# Force

Written by Jerry Ratzlaff on . Posted in Classical Mechanics

## Force

Force 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.

### Contact Forces

• Frictional force
• Tensional force
• Normal force
• Air Resistance force
• Applied force
• Spring force

### Action at a distance Forces

• Gravitational force
• Electrical force
• Magnetic force

### Force Formula

$$F = ma$$          $$force \;=\; mass \;\;x\;\; acceleration$$

$$F = p A$$          $$force \;=\; pressure \;\;x\;\; acceleration$$

Where:

$$F$$ = force

$$a$$ = acceleration

$$A$$ = area

$$m$$ = mass

$$p$$ = pressure

## Applied Force

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

## Average Force

Average force is used when the velocity was not measured precisely.

### Average Force FORMULA

$$\bar F = m \frac { v_f \;-\; v_i } {t}$$          $$average \; force \;=\; mass \; \frac { final \; velocity \;-\; initial \; velocity } { time }$$

$$\bar F = m \frac { \Delta v } {t}$$          $$average \; force \;=\; mass \frac { velocity \; differential } { time }$$

Where:

$$\bar F$$ = average force

$$m$$ = mass

$$t$$ = time

$$\Delta v$$ = velocity differential

$$v_f$$ = final velocity

$$v_i$$ = initial velocity

## 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

Centripetal force ( $$F_c$$ ) is when an object keeps traveling along a axis of rotation and this force is acting always towards the center.

### Centripetal Force formula

$$F_c = \frac { m v^2 } { r }$$          $$centripetal \; force \;=\; \frac { mass \;\;x\;\; velocity^2 } { radius \; of \; circular \; path }$$

$$F_c = m a_c$$          $$centripetal \; force \;=\; mass \;\;x\;\; centripetal \; acceleration$$

Where:

$$F_c$$ = centripetal force

$$m$$ = mass

$$v$$ = velocity

$$r$$ = radius of circular path

$$a_c$$ = centripetal acceleration

Solve for:

$$v = \sqrt { \frac { F_c r } { m } }$$

## Concurrent Force

All of the forces act at the same point.

## Drag Force

Drag force ( $$F_d$$ ) or drag for any body moving through a fluid (gas or liquid), is the force exerted perpendicular and in opposition to the direction of travel.

### Drag Force Formula

$$F_d = \frac {1} {2} \rho v^2 C_D A$$          $$drag \; force \;=\; \frac {1} {2} \; \left( \; densiry \;\;x\;\; velocity^2 \;\;x\;\; drag \; coefficient \;\;x\;\; area \; \right)$$

$$F_d = \frac { \rho v^2 C_D A} { 2 }$$          $$drag \; force \;=\; \frac { densiry \;\;x\;\; velocity^2 \;\;x\;\; drag \; coefficient \;\;x\;\; area } { 2 }$$

Where:

$$F_d$$ = drag force

$$A$$ = cross section perpendicular to area flow

$$C_d$$ = drag coefficient

$$\rho$$ = density

$$v$$ = velocity

## Force Exerted by Contracting or Stretching a Material

Any strain exerted on a material causes an internal elastic stress.  The force applied on a material when contracting or stretching is related to how much the length of the object changes.

### Force Exerted by Contracting or Stretching a Material Formula

$$F = \frac { E A l_c } { l_o }$$          $$force \; exerted \;=\; \frac { modulus \; of \; elasticity \;\;x\;\; cross-section \; area \;\;x\;\; change \; in \; length } { origional \; length }$$

Where:

$$F$$ = force exerted

$$A$$ = origional cross-section area through which the force is applied

$$E$$ = modulus of elasticity

$$l_c$$ = change in length

$$l_o$$ = origional length

## General Three-dimensional Force

All other combinations of nonconcurrent, nonparallel and noncoplanar forces.

## Lift Force

Lift force ( $$L$$ ) for an body moving through a fluid (gas or liquid), is the force exerted perpendicular to the direction of travel.

