ASSUMPTION UNIVERSITY
Faculty of Engineering
Physics Laboratory I
1. Experiment:
: Force table
2. Objective:
: 1. To determine the equilibrant of two concurrent forces and then three
concurrent forces by using force table.
2. To determine the resultant of two concurrent forces and then three
concurrent forces theoretically by using addition of forces using
vector addition rules (analytical method and graphical method) and
verify the results using force table.
3. Apparatus:
: Force table, weight hangers, assorted weights, pulleys, graph papers.
4. Theory:
: A vector represents a force. Vectors are quantities that have both magnitude
and direction and follow specific rules of addition. If two or more forces are acting on an
object there will be a single force as the same effect on that object and that single force is
called resultant force. The process of finding resultant force is called composition of forces.
The part of the force effective in some particular direction of a force is called a component
of the force. The process of finding components of force in specified directions is called the
resolution of force.
The processes of composition and resolution may be performed by graphical
method or analytical method. If (Figure 1.) is the force being considered, the analytical
method of finding the components consists of applying the proper trigonometric relations to
the triangles formed by the force
and
and its components. As shown in Figure 1 the forces
x
are the horizontal and vertical components, respectively, of the force .
Graphical method can be used by drawing force diagram (or) vector diagram
on a graph paper with suitable scale. Parallelogram method can see on the force diagram.
From the force diagram, resultant force, component of forces and equilibrant can be
measured according to the scale.
When two or more forces are acting on an object, if the object is still at rest
without moving or rotation is called the object is in static equilibrium.
The single force, which will hold a system of concurrent forces (force
y
acting though a common point) in equilibrium, is called the equilibrant ( ) of the system. It is
equal in magnitude to the resultant ( ), but opposite in direction. Equilibrant can be found by
performing experiment using the force table. Direction of equilibrant ( ) = o +180o and
magnitude of = Gravitational force (weight) will be used in this force table experiment.
Composition of forces
If
x
and
y are
given,
Resolution of force
y
θ
Resultant force ( ) or ( )
(or)
=
If magnitude of force
and direction of force
(angle  ) is given,
f x2  f y2
x
Component of forces
Direction of resultant force
o = tan1
=
y=
x
fy
fx
Fig. 1
1-
cos 
sin 
Application of theory concepts on force table experiment
Masses are placed on weight hangers attached to the end of the strings running over the
pulleys to provide the needed force (gravitational force or weight). After that, all assigned forces are
acting on the ring and can be seen on the force table.
[Total weight of masses and weight hanger create tension (force) in the strings. Be notice that the
weight of the hanger constitutes a portion of the suspended weight. ]
When the vector sum of these forces (tensions) is zero on the force table, the ring is in
equilibrium and need to rests in a position concentric with the center of the force table.
[Note: - To be in equilibrium and rests in a position concentric with the center of the
force table, the ring must be centered at the post. Only when the ring is centered at the post, correct
direction of force can be seen on the force table according to the degree divisions on the force
table.]
To balance the force on the force table, a force that is equal in magnitude and opposite
in direction must counter-balance the resultant. This force is the equilibrant.
Example of force diagrams for the forces
equilibrant.
Suspended weight (acting force on the string)
1,
2
and
3
and their resultant and
= (Weight of masses on the hanger) +
(Weight of the hanger)
= (Total mass on the hanger + mass of the hanger) (Acceleration due to gravity) = mg
f2
f1
3.3 N
o
120
R
o
45
240
2.0 N
2.4 N
o
2.1 N
2.1 N
E
4.2 N
f3
5. INSTRUCTIONS
5. (a) Instruction (1)
1. Set the force table to be in horizontal position by using leveling screws.
2. Take an assignment of Assignment 1 (two concurrent forces arrangement) from your
Achan.
3. Place pulleys on the force table at the positions of the two assigned forces.
4. Suspend the required proper amount of weight according to the assigned forces on each
hanger attached to the string running over the pulley. [Each hanger has 50g mass for
small size (or) 100 g mass for bigger size.]
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5. Find the position of the pulley by using the third string in the required direction to
produce equilibrium, and then set the pulley at the required position.
6. Suspend the required proper amount of weight on the hanger attached to the third string
running over the pulley until equilibrium is established. The equilibrant is established
for given two forces.
7. Calculate the vector sum of the horizontal components
x
and the vector sum of the
vertical components y of assigned two forces. Consider the sum of x and y as single
force that is the resultant force. Then calculate the direction of resultant force.
8. Draw the vector diagram (force diagram) of the system including assigned two forces,
resultant force and equilibrant with labels and indicate their directions on a graph paper.
9. Record your data in the data table.
5. (b) Instruction (2)
1. Set the force table to be in horizontal position by using leveling screws.
2. Take an assignment of Assignment 2 (three concurrent forces arrangement) from your
Achan.
3. Place pulleys on the force table at the positions of the three assigned forces.
4. Suspend the required proper amount of weight according to the assigned forces on each
hanger attached to the string running over the pulley. [Each hanger has 50g mass for
small size (or) 100 g mass for bigger size.]
5. Find the position of the pulley by using the fourth string in the required direction to
produce equilibrium, and then set the pulley at the required position.
6. Suspend the required proper amount of weight on the hanger attached to the fourth
string running over the pulley until equilibrium is established. The equilibrant is
established for given two forces.
7. Calculate the vector sum of the horizontal components
x
and the vector sum of the
vertical components y of assigned three forces. Consider the sum of x and y as
single force that is the resultant force. Then calculate the direction of resultant force.
8. Draw the vector diagram (force diagram) of the system including assigned three forces,
resultant force and equilibrant with labels and indicate their directions on a graph paper.
9. Record your data in the data table.
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6. Assignment questions
1. How can you explain resultant of forces?
2. How can you explain component of a force?
3. What does mean equilibrant?
4. What kind of forces do you use for the assigned forces on the force table? How can you
calculate the magnitude of assigned forces? Explain.
5. How can you set the instrument to get the correct direction of force according to the
given angle value on the force table?
6. How can you set the instrument to get the correct direction of equilibrant on the force
table according to the given assigned forces?
7. What is the function of pulley on the force table?
8. Why does the ring need to be centered at the post on the force table in finding the
equilibrant?
9. In a certain experiment using a force table, the system is in equilibrium at the center post
with four forces are acting on the center ring and all forces are not in straight-line
positions. If equal weights are taken away from each hanger, should the system be still
in equilibrium at the same position? Explain.
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Name
Code
Sec.
RECORD DATA
(Instruction (1)
Assignment I (You must show complete theoretical calculations on separate sheet.)
Table 1
Force
Magnitude of force
Used total mass
(kg)
(N)
Direction
(degree)
1
2

