Date: ____________________
EXPERIMENT # 6
To verify Principle of Moments.
PURPOSE:
To prove that body is in equilibrium when sum of all clockwise moments is equal to sum
of all counter clockwise moments. i.e
∑CWM = ∑CCWM
APPARATUS:
Moment Balancing Apparatus
Weights
Hangers
F1 F2 F3 F4
Fig.1 - Moment Balancing Apparatus
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Engineering Mechanics – Experiments Manual
RELATED THEORY
Moment
Rotational tendency of a body due to applied forces is called moment. Moments is also
referred to as torque.
Fig.2 - Practical examples of moment
Moment is a vector quantity
uantity that represents the magnitude of force applied to a
rotational system at a distance from the axis of rotation.
The moment of a force about a pivot is the product of a force (F) applied and the
perpendicular distance (d) from the pivot.
M
d F
Moment = F x d
where
Unit for F is Newton (N) and d is metre (m); Moment is Nm
Nm.
Principle of Moments
The Principle of Moments,, also known as Varignon's Theorem, states that
“The
The moment of any force is equal to the algebraic sum of the moments of
the components of that force.
force.”
M = r x F2 = r x F sinƟ
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Engineering Mechanics – Experiments Manual
It is a very important principle that is often used in conjunction with the Principle of
Transmissibility in order to solve systems of forces that are acting upon and/or within
a structure.
Principle of moments for a body in equilibrium
An object is in equilibrium if the sum of all anticlockwise moments about the pivot is
equal to the sum of all clockwise moments about the same pivot.
Fig.3 - Physical example of equilibrium
Person A’s weight is trying to turn the seesaw anticlockwise whilst person B’s weight is
trying to turn the seesaw clockwise.
Person A’s Moment = Force x perpendicular distance from fulcrum
1000 x 1 = 1000 Nm
Person B’s Moment = Force x perpendicular distance from fulcrum
500 x 2 = 1000 Nm
Persons A’s moment = Persons B’s Moment
Anticlockwise moment = Clockwise moment
Therefore seesaw is in equilibrium.
Effect of the position of the centre of gravity on an object
The lower the centre of gravity, the more stable is an object. Centre of gravity can be
lower by making the base of the object as wide as possible. In additional, making the
object short is as well another way of lowering the centre of gravity.
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Engineering Mechanics – Experiments Manual
PROCEDURE
Paste the graph paper on the rotating wheel of apparatus.
Put weights in hangers.
Wait for a while until equilibrium is produced.
Calculate perpendicular distance from line of action of force to the center of moment.
Calculate the clockwise and counter clockwise moments. For the system to be in
equilibrium, clockwise and counter clockwise moments must be equal.
OBSERVATIONS AND CALCULATIONS
Clockwise Moments Clockwise Moments
%age
Sr. Force Distance Moment Force Distance Moment diff.
# (F) (d) (M=Fd) (F) (d) (M=Fd)
N mm N-mm N mm N-mm
∑CWM = ∑CCWM =
∑CWM = ∑CCWM =
CCWM − CWM
%age Difference = × 100
CCWM
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Engineering Mechanics – Experiments Manual
PRECAUTIONS
All the pulleys of balancing apparatus should be free to rotate firmly about their own
axis of rotation.
Distance b/w the origin and line of action of force should exactly be perpendicular.
Try to avoid errors while extending and shifting the line of action of force.
The sense of rotation should be noted properly.
RESULTS
Sr. # ∑CWM ∑CCWM %age Diff.
N-mm N-mm
1
COMMENTS
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