Statics – SS3 Further Mathematics Lesson Note (Second Term)

A force is an action that tends to change the state of a body at rest or in uniform motion in a straight line. Forces acting on a body can be combined using a polygon of forces, which gives their resultant. A single force can also be split into horizontal and vertical components, called resolution of forces.

Behavioural objectives

By the end of the lesson, students should be able to:

• define force;
• explain what a polygon of forces is;
• explain what is meant by resolution of forces;
• find the horizontal and vertical components of a force inclined to the horizontal.

What is a force?

Force is that action that tends to change the state of a body at rest or in uniform motion in a straight line.

What is a polygon of forces?

A polygon of forces is a broken line that is constructed to determine the resultant vector (geometric sum) of a given system of forces.

What is resolution of forces?

Resolution of forces is the splitting of a given force into two parts. One part acts along the x-axis and is called the horizontal component. The other acts along the y-axis and is called the vertical component.

If a force P acts at a point at an angle θ to the x-axis, then:

• horizontal component = P cos θ
• vertical component = P sin θ

Example: resolution of forces

A force P is 230 N. It is inclined to the horizontal at an angle of [angle missing]. Find the horizontal and vertical components of P.

Evaluation

1. Define force.
2. What is a polygon of forces used for?
3. What is meant by resolution of forces?
4. A force P acts at an angle θ to the x-axis. Write down its horizontal and vertical components.

Assignment

Work on the following questions from New Further Mathematics Project 3:

• Page 186, exercise 12, questions 1, 2, 3, 5, 7 and 8.
• Page 258, revision exercise chapter 12, questions 13, 17, 20 and 23.