Scalars, vectors, and units
Statics is the study of bodies that do not accelerate, from bridges and buildings to shelves and cranes. It begins with describing forces precisely.
What statics is
Statics is the branch of mechanics that studies bodies at rest or moving at constant velocity, where the net force and net moment are zero. Engineers use it to size beams, cables, bolts, and foundations so that structures stand safely. It is usually the first engineering mechanics course, followed by dynamics and mechanics of materials.
A short history
Archimedes, around 250 BCE, stated the law of the lever. Simon Stevin, in 1586, analysed forces on inclined planes with a famous chain-loop argument. Pierre Varignon, around 1687, published the principle of moments, and Isaac Newton's laws of motion, published the same year, provide the foundation: a body stays in equilibrium when the net force on it is zero.
Scalars and vectors
A scalar has magnitude only, such as mass, length, time, or temperature. A vector has magnitude and direction, such as force, displacement, or velocity. Vectors are drawn as arrows and written in bold or with an arrow above the symbol; their magnitude is always positive.
SI units
In the SI system, length is measured in metres, mass in kilograms, and time in seconds. Force is a derived unit, the newton: 1 N = 1 kg·m/s squared. Engineering loads are often in kilonewtons (1 kN = 1,000 N) and stresses in pascals or megapascals.
Mass and weight
Weight is the gravitational force on a mass: \(W = mg\), with \(g = 9.81\) m/s² at Earth's surface in engineering practice. A 100 kg mass weighs 981 N, a little under 1 kN. Mass is a scalar in kilograms; weight is a force vector pointing toward Earth's centre.
Idealisations
Statics simplifies reality: a particle is a body whose size does not matter, so all forces act at one point; a rigid body does not deform; and a concentrated force acts at a single point. These models are accurate when deformations are small, which they usually are in well-designed structures.
Significant figures and checks
Engineering answers are usually given to three significant figures, matching typical precision of loads and dimensions. Always check units and orders of magnitude: a household shelf bracket carrying thousands of kilonewtons signals an error somewhere.
Worked example
A crate of mass 250 kg sits on a warehouse floor. Its weight is 250 x 9.81 = 2,452.5 N, about 2.45 kN. Since the crate is at rest, the floor pushes up with an equal 2.45 kN normal force, so the net force is zero, the defining condition of static equilibrium.
Key takeaways
Statics analyses bodies with zero net force and moment, building on Archimedes's lever law, Stevin's inclined plane work (1586), and Newton's laws (1687). Scalars have magnitude only; vectors have magnitude and direction. Force is measured in newtons, with 1 kN = 1,000 N. Weight is mg with g = 9.81 m/s squared, so 100 kg weighs 981 N. Particles, rigid bodies, and concentrated forces are useful idealisations. Report answers to about three significant figures and check units.
Flashcard
Mechanics of bodies with zero net force and moment
Check your understanding
What is the weight of a 250 kg crate? (g = 9.81 m/s^2)