## Kinetic Friction

Kinetic friction comes into existence when there are moving surfaces means in other words we can say that the force which comes into existing between moving surfaces is known as kinetic friction.

For all the cases an opposite force acts in the direction of the force that displaces the object and is responsible for movement of object. The dependency of the total force will be on the friction coefficient of of the body.

It is a kind of force that works in the opposite direction of a moving object or we can say that frictional force grip a sliding object or body.

## Formula for Kinetic Friction

The coefficient of kinetic energy is denoted by- “ mu” with a base “k”.

It is the product of the coefficient and the force that is normally acting upon the body.

Hence for this case -

${F}_{K}={\mu}_{k}N$

where

1. ${F}_{k}$=force of kinetic friction.

2.${\mu}_{k}$ =coefficient

3. N=normal acting force

## Applications

- Friction plays a very important role in our daily life. As we rub two surfaces in that case friction also comes into existence and the motion converts into heat in that case.
- The wear and tear of machines and appliance is also an application of kinetic friction. So we need lubricants to reduce it.

## Coefficient

The ratio of the normal force and the frictional force acting on the surface defines the coefficient of friction.

It is represented by-“mu”(μ)

Numerically

$\mu =\frac{F}{N}$

Where f denotes the frictional force and n denotes the normal force.

As the ratio of the coefficient is force thus it becomes dimensionless as both the terms get canceled out. Depending upon the type of friction the coefficient varies.

The force that opposes the force applied on the body is the friction force in the case of static friction. The body will remain at rest until the frictional force of the static condition is overcome.

The motion of the object is opposed by the frictional force in the case of kinetic friction.

## Machines Application

For the wheel to resist motion and not roll over the surface, this condition is caused due to deformation of the force. Tangential frictional force is not responsible for the resistance that occurs.

For a condition where a rolling of cylinder is occurring over a surface the normal force in this case is tangential to the point of contact. The cylinder moves with a constant velocity.

No Rolling Resistance.

## Static Friction

Static friction is friction or force which is responsible for keeping a body or object at rest. Static friction can be explained as the frictional force experienced when we move a body that is at rest, without doing any relative motion between that body and the surface on which it is available.

For the body to remain at rest the frictional force balances the force applied on body. The static frictional force is also known as self-regulating force.

That is static friction is always equal and opposite to the applied force.

### Examples of static friction

1. Pen on a table.

2. Cloths are hanging on the wall

3. A cycle is parked on a hill.

### Laws of static friction

- The area of contact is not a dependent parameter for maximum friction.
- The normal force is comparative to the maximum force in case of static friction. It means the normal force is directly proportional to the maximum force.

BASIS OF COMPARISION | STATIC FRICTION | KINETIC FRICTION |

Basic | It is related to the body at rest | It is related to the body at motion |

Magnitude | More | Comparative less |

Denoted as | F_{S} | F_{k} |

Expression | _{μsFn} | _{μkFn} |

Magnitude of force | Dependent | Independent |

Nature | It is in opposition to the beginning of motion | It is the opposition relative to the motion of the body. |

Value | Can be zero | Can never be zero. |

When it acts | When relative motion is absent | When relative motion is present |

Example | Paper placed on the table | Moving a toy car over a tabletop. |

**Similarities Between Static Friction and Kinetic Friction**

In both, the case means in static friction and in kinetic friction both are resistive forces. They both act against the movement which is between two surfaces that are in contact with each other and proportional to the perpendicular force between the two objects.

**Assumptions Regarding Friction**

Friction is a very important and complex force which acts differently under different condition. There are three assumptions that are taking regarding friction-

- The normal force is proportional to the frictional force.
- Relative velocity is not involved in the frictional force.

The proportionality occurs between the friction and normal force irrespective of the area of contact.

- For two sliding or contact rough surface, the actual contact or sliding area considered is the portion of the total area where the spot is touched i.e the sliding occurs.
- Increment of actual contact or sliding area because of the greater normal force which results in the frictional and area proportionality which means for a greater normal force in the condition of greater applied force, the friction and contact area increases.

**Friction Types**

- Dry Friction (Coulomb Friction) : Friction acting between two surfaces which are unlubricated.
- Fluid Friction: Friction acting between layers of fluid with varying velocity. It is dependent upon the viscosity.
- Internal Friction: For low limit of elasticity and cyclic loading internal friction is responsible.

**Dry Friction Mechanism**

A weight W of block placed on horizontal surface. Forces acting on the block are its weight and

A horizontal force P is applied on the block. For equilibrium a horizontal component of force F is presents which Static-Friction forces.

${F}_{s}={\mu}_{s}N$

An increment in P will let the block to move and F will continue to become smaller for this case.

${F}_{k}={\mu}_{k}N$

${\mu}_{s}$ denotes Coefficient of Static Friction

${\mu}_{k}$denotes Coefficient of Kinetic Friction

### Static-friction force Maximum Condition

${F}_{s}={\mu}_{s}N$

### Kinetic-friction force

${F}_{k}={\mu}_{k}N$

**The static friction force for maximum condition and kinetic force of friction are**

- Direction proportional to the normal force.
- Dependent on type and condition of contact surfaces
- Independent of contact area

**For example:**

Determine the maximum angle θ before the block begins to slip.

μs denotes the coefficient of friction for the surface of block and inclined surface.

Solution,

The free body diagram of the block will be

$\begin{array}{l}{\displaystyle \sum F{}_{x}=0}\\ mg\mathrm{sin}\theta -F=0\\ F=mg\mathrm{sin}\theta \\ {\displaystyle \sum {F}_{y}=0}\\ -mg\mathrm{cos}\theta +N=0\\ N=mg\mathrm{cos}\theta \\ \frac{F}{N}=\mathrm{tan}\theta \end{array}$

Max angle occurs when,

$F={F}_{S}={\mu}_{s}N$$$

Hence, for impending motion,

$\begin{array}{l}{\mu}_{s}=\mathrm{tan}{\theta}_{\mathrm{max}}\\ {\theta}_{\mathrm{max}}=\mathrm{tan}-{\mu}_{s}\end{array}$

Hence, the maximum value of θ is known as the Angle of Repose.

**Question**

A 300 N block is placed on a inclined plane for which a 100 N force acts on it. Coefficient for static and kinetic friction are μ_{s}= 0.25 and μ_{k}= 0.20 that exists for the surface. State if equilibrium condition exists for the block and determine the frictional force.

**Solution,**

We draw the free body diagram,

For the equilibrium condition

$\begin{array}{l}{\displaystyle \sum {F}_{x}=0}\\ 100-\frac{3}{5}(300)-F=0\\ F=-80N(\text{Factingupwards})\\ {\displaystyle \sum {F}_{y}=0}\\ N-\frac{4}{5}(300N)=0\\ N=240N\end{array}$

Now, we calculate maximum friction force and compare it with the friction force required for equilibrium. If the value of frictional force is greater then it will not slide.

$\begin{array}{l}{F}_{s}={\mu}_{s}N\\ {F}_{s}=0.25(240)=60N\end{array}$

$\begin{array}{l}{F}_{k}={\mu}_{k}N={F}_{actual}\\ {F}_{k}=0.20(240)=48\end{array}$

The block will slide down the plane along F.

If the maximum friction force is less than the friction force required for equilibrium, the block will slide. Calculate kinetic-friction force.

$\begin{array}{l}{F}_{k}={\mu}_{k}N={F}_{actual}\\ {F}_{k}=0.20(240)=48\end{array}$

**Context and Application**

When we walk on a rough surface then the surface resists the motion of our walk which is an application of friction. This topic is studied in school levels as well as

Bachelors in Science (physics)

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