Center of Gravity Apparatus

CENTER OF GRAVITY APPARATUSSTUDENT NAME - PRESVIN VINOD STUDENT NO. - 10044584

PASSPORT NO. - H1428404 INSTRUCTOR NAME - DEWIKA NAIDU

2/23/2012

OBJECTIVE

To establish the position of the center of gravity of several different shapes by experiment and to confirm with values derived from calculus or reference book.

EQUIPMENT

LS 12039 Center Of Gravity Apparatus, flat shapes, weighted cords with plumb-bob, ruler and marker pen.

THEORY

Center of gravity A body is composed of an infinite number of particle of different size, and so if the body is located within a gravitational field,then each of these particles will have weight .These weights form an approximately parallel force system, and the resultant of this system is the total weight of the body, which passes through a single point called the center of gravity.

Composite bodies

A composite body consist of a series of connected simpler shaped bodies, which may be rectangular, triangular, semicircular, etc. Such a body can often be sectioned or divided into composite parts and ,provided the weight and location of center of gravity of each of these parts known, we can then eliminate the need for integration to determine the center of gravity of the entire body.Formula rather than account for an infinite number of differential weights we have instead a finite number of weights.

Here

x,y,z represent the coordinate of center of gravity G of the composite body .

x,y,z represent the coordinate of the center of gravity of each composite parts of the body

W is the sum of all weigts of all composite parts of the body or simply the total weight of the body.

The centroid of composite lines, areas and volumes can be found analogous to the above equation, however by replacing the W’s by L’s ,A’s, and V’s.

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METHODOLOGY

Select a particular flat shape to determine its center of gravity. Suspend the object on the pin provide on the gravity apparatus board. Then suspend the weighted cord with the plumb-bob on the same pin and observe the line of

action. Using a marker pen mark the upper most, middle and the lower most point of the suspended

cord which would be later used to draw a line. Repeat the above two steps by changing the points of the object to be suspended on the pin so

that different lines of action can be obtained. Repeat the experiment to obtain center of gravity for other flat shapes. Note down the center of gravity of the object from the base of each flat shape.

RESULTS

1. EQULATERAL TRIANGLE

a. b. y

35.07cm

35.5cm

12 cm x 40.5cm

40.5cm

a. Center of gravity found during experiment is 12 cm

b. Center of gravity found after calculation or theoretical method is 11.67

This result was obtained using c=13h

The percentage of error between the theoretical and experimental result a is 2.75 % .

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2. SEMI CIRCLE y

a. b.

b

37.1cm

36.5cm

40cm 8cm x

a. The center of gravity by experimental was (20,8)

b. By using the formula of center of gravity of composite body we have

(using Area instead of W)

X = 20 cm Y= 8.49cm

The percentage of error between the experimental and theoretical result is 5.8 %

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AREA cm X cm Y cm xA cm yA cm

314 20 8.49 6283.2 2667.2

x

3. CIRCLE 17.5cm b.a.

y

35.5cm 17.5

17.5cm

35.5cm

a. The center of gravity by experimental was (17.5,17.5)

b. By using the formula of center of gravity of composite body we have


X = 17.5 cm Y= 17.5cm

The percentage of error between the experimental and theoretical result is 0%

4. L Shape

4


962.113 17.5 17.5 16837 16837

36.1cm

38.8cm 38cm

8cm

35cm

16.7 cm

a. By The experimental we can conclude that the center of gravity of this shape is 13.5 cm .b. The values calculated by the experiment is 23.5 this could be because of inappropriate use of

the equipment for achieving the center of gravity .

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5. T SHAPE

y

35 cm

8cm 4

10..4cm

13.5cm

27cm 1 2 3

x

8cm

(Using the same dimensions of the shape in Cartesian Coordinate for calculation)

a. The center of gravity by experimental was (17.3cm,8.6cm)b. By using the formula of center of gravity of composite body we have


X = 17.49 cm Y= 8.36 cm

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-364.5 6.75 13.5 -2460.38 4920.75

216 17.5 13.5 3780.00 2916.00

-364.5 28.25 13.5 10297.1 4920.75

280 17.5 31 4900.00 8960.00

∑=-233 ∑=4077.48 ∑=2034.5

The percentage of error between the experimental and theoretical result is 1.1% in x axis and 2.7% in yaxis

x 28.5cm

6. TRAPEZIUM

25cm 28.5cm 25cm 1 2

y

40cm 26cm

(Using the same dimensions of the shape in Cartesian Coordinate for calculation)

a. The center of gravity by experimental was (25cm,11.6cm)b. By using the formula of center of gravity of composite body we have

(Using Area instead of W weight)

X = 17.5 cm Y= 11.6 cm

7


650 13 12.5 8450 8125

175 34.33 8.33 6007.75 1457.75

∑=-825 ∑=14457 ∑=9582.75

The percentage of error between the experimental and theoretical result is 30% in x axis and 0.8% in yaxis

DISCUSSION

SOURCES OF ERROR

There could be random error caused due to the air resistance effecting the suspended bob from its actual position.

There could be parallax error caused while measuring and taking down the length of flat shape and also the measurement of center of gravity.

There could be error when tracing the suspended bob on the flat shape, as this may differ from actual position of the suspended thread .

There could be fault in the apparatus leading to systematic error. The marker pen used on the flat also adds to the sources of error because the line

drawn is thick having its own width. There could be error caused by the thread suspending bob as it could be elastic.

OTHER OBSEVATION

The error in the simple composite body like triangle, sphere , and semicircle have the least amount of error.

But as the composite body becomes complex the error increase. Which can be seen in T shape and the L shape.

CONCLUSION

The experiment could be improved by placing an carbon paper on the flat shape and pressing the suspended cord against it. This would reduce the parallax error and the error caused with the usage of marker pen on the flat shape.

There could be more no. of reading taken to get a more precise result with minimal error

Thread used should not be elastic so that a better and a more accurate result could be obtained.

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Center of Gravity Apparatus