Sample Computations

Technological University of the Philippines College of Science Physics Department

Experiment No Individual Report

Center of Gravity Submitted by: Irish Charmaine H. Celestial

Submitted to: Prof. Ma. Dolores Tabanera

TABLE OF CONTENTS

I.

Objectives ………………………………………………………… 3

II.

Experimental Set-Up ……………………………………………...3

III.

Theory ……………………………………………………………..4

IV.

Procedures ………………………………………………………...4-5

V.

Data and Tables ……………………………………………………5-9

VI.

Sample Computations ……………………………………………..10

VII.

Observations ……………………………………………………….10

VIII.

Data Results and Analysis ………………………………………...11

IX.

Conclusion ……………………………………………………….....11

X.

Application …………………………………………………………12

XI.

Reflection …………………………………………………………..12

III. THEORY: The center of gravity of a body is the point at which its weight is concentrated. This point may be within or outside the body. This is the point where it balances itself when on knife-edge support. In regularly-shaped bodies, the center of gravity is located at its geometric center. In irregular elongated bodies, it can be located by balancing method. In irregular flat bodies like a sheet metal or board, it is located by dropping two or more plumb lines from different points of suspension. The intersection of these plumb lines is the center of gravity.

IV. PROCEDURES:

A. The Plumb Line Method The materials needed were prepared. The shapes of regular object, irregular object, a letter, and a number were cut out from the cardboard pieces. Small holes at noncollinear points A, B, C were punched on each piece. A cardboard piece was suspended by means of the nail-like support mounted on the stand through the hole at point A. The cardboard was hung loosely from the support. A plumb bob was suspended from the support with the cord extending down in front of the cardboard. A line was drawn on the cardboard along the path of the cord. The cardboard was removed and was suspended again through another hole. The line was drawn again. The intersection of the two lines was marked as C (the center of gravity). These steps were repeated for the other shapes indicated.

B. Center of Gravity by the Principle of Moments

The meter stick was weighed assuming that its weight (W1) to act at the 50-cm mark. A load (W2) of 20 g-wt was placed at the 10-cm mark and by trial, the center of gravity (C) of the system by balancing it on the knife edge. The distances between the balance point and the positions of the forces W1 and W2 were measured. These were recorded as L1 and L2, respectively. The ratios L1/ L2 and W2/W1 were found. The ratios and the percentage difference were computed. These steps were repeated varying the value of W2 as well as its position to complete three trials. The data and results were tabulated.

V. DATA AND RESULTS

Table for Center of Gravity by the Principle Moments

W1 = 57 g-wt Trial 1 2 3

W2

L2

(g-wt)

(cm)

20 50 100

30 21.5 14.8

VI. SAMPLE COMPUTATIONS Trial 1: L1=10 L2=30

L1

L1/L2

W2/W1

Percent

(cm) 10 18.5 25.2

0.333 0.860 1.703

0.35 0.877 1.754

Difference 4.98 % 1.96% 2.95 %

L1/L2 = 10/30 Trial 1: W2/W1 = 20/57 (g-wt) = 0.35 For Percent Difference: Difference of two values Percentage Difference= Average of two values

0.333- 0.35 =

---------------------------

X 100 = 4.98 %

(0.333 + 0.35) / 2

VII. OBSERVATIONS: In all the cut-out shapes of the objects, it can be observed that all the lines drawn intersect at a common point which is denoted as C. In addition to that, the greater the number of holes tested, the greater the accuracy of getting the point of the intersection of the lines. Moreover, whatever the positions of the holes, it always comes out to a common point. For the center of gravity by the principle of moments, it can be observed that the center of gravity of the meter stick is at its midpoint which is at 50-cm.The greater the mass of the load applied, the lesser the distance between the balance point and the position of the force. The percentage differences computed are not that large so there are fewer errors in performing the activity.

VIII. DATA RESULTS AND ANALYSIS:

The common point intersected by the lines drawn in each piece represents the center of gravity. It is where the weight of an object more concentrated. This point may not always be inside the object, it is sometimes on its outside part. In regular-shaped objects like in circle, the center of gravity is at its geometric center. The plumb line method is very helpful in finding the center of gravity in irregular-shaped objects. The balancing method used in the second part is also an effective method wherein a meter stick balanced itself in the knife-edge. The balance point depends upon the mass of the load.

IX. CONCLUSION: Based on the performed activity, I therefore conclude that the center of gravity is the point where weight is concentrated. The sum of all the particles’ weights that compose the matter may be considered as concentrated at one point. Locating the center of gravity of an object may de done in different ways. For regular-shaped objects, the center of gravity is at their geometric centers. For the irregular-shaped objects, the plumbline method may be used. Balancing method is also an effective way in locating the center of gravity of either regular or irregular shapes of the objects. In addition, the center of gravity is also related to stability. The conditions of equilibrium are affected by the center of gravity. A slight movement of an object having CG at its highest point will cause it to top over while an object with CG at its lowest point is more stable.

X. APPLICATION:

Locating the center of gravity of an object is very important in our daily lives.

XI. REFLECTION: The topic, which is the center of gravity, is hard to understand without performing the experiment.