# Force and Force Equilibrium

## What is a Force

A force is defined as a push or pull action imposed on one object by another object. Forces are best understood and defined by Newton’s Laws of motion, these state:

1. An object will continue to move in the same direction and the same velocity (speed) until a force acts upon it, this is known as an action.
2. A force, F, is defined as F = m a, where m is the mass of an object, and a is the acceleration (rate of change of velocity).
3. Every action has an equal and opposite reaction.

One of the key principles identified is F = ma, this can be used to establish a force an object exerts given its mass and acceleration

In the metric system, the typical units for mass are the kilogram, kg, and the typical units for acceleration are m/s², this gives the units of force equal to kg m/s², this is often expressed in newtons with the symbol N, 1 Newton on earth is approximately 100g.

The simplest application of this is to derive the force exerted by what appears to be a static mass, sat on the surface of planet earth. The mass is being held against the surface by the gravitational attraction of the earth, this imparts an acceleration due to gravity equal to 9.81m/s2 to the object For a given mass, the force of the object can be calculated
For rough engineering calculations, the acceleration due to gravity, g, can often be rounded from 9.81 to 10. In most cases this will give an overestimate of the force an object exerts and is therefore usually a safe rough assumption.
People often use the terms mass and weight incorrectly. Most people when asked how much they weigh will answer 12 Stone/80kg/160lbs, this is actually their mass, they would actually weigh 780 newtons.

To use the equation F=ma in a different manner. If an object was at rest and a force was applied to it, then we could work out the acceleration that would occur by rearranging the equation F=ma into a = F/m. Hence, if a force applied to an object it would undergo an acceleration.
If we re-visit our static mass sat on the surface of planet earth, then we will see that:

1. We can establish a value for the force the mass imparts, and
2. we can also observe that the mass is not moving or accelerating.

Hence, there must be some force acting on the force other than gravity to prevent the mass accelerating. In this case force equilibrium (the balancing of forces) is provided by the force of the mass pushing down and the force of the earth’s surface pushing up. As all the forces in the system are equal then the object remains static.

This is the principle of “Force Equilbrium” a state where all forces in a system are in balance, there is no net “out of balance force” and no acceleration of the system.
For most Civil and Structural Engineering applications force equilibrium is one of the governing principles, buildings and structures should stay where they are and not accelerate away!
In other field of Engineering, particularly Mechanical and Aeronautical Engineering, acceleration and motion is actively encouraged and out of balance forces are often imposed.