# What are the forces at a point that affect engineering problems?

In our last article, we looked at how we can solve practical problems that involve distance and velocity.  Now we’re going to look at forces at a point, what they are, and how they can affect engineering problems.

Before we jump in, let’s check out the definitions of some of these forces to make sure we fully understand them.

## Centre of Gravity

The centre of gravity of an object is a point where the resultant gravitational force acting on the object may be taken to act.  For a thin, uniform rod, the point of balance and hence the centre of gravity are halfway along the rod, as shown in the image below.  The centre of gravity of a circular object is at the centre of the circle, as shown in the image below:

## Equilibrium

An object is in equilibrium when there is no tendency for the object to move due to forces acting on it.  We can divide the state of equilibrium into three groups:

1. If an object is in stable equilibrium and a disturbing force is applied, the centre of gravity is raised.  When the disturbing force is removed, the object returns to its original position.  A ball bearing in a hemispherical cup is in stable equilibrium.
1. When an object is in unstable equilibrium and a disturbing force is applied, the centre of gravity is lowered.  The object moves away from its original position.  A ball bearing balanced on top of a hemispherical cup is in unstable equilibrium.
1. When an object is in neutral equilibrium and has a disturbing force applied, the centre of gravity remains at the same height.  The object doesn’t move when the disturbing force is removed.  A ball bearing on a flat, horizontal surface is in neutral equilibrium.

## Mass

The mass of an object has an SI unit of kilograms, with the symbol m and the unit kg.  It can be defined in one of these ways:

• A measure of the amount of matter in the object.
• A measure of the resistance of an object to being accelerated.

## Forces

When forces are all acting in the same plane, they are called coplanar.  When forces act at the same time and at the same point, they are concurrent forces.  Force is a vector quantity, and has a magnitude and direction.  It can be represented graphically by a line drawn to scale in the direction of the line of action of the force.

A force is a push or full and alters an object’s state of rest or uniform motion in a straight line.  The action of one component on another and the weight of a component are examples of forces.  A force moves or tends to move an object in the direction of its action. A force is characterised by its magnitude and direction and its effect is influenced by its point of application.

The unit of force is the Newton (N). This is defined as the force required to cause a mass of 1 kg to experience an acceleration of 1m s-2

## Components of a force

It is possible to replace a single force by two other forces in any two convenient directions. The forces are then said to be resolved into the components of the single force. The most convenient choice of directions in which to resolve a force is two directions at right angles to each other.

In general, the component of a force is the original force F multiplied by the cosine of the angle between the direction of F and the direction of the component required.

In the above diagram,

The x-component of F: Fx=Fcos

The y-component of F: Fy=Fsin

In our next article, we’re going to look at how we can use engineering concepts to solve practical problems, so make sure you keep an eye out for it.

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