# 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.

## Formulas that use Force

 $$\large{ F = m \; a }$$ $$\large{ F = \frac {\Delta p}{\Delta t} }$$ $$\large{ F = \frac {I}{\Delta t} }$$ (impulse) $$\large{ F = \frac{M}{l} }$$ (moment) $$\large{ F = \frac{P}{v} }$$ (power) $$\large{ F = \frac{P \; t}{d} }$$ (power) $$\large{ F = p \; A }$$ (pressure) $$\large{ F = -k_s \; \left( x - x_0 \right) }$$ (spring constant) $$\large{ F = \sigma \; A_c }$$ (stress) (yield strength) $$\large{ F = \frac {\tau}{l} }$$ (torque) $$\large{ F = \frac {\tau}{d} }$$ (torque) $$\large{ F = \frac{W}{d} }$$ (work)

### Where:

$$\large{ F }$$ = force

$$\large{ a }$$ = acceleration

$$\large{ A }$$ = area

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

$$\large{ d }$$ = displacement

$$\large{ x }$$ = 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.

Tags: Equations for Force