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Resultant and Equilibrant Forces

Omeir, Amna Ali M.; Orfanel, Jessel Ann R.; Paelmo, Vicente B.; Pitong, Carmirose R.; Punzalan,
Cristina A.
Group No. 6: 2F-MT
8 September 2016
Mesias, Justin; Nieto, Xandro

The sum of two or more vectors is called the
resultant force. The resultant force can be calculated
using the method of vector addition. To achieve manipulation of forces in a controlled and measurable
equilibrium, the equilibrant force should be added in way. The Force Table can be used to establish
the resultant force. Equilibrant force points exactly in
the opposite direction of the resultant force.

In this experiment, the washer was positioned

equilibrium for a given object and then the addition of
and balanced in a force table using the pulleys and
vectors can be observed and measured.
strings. The pulleys were being adjusted in such a way
that the washer was in the center of the force table at
the point where all forces reached equilibrium. The
resultant and equilibrant forces is to be determined
using the component method. Moreover, one gains
experience using the force table and applies the
knowledge and concepts about vector addition,
resultant and equilibrant forces.


In physics, the mathematical quantities used to

describe the motion of objects can be divided into two
categories. These are Scalar quantities and Vector Figure 1. The Force Table
quantities. Scalar quantities can be fully described by
magnitude (or a numerical value) alone, setting aside
direction. On the other hand, Vector quantities require
both magnitude and direction for it to be fully
The tool uses strings which are tied to a ring
described. In this experiment, we focus more on Vector
quantities because we are working with forces. that serves as the object that the forces act on. The
strings are then hung over the circular table via pulleys.
The performed experiment uses a physics lab Attached on these strings are the weights situated in
apparatus called a Force Table (Figure 1) to different directions, which are the ones that produce the
demonstrate and allow the students to grasp a thorough
forces. In a usual scenario, two or more forces are
understanding of the concept of resultant and
equilibrant forces, as well as the vector addition of specified, and then one other force is added so that it
forces. This tool is based on the principle of balances out the effect of the other forces. The force
equilibrium. It allows the application and that balances or cancels out the effect of other forces,
and brings the object to equilibrium is called the
equilibrant, . When this force is added to the force
system, and the objects reach the state of equilibrium, as the equilibrant, because it is the force that
the sum of all the vector forces is equal to zero. Thus,
the equilibrant is equal to the negative of the
resultant, , which is the vector sum of two or more
allowed the object to reach equilibrium. This thereby
allows us to obtain a specific magnitude and direction
for each of the three concurrent forces.
The formula for two given forces and their equilibrant

There are two ways to compute for the

The equilibrant, has the same magnitude resultant: the Parallelogram method and the
Component method, but in this experiment, we focused
on the use of the Component method in adding vectors.
With all three individual forces determined, we derived
as the resultant, but they are opposite in direction. the experimental resultant forces by computing for the
negative vector any one of the three forces given the
two other forces.

This is shown in Figure 2. The component method mainly uses the

summation of the x (horizontal) and y (vertical)
components to solve for the magnitude and direction of
the resultant force. The formula for the summation of
the x (horizontal) and y (vertical) components are as

Where is the horizontal component of

Figure 2. Illustration of the equilibrant and resultant

and is the vertical component of , and

During the manipulation process to attain

equilibrium, two of the three force table clamps are is the horizontal component of and
kept in place to remain in their initial position. Only the
third force table clamp was adjusted in such a way that
the ring remains stable in the center. This indicates that
is the vertical component of .
the third force has successfully balanced out the effect
of the two other forces. It also means that the forces
exactly cancel out each other, leaving the object in the
state of equilibrium. In this case, the third force serves When using the component method, firstly, it
is very important to know the magnitude and direction
of your two individual forces. For the direction, we
checked the values of the angles where the strings were
lying. On the other hand, for solving the magnitude, the wherein r is the magnitude of the force and
following formula is used:

is the direction.
After getting the values of each forces x and
y components, we then add the x components of
to get the summation of their x

components. Similarly, we also add the y components

to get the summation of their y components. Here, we
use the formula previously mentioned above.

where m stands for mass in kilograms, while g stands

for gravity, which has a constant value of

. The unit for magnitude is Newtons (N).

To solve for the
resultant magnitude,
we use the Pythagorean
Theorem wherein

is the resultant, is

and is . The formula to be used is:

Figure 3. Illustration of a vector

After solving for the value of the magnitude, the

direction of the resultant can now be computed. To
After solving for the magnitude and direction
solve for the direction, (Figure 3), we use the
of the individual forces, these are then broken down
into their x (horizontal) and y (vertical) components arctangent or inverse tangent function:
using the following trigonometric functions: cosine for
x (horizontal component) and sine for y (vertical
component). (Figure 3)

But remember that the direction still depends on your

left the pin on the middle to hold the masses. Then, the
and components. If your and are group loaded the force table with weights which values
were converted to Newtons with the use of the formula
both positive, it means that your is in Quadrant I. If or
this is so, then we do not do anything. The direction we
have solved for will remain the same. It will be equal to
its reference angle, . (1) On the other hand, if your

is negative and your is positive, it

The values are as
means that your is in Quadrant II. If this is so, then

you must first subtract your reference angle from 180.

