- 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 35^{0} with the horizontal is 45N. Find the force F.

**GENERAL EVALUATION**

- The forces of magnitude 35N and 45N act on a particle in the directions 180
^{0}and 315^{0}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.

- 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.

**READING ASIGNMENT**

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 120^{0}. 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) 60^{0} (b) 120^{0} (c) 180^{0}

3. A force P of magnitude 60N makes an angle of 40^{0} 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 120^{0} to each other.

(a) 2√61N (b) 61√2N C 39N