Representing Force

What is a vector?QUANTITIES IN SCIENCE

There are two types of quantities in science:

Scalar quantities.

Vector quantities

Scalar quantity: It is a quantity which has only magnitude. They can be totally described by a number and a unit. Volume, area, temperature, energy, speed, mass, time are all scalar quantities.

Vector quantity: It is a quantity which has both magnitude and direction. Force, velocity, acceleration, and displacement are vector quantities.

What is a vector?

An arrow drawn to scale is called a vector.

A vector has the following properties:1. A point of application (where it is applied)2. A magnitude (or size)(how large it is)3. A direction

All the forces applied to the bricks shown below have the same magnitude, 20N, but they are all different forces since their directions are different.

Example:Show the following forces using vectors.

a) A block is pulled to the east with a force of 4 N.

b) A chest is pulled to the southwest with a force of 3 N.

c) Three forces act on a block to move it, one with 2 N due north, one with 3 N due east and one with 3 N due west.

COMBINING FORCES

Resultant force (R): It is a single force which has the same effect as two or more forces acting together.

Component forces: They are the forces that form a resultant.

The arrowhead () over each letter shows that it is a vector quantity, which means the quantity also has a direction.

Rule for addition of vectors (forces): Rule for addition of vectors (forces):

1. Add the forces head to tail without changing their magnitude and direction

2. Draw a force from the tail of the first to the head of the last.

Combining Forces Acting in the Same Direction

To find the magnitude of a resultant of two forces acting in the same direction we add the magnitudes of the components.

Combining Forces Acting in Opposite Directions

Let F1 and F2 be forces in opposite directions and let F1 be greater than F2. Then the magnitude of the resultant is The direction of the resultant force is in the direction of the greater force.

Example:What will be the net force on the box in the

figure below, if it is pulled by the two different forces in opposite directions?

TURNING EFFECT OF FORCES

If a force is applied on a body which is suspended, hinged or pivoted, the force may cause the body to turn.

Moment of force The turning effect of the force is called

moment.

Conditions for Equilibrium There are two conditions for equilibrium:

1. The sum of the forces in one direction must be equal to the sum of the forces in the opposite direction.

Conditions for Equilibrium 2. The sum of the clockwise moments about any

point must be equal to the sum of the anti-clockwise moments.