COPLANAR and NON-COPLANAR FORCES

Introduction: This unit seeks to introduce to you the different systems of forces. The prerequisite for this is the concept of a force and the various forms of forces occurring in nature. In addition to this, you should have the basic knowledge of algebra, co-ordinate geometry, trigonometry and a little bit of calculus.

COPLANAR and NON-COPLANAR FORCES

Introduction: This unit seeks to introduce to you the different systems of forces. The prerequisite for this is the concept of a force and the various forms of forces occurring in nature. In addition to this, you should have the basic knowledge of algebra, co-ordinate geometry, trigonometry and a little bit of calculus.

Objectives: After studying this unit, * you should be able to identify the different systems of forces, * concurrent forces vector ally, resolve forces into components, * forces by components, find the moment of a force, * find the resultant of non-concurrent forces.

COPLANAR and NON-COPLANAR FORCES

System of Forces:

The action of one body on any other body can be called a force. These actions may be of various forms: gravitational force known as weight of a body, force exerted by an elastic spring, force exerted by a locomotive on the train by the track.

To specify a force, you need to know its magnitude, direction and the point of application. The magnitude is in Newton in SI unit. By drawing a line to scale showing the magnitude, the arrowhead indicating direction. Such a straight line is called a vector.

A combination of several forces acting on a body is called a system of forces or a force system.

Example Consider a sphere of mass m suspended by means of a string resting against a

smooth wall, as shown in Figure 1. What are the forces acting on it?

Solution: Let us identify the forces acting on the sphere. These are as follows: 1) Weight of the sphere W = mg acting vertically downwards from the centre of gravity of the sphere. 2) Tension in the string Reaction offered by the wall. Thus, the sphere is subjected to a system of three forces as shown in Figure 2.

Figure 1 Figure 2

* If coplanar forces is acting on a body

===> its total effect is usually expressed in terms of its resultant.

* Force being a vector quantity the resultant

===> by using vector algebra

e.g.) if the resultant of two forces is to be found out then

the law of parallelogram of forces is used.

1. COPLANAR FORCES

* If coplanar forces is acting on a body

===> its total effect is usually expressed in terms of its resul-tant.

* Force being a vector quantity the resultant

===> by using vector algebra

e.g.) if the resultant of two forces is to be found out then

the law of parallelogram of forces is used.

Law of Parallelogram of Forces :

If two forces acting at a point are such that they can be repre-sented

in magnitude and direction by the two adjacent sides of paral-lelogram,

the diagonal of the parallelogram passing through their point of inter

section gives the resultant in magnitude and direction.

1. COPLANAR FORCES

Law of Parallelogram of Forces : Consider two forces P and Q acting at point 0 in the body as

shown in Figure (a). Their combined effect can be found out by con-

structing a parallelogram using vector P and vector Q as two adjacent

sides of the parallelogram as shown in Figure (b). The diagonal passing

through 0 represents their resultant in magnitude and direction.

Figure (a) Figure (b)

1. COPLANAR FORCES

Law of Polygon of Forces :

If more than two forces are acting on a body, then the resultant can be found

by repeated applications of parallelogram law or the triangle law.

Consider five forces each of 80 N acting at o in a body. Draw forces of polygon and show the resultant of all the forces.

Let us construct a polygon such that the forces A, B, C, D and E represent the sides of

a polygon taken in order, each force being drawn from the end of earlier force then

their resultant is represented by the line joining the starting point of the first force A

to the end of the last force E.

1. COPLANAR FORCES

Resolution and Composition:

Splitting the force into components ===> Resolution of a force - for determining

the resultant Finding the resultant of any number of forces ===> Composition of forces

A force making an angle 0 with respect to x axis as shown in Figure, can be resolved into two components FX, and FY, acting along x and y axes respectively.

1. COPLANAR FORCES

Example (Resolution and Composition)

A force of 120N is exerted on a book in the ceiling as shown in Figure 1.

Determine the horizontal and vertical components of the force.

Solution:

Figure 1