quantity

force

An interaction that changes the motion or shape of an object.
18 related articles · 6 formulas

Description

Force is the fundamental interaction that changes the motion or shape of an object. It is the push or pull that causes a body to accelerate, deform, or alter its trajectory. In physics, force is a vector quantity, meaning it has both magnitude and direction, and is measured in newtons. The concept is central to classical mechanics, where Newton's laws describe how forces affect motion, and extends to modern physics, where forces are understood as exchanges of particles or curvature of spacetime.

History

The modern concept of force was formalized by Isaac Newton in his 1687 work 'Principia Mathematica', where he stated the three laws of motion. Earlier ideas existed in Aristotelian physics, but Newton's quantitative treatment laid the foundation for classical mechanics.

How it works

Forces arise from fundamental interactions: gravitational, electromagnetic, strong nuclear, and weak nuclear. In everyday contexts, forces like friction, tension, and normal reaction are macroscopic manifestations of electromagnetic interactions between atoms. When a force acts on an object, it imparts momentum, changing the object's velocity according to Newton's second law (F = ma). Deformation occurs when internal forces within a material resist external applied forces, leading to stress and strain.

In practice

Forces are engineered in countless technologies, from structural engineering (load-bearing beams) to aerospace (thrust and lift) and everyday devices like brakes and springs.

Fun fact

The strongest known force, the strong nuclear force, is about 10^38 times stronger than gravity, yet it operates only over subatomic distances.

Concept graph →

Formulas

$$F = -\frac{GMm}{r^2} - \frac{4\pi}{3} G m r \rho (1+3w)$$
Gravitational force modified by dark energy pressure, vanishes at w=-1/3.
What is in the formula
FvariableGravitational force magnitude — force newton
MvariableMass of the central object — mass kilogram
mvariableMass of the test particle — mass kilogram
rvariableDistance between masses — distance metre
ρvariableEnergy density of the cosmic fluid — energy density joule per cubic metre
wvariableEquation-of-state parameter of the fluid — equation of state parameter
GconstantUniversal constant of gravitation — gravitational constant = 6.67430e-11 cubic metre per kilogram per second squared
$$F = \frac{2 A s}{c} \cdot \frac{1 - v/c}{1 + v/c}$$
Force on a moving solar sail due to reflected light.
What is in the formula
FvariableForce on the sail — force newton
AvariableArea of the sail — area square metre
svariablePoynting flux (power per unit area) of incident light — irradiance watt per square metre
vvariableSpeed of the sail relative to the light source — velocity metre per second
cconstantUniversal constant, speed of light in vacuum — speed of light = 299792458 metre per second
\cdotoperatorProduct of quantities — multiplication
\frac{1 - v/c}{1 + voperatorRatio of reflected to incident photon energy and rate — doppler factor squared
$$F = -\gamma v$$
Friction force is proportional and opposite to velocity.
What is in the formula
FvariableFriction force — force newton
γvariableDamping coefficient (friction coefficient) — damping coefficient kilogram per second
vvariableVelocity of the object — velocity metre per second
$$\mathbf{F} = m \mathbf{a}$$
Force equals mass times acceleration.
What is in the formula
FvariableNet force vector — force newton
mvariableInertial mass — mass kilogram
avariableAcceleration vector — acceleration metre per second squared
$$\mathbf{F} = G \frac{m_1 m_2}{r^2} \hat{\mathbf{r}}$$
Force between two masses is proportional to product and inversely to square of distance.
What is in the formula
\mathbf{F}variablegravitational force vector — force newton
m_1variablemass of first object — mass kilogram
m_2variablemass of second object — mass kilogram
rvariabledistance between the centers of mass — distance metre
\hat{\mathbf{r}}variableunit vector pointing from one mass to the other — unit vector
GconstantNewtonian gravitational constant, fundamental constant of gravitation — gravitational constant = 6.67430e-11 cubic metre per kilogram per second squared
$$F = P \cdot A$$
Force equals pressure times area.
What is in the formula
Fvariableforce exerted on the sphere — force newton
Pvariablepressure applied to the surface — pressure pascal
Avariablearea over which pressure acts — area square metre

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