E (Equilibrant)
Experimental
(By experiment)

R ( Resultant)
Theoretical
(By calculation)
Table 2
(Instruction (2)
Assignment 2 (You must show complete theoretical calculations on separate sheet.)
Force
Magnitude of force
(N)
1
2
3

E (Equilibrant)
Experimental
(By experiment)

R ( Resultant)
Theoretical
(By calculation)
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Used total mass
(kg)
Direction
(degree)
Some concepts, important points and examples
One newton is the amount of net force that gives an acceleration of one meter per second
squared to a body with a mass of one kilogram. [1 N = 1 kg . ms-2]
(a) Description of force table
Vectors are quantities that have both magnitude and direction and follow specific rules of
addition. A vector represents a force. One of the conditions for a body to be in static equilibrium (not
accelerating) is that the vector sum of all the forces acting on th
If a
number of nonparallel forces are acting at the same point on a body, it can be shown that a single
force, which will produce the same effect on the body, may replace them. Such a force is called the
resultant (R) of the original forces. The process of finding this resultant is called the composition of
forces. The single force, which will hold a system of concurrent forces (force acting though a
common point) in equilibrium, is called the equilibrant (E) of the system. It is equal in magnitude to
the resultant (R), but opposite in direction. In the diagram R = -E
FY
R

FX
E
The force table is a circular steel table that has the angles 0o to 360o inscribed on
the edge. To use the force table, pulleys are placed at the angles specified, with the strings attached
to the center ring running over the pulleys. [We will use the gravitational force (or) weight for
force table experiment. Weight of an object, W = mg (where g is acceleration due to gravity)]
Masses are placed on weight hangers attached to the end of the strings to provide the needed force
(gravitational force or weight). [That total weight of masses and holder create tension (force) in the
strings.] NOTE, that the weight of the hanger constitutes a portion of the suspended weight.
When the vector sum of these tensions is zero, the ring is in equilibrium and rests in a position
concentric with the center of the force table. To balance the force on the force table, a force that is
equal in magnitude and opposite in direction must counter-balance the resultant. This force is the
equilibrant.
In this laboratory you will add some forces acting on a body both graphically and using
components, by adding the vectors, the resultant vector is found and that can determine what
additional force must be added to achieve equilibrium.
(b) Important points for handling force table
1. Force table should be in horizontal position.
2. To check for equilibrium and to minimize the effects of friction in the pulleys, raise the
ring a short distance above the table and release (jiggle), noting the new position it takes.
3. The ring must be centered at the post to get the correct direction of force on the force table
after jiggling.
4. To get the correct direction on the force table according to the given angle value, the edge
of the pulley holder and the string should be the same position with the mark of
required angle position exactly.
5. The weight of the hanger constitutes a portion of the suspended weight.
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