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Centre of Gravity of a Body

Extracts from this document...

Introduction

Physics TAS Experimental Report                

Centre of Gravity of a Body

Centre of Gravity of a Body

Report Type:

Brief

Date:  26th October, 2007

Mark:      / 10

Objective:

To determine the centre of gravity of a body of different shapes.

Results:

image08.jpg

(a) Circle

image09.jpg

(b) Rectangle

image12.jpg

(c) Isosceles Triangle

image13.jpg

(d) L-shaped

image14.jpg

(e) Nut-shaped

image15.jpg

(f) Compound Body

The intersections of the lines above are the centres of gravity of the particular shapes.

Conclusion:

  • It is unnecessary for the centre of gravity to be situated inside the body.
  • For regular shapes, their centres of gravity are actually their geometric centres. Generally, the centres lie on the axes of symmetry.
  • For irregular shapes, their centres of gravity can only be found by experimental methods. They always locate at the more massive part.
  • For a compound body, the centre of gravity is the mid-point of the centres of gravity of its components.
...read more.

Middle

Circle

Circumcentre

Rectangle

Intersections of Diagonals

Isosceles Triangle

Intersections of Medians

Table 1 – Theoretical Values of Centre of Gravity for Different Shapes

The theoretical value of L-shaped lamina is illustrated as follow: image00.pngimage00.pngimage16.pngimage00.png

Figure 1

Figure 2

Figure 3

Figure 4

Divide the shape into two rectangles, as shown in Figure 2. A dotted line is drawn by joining the centre of gravities of separated rectangles, which are the intersections of the diagonals. Then the center of gravity of the shape must lie on the dotted line. Similarly, as shown in Figure 3, another dotted line, where the centre of gravity must lie on it, can be found. As the center of gravity of the shape must lie along the two dotted lines, it is obvious that it is at the intersection of these two lines, as shown in Figure 4.

It

...read more.

Conclusion

s of the vertical string and the edges of the cardboard on the cardboard, the markings may deviate from the original position.The density may not be uniform throughout the lamina.








  1. Others

Here is the proof showing why the centre of gravity lies on the more massive part in an irregular body:

Let G be the centre of gravity of the object, m1 and m2 be the centre of gravity of the upper and lower part of the object, where
m1 < m2. They are distanced from each other by length d. Besides, x is the distance between m1 and G.

A simplified diagram is shown on Figure 6.

Then image10.pngimage10.png

 m1 < m2

 m1 + m2 < 2m2

  • image11.pngimage11.png

Therefore, G is closer to m2 and the centre of gravity of the object should be lie on the more massive part.

image05.pngFigure 5

Figure 6image02.pngimage07.pngimage03.pngimage01.pngimage06.pngimage04.png

- End of Report -

...read more.

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