Physics Lab Report 2.0 Resultant and Equilibrant Forces

Resultant and Equilibrant Forces Esturco, Miguel S.; Garcia, Ian Thadeus S.; Gatchalian, Jeremiah S.; Katigbak, Jose Seatiel V.; Lacorte, Alice L. Group No. 3: 2JMT 09 September 2016 Mesias, Justin, Pascua, Esperanza

Introduction Forces exist as a result of an interaction between objects. Since force is a vector quantity, it has both magnitude and direction. Vectors are commonly represented using diagrams illustrated through arrows. The resultant force is the vector sum of two or more vectors. To accurately determine the resultant vector, a force table is used. A force table is a physics laboratory apparatus that consist of strings attached on a center ring on which is acted upon by a force. In the experiment, the researchers are expected to accurately balance the three weights acting upon each other using a force table. The experimenters should be able to manipulate the angles successfully in order to balance the forces on the weights. At the end of this experiment, the researchers should be able to compute the equilibrant forces in order to check if the gathered data of factors would suffice the theories. Theory A resultant force is an individual force combinative of a system of forces acting on a given body. Significant with resultant force is the fact that it has the same effect on the object as the original system of forces. It is as if the same forces are applied on the body when the original system is disconnected and replaced with said resultant force. To find the magnitude of the resultant force, one could use:

Where, R = Magnitude of resultant vector α = Direction of resultant vector P = Magnitude of vector P Q = Magnitude of vector Q θ = Angle between two vectors Then treat the summation of the X and Y components as legs of a triangle. With this in mind, the hypotenuse of the triangle created is equivalent to the resultant force based on the head-to-tail method. Thus, one could use the Pythagorean Theorem. C2 = A2 + B2

To compute the direction of the resultant force given the summation of all the X and Y components of the system, one could use the law of tangents. It is a statement about the relationship between the tangents of two angles of a triangle and the lengths of the opposing sides. Equilibrant Force is defined as a force that brings the body, of which a system of forces is applied, to a state of equilibrium. It is in fact equal in terms of magnitude and opposite in terms of the direction of the resultant force. Equilibrant force is a single force that, when applied to a moving body, will bring it to a halt where in it is motionless. To compute the equilibrant force, one could simply equate it to the resultant force due to its definition. When it comes to direction, it is exactly 180° from whatever the angle of the resultant force is. Results and Discussions Table 1.A shows the data gathered from the experiment using the force table. In the said experiment, three yarns with weights were used and manipulated to be able to get the ring stable and make the center of the table. Thus, different magnitude and different direction were applied to the specific forces. Table 1.A Fi F1 F2 F2 F3 F1 F3

Individual Forces Magnitude 0.1444 N 0.1110 N 0.1110 N 0.8230 N 0.1444 N 0.8230 N

Direction East 36º N of W 36º N of W 29º W of S East 29º W of S

Table 1.B shows the forces that result when two specific forces are combined. Table 1.B Resultant Forces (Experimental) Ri Magnitude Direction Fa 0.8230 N 29º E of N Fb 0.1444 N West Fc 0.1110 N 36º S of E Table 1.C shows the equilibrant forces which are the forces that have the same magnitude as

the resultant forces but only pointing at the opposite direction. Table 1.C Equilibrant Forces (Experimental) Ei Magnitude Direction FA 0.8230 N 29º W of S FB 0.1444 N East FC 0.1110 N 36º N of W Table 1.D shows the resultant forces that were computed from the given data Table 1.D Ri Fa Fb Fc

Resultant Forces (Computed) Magnitude Direction 0.0851 N 50.07º N of E 0.1638 N 8.9º N of W 0.0827 N 28.85º S of E

Conclusions and Recommendations Questions and Answers 1) Differentiate the resultant and equilibrant two forces. The resultant is the vector sum of all the individual vectors. It can be determined by adding the individual forces together using vector addition methods. Equilibrant is a vector that is the exact same size as the resultant would be, but the equilibrant points are exactly in the opposite direction.

3) If two forces with the same magnitude were exactly in opposite directions, what is the magnitude and the direction of their resultant? What is the magnitude and direction of their equilibrium? The magnitude of both resultant and equilibrant are zero and they will have no direction. 4) Use the component method to find the magnitude and direction of the resultant of the concurrent forces given below: a) b) c) d)

A = 2000 N at 0∘ B = 1500 N at 60∘ C = 1000 N at 150∘ D = 3800 N at 225∘

Given A = 2000 N at 0∘ B = 1500 N at 60∘ C = 1000 N at 150∘ D = 3800 N at 225∘

xcomponent 2000 750

y-component

-866.03

500

-2687.01

-2687.01

-803.04

-887.97

0 1299.04

r = √(803.042 + 887.972) r = 1197.23 N Φ = tan-1(-887.97/-803.04) = 47.9o (QIII) = 47.9o + 180o = 227.9o

2) If three concurrent forces are in equilibrium, what is the relation between any one of the three forces and the resultant of the other two forces?

Therefore, the Resultant Force is 1197.23 N at 227.9o.

Whichever among the three concurrent force is the equilibrant force of the two forces. They have the same magnitude but are in the opposite direction and their net force is zero.

[1] R. L. Timings, (1990). Mechanical Engineer's Pocket Book

References