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.
Force from static mass
Figure 1: Force exerted by a static mass

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.

Mass force and reaction
Figure 2: Force with equal and opposite reaction

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.

Out of balance forces and equilibrium
Figure 3: Effects of force equilibrium and out-of-balance forces

Accelerations of masses can be caused in a number of different ways:

  • Acceleration due to gravity.
  • The change of speed of a moving object such as acceleration, deceleration and impact.
  • An object moving on a non-straight path, such as around a corner. A velocity is a speed in a given direction, to change the direction an acceleration in another direction is needed, this either requires or gives rise to a force.

To understand the forces applied on objects and materials an Engineer must understand the magnitude of both the mass and the acceleration. Structural Engineers usually deal with static masses (masses with no acceleration) and can allow for dynamic effects by increasing the applied loading by a dynamic increment or impact factor. Mechanical and Aeronautical Engineers will need to quantify the mass and it’s likely acceleration given the function and use of the object being analysed

Often, people will talk about “g-forces” or “3g”, this is a quick way of expressing an acceleration in multiples of the force due to gravity. The acceleration due to gravity on earth is often given the algebraic symbol “g”. Therefore, 3g is an acceleration equal to 3 times that of gravity = 3 x 9.81 = 29.43 m/s². When Formula 1 drivers’ corner or crash, they can experience up to 5g (5 x 9.81 = 49.05 m/s²) accelerations on their body. The force they feel in these instances is therefore 5 times what they would feel if they were stationary.


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