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5.1.4 Force and moments
Wednesday, 05 July 2017
You should be able to:
(a) understand that the weight of a body may be taken as
acting at a single point known as its centre of gravity.
(b) understand a couple as a pair of equal parallel forces
tending to produce rotation only.
(c) define and use the moment of a force and the torque of
a couple.
(d) show an understanding that, when there is no resultant
force and no resultant torque, a system is in equilibrium.
(e) apply the principle of moments to solve problems
involving forces acting in two dimensions.
The centre of mass is the point where all of the mass of
the object is concentrated. When an object is supported
at its centre of mass it will remain in equilibrium.
If the object is uniform, for example a meter stick, the
center of mass will be at the exact geometric center; if
the object is irregular in shape the center of mass will be
closer to the heavier end.
An easy way to determine the location of the center of
mass of a rigid pole is to support the pole on one finger
from each hand. Gently slide your fingers together. When
your fingers meet, you will be at the centre of mass.
Try it with a bat or a broom.
To find the center of mass of an planar object use a plumb
line.
Suspend the mass from each vertex and trace the plumb
line's location. Since the center of mass will fall below the
suspension point the center of mass will be at the
intersection of all of the plumb lines.
Where is the centre of mass here ?
The Moment of a Force (also called torque)
The moment of a force is a measure of its turning
effect.
The moment can be calculate using the following
equation.
Moment = Force ×Perpendicular distance of force from
"pivot"
The two obvious changes the person could make in order
to open the door more easily are he/she could
1. increase the distance "r“
2. push at 90° to the door.
If the angle between the line of action of the force and the
door is 90°, we have
Moment = Fr
This is the maximum value of the turning effect.
What happens when the pairs of forces
shown below act on the green block ?
Two equal and oppositely directed parallel but not
collinear forces acting upon a body. The moment of the
couple (or torque) is given by the product of one of the
forces by the perpendicular distance between them.
If the distance between the horses is d and the force
each one exerts is f. The moment of the couple is given
by:
Moment = (f  ½ d) + (f  ½ d)
=fd