Force

Written by Jerry Ratzlaff on . Posted in Classical Mechanics

Force, abbreviated as F, is the push or pull of an object resulting in a change from rest or motion.  So when you apply force to an object the velocity changes, the change in velocity is acceleration.  Force is a vector quantity having magnitude and direction, some of these include acceleration, displacement, drag, lift, momentum, thrust, torque, velocity, and weight.

Force formulas

 FORMULA: SOLVE FOR: $$\large{ F = m \; a }$$ (acceleration) (mass) $$\large{ F = p \; A }$$ (area) (pressure) $$\large{ F = \sigma \; A_c }$$ (area cross-section) (stress) (yield strength) $$\large{ F = \frac {P_d \; t}{ d} }$$ (displacement) (displacement power) (time) $$\large{ F = \frac{P \; t}{d} }$$ (displacement) (power) (time) $$\large{ F = \frac {\tau}{d} }$$ (displacement) (torque) $$\large{ F = \frac{W}{d} }$$ (displacement) (work) $$\large{ F = \frac {I}{\Delta t} }$$ (impulse) (time differential) $$\large{ F = \frac{M}{l} }$$ (length) (moment) $$\large{ F = \frac {\tau}{l} }$$ (length) (torque) $$\large{ F = \frac {\Delta p}{\Delta t} }$$ (momentum differential) (time differential) $$\large{ F = \frac{P}{v} }$$ (power) (velocity) $$\large{ F = -k_s \; \left( x - x_0 \right) }$$ (spring constant)

Where:

$$\large{ F }$$ = force

$$\large{ a }$$ = acceleration

$$\large{ A }$$ = area

$$\large{ A_c }$$ = area cross-section

$$\large{ d }$$ = displacement

$$\large{ P_d }$$ = displacement power

$$\large{ x }$$ = distance from equilibrium

$$\large{ I }$$ = impulse

$$\large{ l }$$ = length, moment arm

$$\large{ m }$$ = mass

$$\large{ M }$$ = moment

$$\large{ \Delta p }$$ = momentum differential

$$\large{ P }$$ = power

$$\large{ p }$$ = pressure

$$\large{ k_s }$$ = spring constant

$$\large{ x_0 }$$ = spring equilibrium position

$$\large{ \sigma }$$  (Greek symbol sigma) = stress

$$\large{ t }$$ = time

$$\large{ \Delta t }$$ = time differential

$$\large{ \tau }$$  (Greek symbol tau) = torque

$$\large{ v }$$ = velocity

$$\large{ W }$$ = work

$$\large{ \sigma }$$  (Greek symbol sigma) = yield strength

General Three-dimensional Force

All other combinations of nonconcurrent, nonparallel and noncoplanar forces.

Force types

All forces can be divided into two basic types of forces:

• Contact force
• Air resistance force
• Applied force
• Friction force
• Normal force
• Spring force
• Tension force
• Non-contact force
• Gravity force
• Electric force
• Magnetic force

Air Resistance Force

Air resistance force, abbreviated as $$F_{ar}$$, is the force in opposition to a moving object through the air.

Applied Force

Applied force, abbreviated as $$F_a$$, can come from different types of forces, one of them could be Newton's Second Law.  There really is no one formula.

Centrifugal force

Centrifugal force is when a force pushes away from the center of a circle, but this does not really exist.  When an object travels in a circle, the object always wants to go straight, but the centripetal force keeps the object traveling along an axis of rotation.

Centripetal force

The direction of the centripetal force is always toward the center of the circle and perpendicular to the velocity.  Any combination of forces causing a uniform circular motion can be called centripetal force.

Collinear Force

Collinear forces all share the same line of action.

Concurrent Force

Concurrent forces are all acting at the same point.

Coplannar Parallel Force

Coplannar parallel forces can be in the same or opposite direction and are on the same plane.

Electric Force

An electric force, abbreviated as $$F_e$$, is an attraction or repulsion force between any two charged objects.

Friction Force

Friction force, abbreviated as $$F_f$$, is the force an object exerts on the surface of an object as it slides across.

Gravity Force

Gravity force is the force exerted between two masses.

Magnetic Force

A magnetic force, abbreviated as $$F_m$$, is an attraction or repulsion force between electrically charged particles moving in a magnetic field.

Non Coplannar Force

All non coplannar forces lines of action lie on different planes.

Non Coplannar Concurrent Force

All non coplannar concurrent forces act at the same point but their lines of action lie on different planes.

Non Coplannar Non Concurrent Force

All non coplannar non concurrent forces do not meet and their lines do not lie on the same plane.

Normal Force

Normal force, abbreviated as $$F_n$$, is the supported force between two contacting objects.

Spring Force

Spring force, abbreviated as $$F_s$$, is the force that compresses (a repulsive force) or stretches (an attractive force) the spring.

Tension Force

Tension force, abbreviated as $$F_t$$, is the force that is exerted through a rope, string or wire when pulled from opposite directions.