### Lift Force formula

$$L = \frac {1} {2} C_l \rho v^2 A$$          $$lift \; force \;=\; \frac {1} {2} \; \left( \; lift \; coefficient \;\;x\;\; density \;\;x\;\; velocity^2 \;\;x\;\; area \; \right)$$

$$L = \frac { C_l \rho v^2 A } { 2 }$$          $$lift \; force \;=\; \frac { lift \; coefficient \;\;x\;\; density \;\;x\;\; velocity^2 \;\;x\;\; area } { 2 }$$

Where:

$$L$$ = lift force

$$A$$ = area

$$C_l$$ = lift coefficient

$$\rho$$ (Greek symbol rho) = density

$$v$$ = velocity

Solve for:

$$C_l = \frac {2 L} {\rho v^2 A}$$

$$\rho = \frac {2 L} { C_l v^2 A}$$

$$v = \sqrt { \frac {2 L} { C_l \rho A} }$$

$$A = \frac {2 L} { C_l \rho v^2}$$

## Magnetic Force between Parallel Conductors

Each wire creates a magnetic field around the wire.  The force between the two wires is related to the current of the wires and the distance between the wires.

### Magnetic Force between Parallel Conductors Formula

$$F_m = \frac { \mu_o I_1 I_2 } { 2 \pi d }$$          $$magnetic \; force \;=\; \frac { magnetic \; constant \;\;x\;\; wire \; cirrent \;1 \;\;x\;\; wire \; current \; 2 } { 2 \;\;x\;\; \pi \;\;x\;\; distance }$$

Where:

$$F_m$$ = magnetic force

$$d$$ = distance between the wires

$$I_1$$ = wire current (amp) 1

$$I_2$$ = wire current (amp) 2

$$\pi$$ = PI

$$\mu_o$$ (Greek symbol mu) = magnetic constant ($$12.566370614e-7 N A^{-2}$$ )

## Net Canceling Force

Two forces can cancel each other when the foeces act on are equal.

### Net Canceling Force Formula

$$F_n = 0 = F_1 \; - \; F_2$$          $$net \; force \;=\; 0 \;=\; force_1 \; - \; force_2$$

Where:

$$F_n$$ = net force

$$F_1$$ = force 1

$$F_2$$ = force 2

## Net Positive or Negative Force

Two forces can add or subtract to the net force when the forces act on each other.  Forces in the same direction working togeather equal a net force.

### Net Positive or Negative Force Formula

$$F_n = F_1 \; + \; F_2$$          $$net \; force \;=\; force_1 \; + \; force_2$$

$$F_n = F_1 \; - \; F_2$$          $$net \; force \;=\; force_1 \; - \; force_2$$

Where:

$$F_n$$ = net force

$$F_1$$ = force 1

$$F_2$$ = force 2

## Normal Force

Normal force is always perpendicular to the surface it contacts and equal to the weight of the object. Unless there is another external force pushing the object into the contact surface there will be no normal force.

### Normal Force Formula

$$F_n = \frac { f_k } { \mu_k}$$          $$normal \; force \;=\; \frac { kinetic \; friction } { kinetic \; friction \; coefficient }$$

$$F_n = \frac { f_s } { \mu_s}$$          $$normal \; force \;=\; \frac { kinetic \; friction } { static \; friction \; coefficient }$$

Where:

$$F_n$$ = normal force

$$f_k$$ = kinetic friction

$$f_s$$ = static friction

$$\mu_k$$ (Greek symbol mu) = kinetic friction coefficient

$$\mu_s$$ (Greek symbol mu) = static friction coefficient

## Parallel Force

All the forces are parallel (not necessarily in the same direction)

## Rotational Force

### Rotational Force Formula

$$\tau = I \alpha$$          $$rotational \; force \;=\; moment \; of \; inertia \;\;x\;\; angular \; acceleration$$

Where:

$$\alpha$$ (Greek symbol alpha) = angular acceleration

$$I$$ = moment of inertia

$$\tau$$ (Greek symbol tau) = rotational force

## Weight Force

Weight force is the force of gravity or the weight.  The pull of gravity creates downward acceleration of the object falling and factors such as air resistance can affect the weight force.

### Weight Force Formula

$$W = F_g = m g$$          $$weight \;=\; weight \; force \;=\; mass \;\;x\;\; gravitational \; acceleration$$

Where:

$$F_g$$ = weight force

$$g$$ = gravitational acceleration

$$m$$ = mass

$$W$$ = weight

Tags: Equations for Force