Technological University of the Philippines College of Science Physics Department
Experiment No Individual Report
Center of Gravity (14 pages)
Submitted by: Irish Charmaine H. Celestial BSECE- 2C
Submitted to: Prof. Ma. Dolores Tabanera September 5, 2007
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 …………………………………………………….10-11
VIII.
Data Results and Analysis ……………………………………11
IX.
Conclusion ………………………………………………………12
X.
Application ………………………………………………………13
XI.
Reflection ………………………………………………………..14
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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 non-collinear 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
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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
L1 (cm) 10 18.5 25.2
L1/L2 0.333 0.860 1.703
W2/W1
Percent
0.35 0.877 1.754
Difference 4.98 % 1.96% 2.95 %
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VI. SAMPLE COMPUTATIONS
Trial 1: L1=10 L2=30 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.
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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 50cm.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.
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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 plumb-line 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. The center of gravity is the point in or near a body at which the gravitational potential energy of the body is equal to that of a single particle of the same mass located at that point and through which the resultant of the gravitational forces on the component particles of the body acts. The center of gravity (CG) is the center of an object's weight distribution, where the force of gravity can be considered to act. It is the point in any object about which it is in perfect balance no matter how it is turned or rotated around that point. For a finite set of point masses, CG may be defined as the average of positions weighted by mass.
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X. APPLICATION: Locating the center of gravity of an object is very important in our daily lives. The earth pulls down on each particle of an object with a gravitational force that we call weight. Although individual particles throughout an object all contribute weight in this way, the net effect is as if the total weight of the object were concentrated in a single point - the object's center of gravity. In general, determining the center of gravity (cg) is a complicated procedure because the mass (and weight) may not be uniformly distributed throughout the object. The general case requires the use of calculus which we will discuss at the bottom of this page. If the mass is uniformly distributed, the problem is greatly simplified. If the object has a line (or plane) of symmetry, the cg lies on the line of symmetry. For a solid block of uniform material, the center of gravity is simply at the average location of the physical dimensions. (For a rectangular block, 50 X 20 X 10, the center of gravity is at the point (25,10, 5) ). For a triangle of height h, the cg is at h/3, and for a semi-circle of radius r, the cg is at (4*r/(3*pi)) where pi is ratio of the circumference of the circle to the diameter. There are tables of the location of the center of gravity for many simple shapes in math and science books. The tables were generated by using the equation from calculus.
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XI. REFLECTION: The topic, which is the center of gravity, is hard to understand without performing the experiment. I was amazed when I tried to balance the sample shapes of the objects on the point of the intersection of the lines drawn. This only means that the experiment is accurate. I enjoyed working with my group mates when we performed the activity on balancing a meter stick on a knife edge. I really enjoyed cutting out the different figures assigned especially for the irregular object wherein I could design it of whatever shape that I really want. For that I chose an abstract human being who is said to have the center of gravity on his navel. For me, it is an abstract thing because it is not perfectly shaped as a human being. We explored the world of the center of gravity using some simple tools and learned by ourselves. In a regular geometric solid with the uniform density, the center of gravity is the object's geometric center. Finding the center of gravity of irregular objects can be tricky.
