Center of mass
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School
Northern Virginia Community College *
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Course
201
Subject
Aerospace Engineering
Date
Dec 6, 2023
Type
Pages
2
Uploaded by HighnessScorpion8467
1
Center of Mass
Lab goals
•
To understand the concepts of center of mass and center of gravity.
•
To determine it from experiment and compare it with that obtained from theoretical
considerations.
Equipment
•
A sheet of thick paper and three nickels.
•
A small object with a hole such as a bead or nut, and a long string to make a plumb line.
•
A ruler, a pencil, scotch tape, a push pin.
Theory
The center of mass (CM) of an object is that point where the mass can be considered to be concentrated.
The center of gravity of an object is that point at which the force of gravity is considered to act. Even though the
force of gravity acts on all parts of the object, we can assume that it acts from one point which corresponds to
the object’s center of gravity (CG). When there is uniform gravity present in the region, the CM and CG can be
considered to be the same.
For a planar object one can determine the center of mass (or CG since we assume that gravity is uniform
everywhere) by using a plumb line. If the object is suspended from different points along its periphery, a torque
acts on the object due to the force of gravity unless it is placed such that its CG lies in a vertical line directly
below the point from which it is suspended. If a plumb line is hung from the suspension point and lines are
traced along the plumb line location, the intersection of all these lines gives us the location of the center of
mass.
The location of the center of mass is also given mathematically by its coordinates
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, ࠵?
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where
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and
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(1)
where
m
1
, m
2
,
. . . correspond to the masses of the particles and
(࠵?
)
, ࠵?
)
)
,
(࠵?
*
, ࠵?
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)
, … correspond to the
coordinates of the particles.
Experimental Set up and method
1.
Determine the masses of three nickels (typically each has a mass of ~ 5g)
2.
Draw
x-y
coordinate system at the center of a sheet of paper and glue or scotch tape one nickel
approximately at the origin of the coordinate system. Choose two other points (points 2 and 3) with
known
x,y
coordinates and glue the other two nickels at these two points. Try to center the nickels as
best as possible at these points. Now your planar object is ready.
3.
Cut a string (at least as long as the length of the paper plus 5 cm) and make your plumb line by
attaching a small heavy object to the string.
2
4.
Use the push pin to make a hole in the periphery of the object and suspend the plumb line
through it. Use a pencil and ruler to draw along the plumb line and try not to shift the position of the
plumb line.
5.
Repeat the step 4 above for at least two or three more points along the periphery of the object
and you will see that these lines will intersect at one point which corresponds to the center of the mass
of the object.
6.
Determine the
x- and y-
coordinates of this point by measuring it from the origin.
Theoretical determination
Use the values of the known masses of the nickels and their x- and y- coordinates to determine the value of the
x- and y- coordinates of the center of mass using equation (1).
Table 1:
Nickels
Mass in g
X-coordinate (cms)
y-coordinate (cms)
Nickel 1
0
0
Nickel 2
Nickel 3
Coordinates of the center of mass obtained from experiment: x-coord:
y-coord:
Coordinates of the center of mass obtained from the formula: x-coord:
y-coord:
1)
Determine the percent error between the theoretical and experimental x- and y- values.
2)
List possible sources of error in your experimental determination.
3)
In your opinion which set of coordinates for the center of mass is more reliable?
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