3B Scientific Force Table - Manual (Page 2)

2
on the direction in which the forces act. The resul-
tant of two forces acting at the same point in a
single plane is defined as that force which, acting
alone in the same plane, would have the same
effect as the combination of the two forces. A force
of equal magnitude to the resultant but acting in
the opposite direction therefore maintains the
body in equilibrium. The resultant can be obtained
by analysis or by graphical means using various
laws (parallelogram of forces, triangle of forces,
polygon of forces).
A parallelogram of forces represents two forces
acting simultaneously on a body as two adjacent
sides of a parallelogram. The magnitude and direc-
tion of their resultant is then given by the diagonal
originating from the same point.
This theorem can be expressed mathematically as
follows: When two forces A
r
and B
r
acting on a
body with an angle
θ between them, the resultant
R
r
is given by:
θ + + =
cos AB B A R 2 2 2
If
α is the angle between the resultant and force
A
r
then:
θ +
θ
= α
cos B A
sin B
tan
With the law of the triangle of forces, two forces
acting simultaneously on a body are represented in
terms of magnitude and direction by two following
sides of a triangle. The magnitude and direction of
the resultant is then given by following the third
side of the triangle in the opposite direction.
From this it can be determined that a body is in
equilibrium if three forces are acting upon it,
which can be represented by the three sides of a
triangle.
If more than two forces act on a body at once, the
law of the polygon of forces is used. This represents
several forces acting at the same point as following
sides of a polygon where one side remains open. As
for the triangle, following the side that closes the
polygon in the opposite direction gives the resul-
tant force.
Therefore a body is in equilibrium when several
forces act upon it that can be represented as a
closed polygon. The vector sum of the individual
forces is equal to zero and so is the resultant force.
On closer observation, this law can be seen to be a
simple extension of the law of the triangle of
forces. The force table is suitable for demonstrating
vector addition and equilibrium of forces and for
confirming the graphic and analytical methods.
The equilibrium between two or three forces can
be demonstrated and the magnitude and direction
of each force easily determined.
4. Operation
4.1 Equipment Setup
• Place the base on an even surface.
• Screw the centre rod vertically into the base.