Experiment Set-up

Description of design:

In this experiment, we will determine the center of the gravity of the irregularly shaped wooden boards by setting up the apparatus as above. In this experiment, we have to find out the center of gravity of three irregularly shaped boards. On each board, there are three holes for us to hang them on stand and clamp. After marking and drawing the points and lines on the A4 sheet paper which is fixed on the wooden board by the cellulose tape. The intercept point of the lines is the center of the gravity of that irregularly shaped wooden board.

Theory:

Before finding the center of gravity of the irregularly shaped boards, we should know about the background of the experiment and the center of gravity:

The center of gravity is a geometric property of any object. The center of gravity of system is the point where the gravitational force by the earth acts at. The center of gravity is the average location of the weight of an object.

We can completely describe the motion of any object through space in terms of the translation of the center of gravity of the object from one place to another, and the rotation of the object about its center of gravity if it is free to rotate. If the object is confined to rotate about some other point, like a hinge, we can still describe its motion.

In our daily life, many ordinary things are made use of the change of the center f gravity.

Middle

References

Wikipedia (center of gravity)

http://en.wikipedia.org/wiki/center_of_gravity

Experiment 2B: Measurement of the gravitational acceleration (g) using a simple motion

Objectives:

To determine the local acceleration of free fall g using a simple pendulum

## Experimental Design

Apparatus:

 Name of apparatus Number Remarks Plumb line (with bob) 1 pc >1.5 m Stopwatch 1 pc Has zero error (± 0.1 s) Small wood piece 2 pic Plasticine 1 pc To hold the pin as the reference point G-clamp 1 pc To hold the stand firmly Meter rule 1 pc Has zero error (±0.001m) Optical pin with cork 1 pc Stand and clamp 1 pc

Experimental set-up:

Description of design:

In this experiment, we will measure the local gravitational acceleration due to the earth. In order to investigate the objective of the experiment, we should set up all the apparatus as above diagram. The optical pin with cork is fixed at the stand by using the plasticine as the reference point and the equilibrium point. We measure the time taken for the pendulum to complete on rotation by using the stopwatch. From the period and length of the thread, we can calculate the gravitational acceleration. In addition, we can find out g from the slope of the graph to be plotted.

Theory:

To determine the gravitation acceleration due to the earth in the laboratory, we use the simple pendulum set-up to find it out.

The pendulum used performs simple harmonic motion(SHM) which the acceleration is directly proportional to the displacement but always in opposite direction. The forces acting on the bob are the tension in the thread, T (radially inward) and the weight of the bob, mg (vertically downward). In this system, the pendulum also performs circular motion, as the tension does not involve in the speed change, the tension provides the centripetal force. The net force of the system is the tangential component of the weight of the bob.

Conclusion

Θ, hence the motion of the bob does not obey to the definition of SHM. As a result, the bob does not perform SHM., the data and the equations are not suitable in the calculation process. The gravitational acceleration calculated will be incorrect. The third assumption is that there is no air resistance. The air resistance will oppose the motion of the bob and increase the time for one period. It results in the inaccurate data obtained and the final result of the gravitational acceleration calculated. However, the effect of air resistance on the bob cannot be totally removed. So we assume that there is no air resistance. The last assumption is that the centers of mass and gravity are concentrated at the bob.

The experimental errors can be divided into two errors, systematic errors and random errors. The zero errors of the stopwatch and meter rule and effect of air resistance on the bob are belonged to the systematic errors. The other errors mentioned above are the random errors. An experiment with small systematic and random errors is more precise.

Conclusion

By both mathematical and graphical methods, we can find out the gravitational acceleration due to the earth in the simple pendulum set-up.

For mathematical method, the gravitational acceleration is (9.40 ± 0.42) ms-2. For graphical method, the gravitational acceleration is (10.56 ± 1.44) ms-2.  Either the gravitational acceleration calculated from the mathematical method or the one from the graphical method are not equal to the value actual value (9.8 ms-2). It may result from the experimental errors mentioned above. The result will be more accurate if we follow the improvements mentioned. However, the experimental result still is close to the actual value. So it can be said that the experiment result is precise.

In the next time, we can vary the gravitational acceleration by changing the places for experiment on different floors, we can investigate the effect of g on the period.

References

Wikipedia (pendulum)

http://en.wikipedia.org/wiki/pendulum

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