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# Statistics: Definition of concepts and Resultant of two forces

• Definition of Concepts
• Resultant of two forces
• Components resolution of forces

DEFINITION OF CONCEPT

Statics is the study of bodies which remain at rest under the action of given forces.

Mass: This is the quantity of matter contain in a body.  Mass of a particular body does not change and the standard unit is kilogram.

Force: Force is that action which tends to change the state of rest or uniform motion of a body in a straight line.  It’s a vector quantity sine it has magnitude and direction.  The unit of force is Newton.

:.  F = Ma

Where M =  Mass,  a = acceleration.

Composition of Forces:  Two or more concurrent forces can be combined to obtain a single force.  Therefore, resultant force is the force produced or obtained when two or more concurrent forces are combined.

A force can be resolve by

I Graphical Method                   II. Analytical Method.

Analytical Method:  The parallelogram law of composition of two forces is used to find the resultant force of two or more forces.  Hence, parallelogram law states that if two forces acting at a point are represented in magnitude and direction by two adjacent sides of a parallelogram, then the resultants of the two forces, is represented in magnitude and direction by the diagonal of the parallelogram, drawn from the point of action of the two forces.

## Resultant of two forces:

EVALUATION

The vertical component of a force F which makes an angle of 350 with the horizontal is 45N.  Find the force F.

GENERAL EVALUATION

1. The forces of magnitude 35N and 45N act on a particle in the directions 1800 and 3150 respectively.  Find the resultant of these forces giving:

a.   the magnitude correct to the nearest whole number   b. the direction correct to the nearest degree.

1. A vertical force of 6N and a horizontal force of 8N act on a body.  Find the magnitude and the inclination of the resultant force to the horizontal.

Read Composition and Resolution of Coplanar forces on pages 154 to 165 of further mathematics project III.

WEEKEND ASSIGNMENT

1.         Two forces each of magnitude PN are inclined to each other at an angle of 1200. Find the magnitude of their resultant.

(a) P√3 N                     (b) P2N            ( c) PN

2.         Find the angle between the two forces 5N and 6N if their resultant is 8N.

(a) 600             (b) 1200                       (c) 1800

3.         A force P of magnitude 60N makes an angle of 400 with the horizontal. Use the information to answer questions 3 and 4

3.         Find the horizontal component of P

(a) 20N            (b) 45.96N                   (c ) 38.57N

4.         Find the vertical component of P

(a) 45.96N                   (b) 38.57                     (d) 20N.

5.         Find the resultant of forces 8N and 10N inclined at an angle 1200 to each other.

(a) 2√61N                    (b) 61√2N          C 39N