The study of forces is absolutely essential for gaining a profound understanding of the physical world. Whether delving into the realm of statics or dynamics, the concept of forces takes center stage, driving our fascination with the workings of the natural world. In statics, we are captivated by the intricate ways in which structures bear the formidable forces imposed upon them, inspiring the creation of robust and resilient designs. When we venture into dynamics, our focus shifts to the mesmerizing movements of objects propelled by the application of forces. This comprehensive grasp of the nature of force empowers us to embark on a captivating journey through various force classifications and the intricate mechanisms generating these forces. This profound exploration grants us unparalleled insights into the fundamental essence of interacting forces and their profound influence on the behavior of objects.

Simply stated, a force is any agency that is capable of producing an acceleration of an unsupported body. While this definition may seem vague,it is comprehensive. All forces are produced from the interaction of two ormore bodies (or collections of matter), and the interaction between the bodies can take several forms which gives rise to different ways that forces can be produced.

For many purposes, a force can be categorized as being either a contact force or a field force :

Contact force

When two bodies touch, contact forces develop between them. In general, the contact forces are distributed over a finite area of contact, and hence, they are distributed forces with dimensions of force/area. If the bodies touch over only a small region, or if we replace the distributed force by an equivalent concentrated force, then the contact forces are concentrated at a point.

Contact forces are made up of two parts: a normal-direction force and a tangential-direction force, which is also called the friction force.

Examples of contact forces include the forces between your feet and ground when you are standing, and the force applied by air to a building during a blowing wind.

Field force

A force between bodies that acts through space is called a field force . Field forces act throughout the volume of an object and thus have dimensions of force/volume. Field forces are often called body forces.

For many applications, we can represent a field force by a concentrated force that acts at a point. Examples of field forces include the weight of an object, the attractive force between the Earth and Moon, and the force of attraction between a magnet and an iron object.

Although the definition of contact forces given above is useful, more careful consideration of contact at an atomic length scale shows that contact forces are in fact a special case of a field force. As an atom from one surface comes very close to an atom on the opposite surface, the atoms never touch one another, but rather they develop a repulsive field force that increases rapidly as the two atoms come closer. However, the range of distances over which these forces act is very small (on the order of atomic dimensions), and for macroscopic applications, our definition of contact forces is useful.

Units and Unit Conversions

Units are an essential part of any quantifiable measure. Newton’s law F D ma, written here in scalar form, provides for the formulation of a consistent and unambiguous system of units. We will employ both U.S. Customary units, and SI units (International System) as shown in Table Each system has three base units and a fourth derived unit.

Table. U.S. Customary and SI unit systems.

Base Dimension	US Customary	SI Units
Force	pound (lb)	newton* (N) ≡ kg.m/s2
Mass	slug*≡ lb.s2 / ft	kilogram (kg)
Length	foot (ft)	meter (m)
Time	seconds (s)	second (s)

In the U.S. Customary system, the base units measure force, length, and time, using lb, ft, and s, respectively, and the derived unit is obtained from the equation m = F/a which gives the mass unit as lb.s²/ft, which is defined as 1 slug.

In the SI system, the base units measure mass, length, and time, using kg, m, and s, respectively, and the derived unit is obtained from the equation F D ma which gives the force unit as kg.m/s², which is defined as 1 newton, N.

For both systems, we may occasionally use different, but consistent, measures for some units. For example, we may use minutes rather than seconds, inches instead of feet, grams instead of kilograms, and so on. Nonetheless, the definitions of 1 newton and 1 slug are always asshown in Table above.

Dimensional homogeneity and Unit conversions

Of course, the symbol “=” means that what is on the left-hand side of the symbol is the same as what is on the right-hand side. Hence, for an expression to be correct, it must be numerically correct and dimensionally correct.

Normally this means that the left- and right-hand sides have the same numerical value and the same units. All too often units are not carried along during a calculation, only to be incorrectly assumed at the end. Our strong recommendation is that you always use appropriate units in all equations. Such practice helps avoid catastrophic blunders and provides a useful check on a solution, for if an equation is found to be dimensionally inconsistent, then an error has certainly been made.

Unit conversions are frequently needed, and are easily accomplished using conversion factors such as those found in Table 1.2 and rules of algebra. The basic idea is to multiply either or both sides of an equation by dimensionless factors of unity, where each factor of unity embodies an appropriate unit conversion.

Table. Conversion factors between U.S. Customary and SI unit systems.

	US Customary	SI Units
Length	1 in.	= 0.0254 m (2.54 cm, 25.4 mm)*
	1 ft (12 in.)	= 0.3048 m*
	1 mi (5280 ft)	=1.609 km
Force	1 lb	=4.448 N
	1 kip (1000 lb)	=4.448 KN
Mass	1 slug ( 1 lb.s2/ ft)	=14.59 kg

Common prefixes used in the SI unit systems

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