follows: . Also, the angles are measured. The group got
(2) If your is positive and your is
the x and y components using the formulas

negative, it means that your is in Quadrant III. If

this is so, then you must first add 180 to your reference Then the group computed for the summation of x by
angle. (3) Last but not the least, if your and adding each of the pairs horizontal components and of
y by adding each of the pairs vertical components.
are both negative, it means that your is in And then the resultant comes next and was computed
by the group using the formula
Quadrant IV. If this is so, then you must first subtract
your reference angle from 360. (4)

(1) =

On the other hand, The group got the reference
(3) angle by using the formula


The group retained the angle if it is on Q1, 180- if

Q2, 180 + on Q3 and 360 R on Q4.Then the
Results and Discussion computation and results is as follows:
Using the target point values given for vectors
A,B and C,the group created three real vectors that will
be masses hanging from the force table at specified
angles. And then the group measure the real values by
measuring the masses for each of the vectors with its
disk weights. The mass should include the hanger.

The force table should have a center pin or

ballpen so that weight hanging unbalanced does not
crash to the table. For that certain moment, the group
Horizont Vertical
Magnitu Direct
al Compone furthermore it is the angle we computed itself. But we
de ion
Compone nt
immediately recomputed the angles twice and we got it
1.9914 57.0 1.0846 1.6701 correctly.
2.4569 179.0 -2.4565 0.0429
SUM: = =
-1.3719 1.7130 Direction Horizontal Vertical
Component Component
2.4569 N 179.0 -2.4565 0.04287
Magnitude Direction
2.1926 N 128.7 2.2089 N 307.0 1.3293 -1.7641

SUM: = -1.1272 = -1.7641

Resultant Force
Magnitude Direction
Resultant Force Horizontal Vertical
Magnitude Direction
Component Component 2.0575 N 236.8
1.9914N 57.0 1.0846 1.6701
2.2089 N 307.0 1.3293 -1.7641
Conclusions and Recommendations
SUM: = 2.4139 = -0.094 Resultant force is defined as the vector
Resultant Force sum of the forces while Equilibrium force is
defined as the force that equalizes another
Magnitude Direction
force or a resultant force. In this experiment,
2.4157 N 357.8 we were able to balance the object at the
center of the force table by determining the right mass
and position of the pulleys. With all three forces, we
derived the experimental resultant values by computing
for the negative vector of the three forces. The same
procedure goes with computing for the experimental
equilibrant values. Component method was used in
computing the resultant forces.

Based on the results, the experimental and computed

resultant values are close to each other. A very small
difference on their values was recorded. The
experimental equilibrant force on the other hand was
the negative vector of each of the three forces. They
have the same magnitude but are opposite in direction.
Sources of error encountered may include (1)
The resultant forces or the experimental shouldve or the initial measurements of the pulleys were
atleast as same as the computed forces or the resultant. inaccurately obtained because it is not properly placed
On the other hand the equilibrant forces was in the on the triple beam balance. (2) The weights of the
other side of the force we are referring to,thus the pulleys were not properly distributed in the force table
magnitude will be retained and its angle will be on the due to incorrect angle position.
reference point. We encounter some difficulties on the
For those students wanting to repeat this
experiment when we are encoding the angles because
experiment, make sure to follow carefully the
some of the angles is not the reference angle
procedures given. The values should be recorded and
tabulated accurately. The students must also be careful
in computing for the values so that expected results Vector X Component Y Component
will be computed. A 2000 0
B 750 1299
Questions and Answers C -866 500
1. Differentiate between the resultant and the D -2687 -2687
equilibrant of two forces. -803 -888

A resultant force is a force which is the sum of

two or more vector forces. It is usually computed using (803) 2 (888) 2
the component method. If a resultant force acts on an Magnitude =
object then that object can be brought into equilibrium = 1197.2 N
by applying an additional force that exactly balances
this resultant. Such a force is called the equilibrant and y
is equal in magnitude but opposite in direction to the x
original force acting on the object. Thus, equilibriant Direction = -tan
force is the negative vector of the resultant force. 888
2. If three concurrent forces are in equilibrium, 803
= -tan
what is the relation between any one of the
three forces and the resultant of the other two = 47.87 + 180 = 227.9
forces ?
= 1197.2 N , 227.9
Any one of the three forces in equilibrium is = 1997 N, 228
the negative vector of the resultant of the two other
forces. This means that they possess the same
magnitude but are opposite in direction and vice-versa. Henderson, T. (n.d.). Resultants. Retrieved September 7,
2016, from
3. If two forces with the same magnitude were
exactly in opposite direction, what is the 1/Resultants
magnitude and direction of their resultant ?
Henderson, T. (n.d.). Scalars and Vectors. Retrieved
What is the magnitude and direction of their September 7, 2016, from
equilibrium ?
If two forces are equal but are in opposite
direction, then they will cancel each other out. The
resultant force would be 0. There will be no magnitude Henderson, T. (n.d.). Addition of Forces. Retrieved
and direction for the equilibrant because there is no September 7, 2016, from
value for the resultant force.
4. Use the component method to find the
magnitude and direction of the resultant of the
concurrent forces given below:

A = 2000 N at 0 Lab 3: Vectors and the Force Table. Retrieved September 7,

2016, from
B = 1500 N at 60 2120/Lab%20Writeups/force_table.htm

C = 1000 N at 150 Luebkeman, C. H., & Peting, D. (1998). The Elements of

Coplanar Force Resolution. Retrieved September 7, 2016,
D = 3800 N at 225 from