Greasy friction

If two metallic surfaces are wetted with a small amount of lubricant, a very thin film of the same is formed on each of the surfaces. This thin film is of molecular thickness. It adheres to the surface and is known as absorbed film. 

The property of a lubricant to form a layer of molecular thickness on a metallic surface is known as its oiliness. 

If two lubricants of equal viscosity are used to lubricate two metallic surfaces under identical conditions, it is found that one reduces the friction more than the other and is said to have greater oiliness. 

Now, What is Greasy friction?

The friction of two surfaces, when they are wetted with an extremely thin layer of lubricant and metal-to-metal contact can take place between high spots is known as greasy friction or boundary friction. 

The friction laws governing greasy friction are similar to those for solid or dry friction. 

Laws of friction

There are total five basic laws of friction so now let we check it out one by one.

Experiments have shown that the force of solid friction 

• is directly proportional to the normal reaction between the two surfaces.
• opposes the motion between the surfaces.
• depends upon the materials of the two surfaces.
• is independent of the area of contact.
• is independent of the velocity of sliding.

The last of these five laws is not true in the strict sense as it has been found that the friction force decreases slightly with the increase in velocity. 

What is moment of a force

The general definition of the moment of force :

Moment of force is defined as a product of force and the moment arm. Now the question arise in your mind that what is moment arm? The moment arm is the perpendicular distance between the line of action of the force and the centre of moments. 

In mechanics moment of force is turning effect produced by force, on a body, on which it acts. 

Moment of force = Force applied × Perpendicular distance from the fixed axis. This formula is applied to calculate the moment of force for balanced as well as unbalanced forces. 

In the above figure the moment of force = ( P × l ) N-m

If the force is in Newton and moment of force is in meter then the unit of moment of force is Newton-meter ( N-m ).

Lami theorem is applicable only for

Application of Lami's theorem :

Lami's theorem is used to describe an equilibrium of three forces but not for more forces. 

It isn't much used any more since the development of vector algebra in the 1900s. 

Lami's theorem applicable to more than three forces by resolving the system into 3 forces and make sure that none of the three angles is greater than 180°.

Lami's Theorem

Lami's theorem is related to the system of forces like the magnitude of three coplanar, concurrent and non-colinear forces that keeps a body in static equilibrium. 

Lami's theorem statement :

It is stated that if three coplanar forces acting at a point be in equilibrium, then each force is proportional to the sine of the angle between the other two forces. 

Now we consider the three forces A, B and C acting on a particle or rigid body that all forces making respective angles α, β and γ with each other.

Now we can represent the Lami's theorem in mathematically :

A / sinα = B / sinβ = C / sinγ

You also check it out the Lami theorem is applicable only for what type of applications.

System of forces

When a mechanics problem or system has more than one force act on a body, it is known as a system of force OR Force system.

There is a various system of forces following below :

1. Coplanar forces: The forces, whose line of action lie on the same plane that is known as coplaner forces. 

There are four types of coplanar forces system :

• Collinear force system: When the lines of action of all the forces of a system act along the same line, this force system is called collinear force system.

• Parallel force system: When the line of action of all the forces of a system is different and parallel to each other, this force system is called a parallel force system. 

• Concurrent force system: When the forces extended and it passes through a single point this system is called the concurrent force system.  

The point is called the point of concurrency. The lines of actions of all forces meet at the point of concurrency. 

Concurrent forces may or may not be coplanar.

• Non-concurrent force system: In the system, all the forces do meet at a common point of concurrency, this force system is called non-concurrent force system. 

Parallel forces are an example of this type of force system. 

Non-concurrent forces may be coplanar or non-coplanar.

2. Non-coplanar forces: The forces, whose line of action don't lie on a single plane is called non-coplanar forces or Space forces. 

There is three non-coplanar force system :

• Parallel force system: When the line of action of all the forces of a system is different and parallel to each other and also both are in a different plane, this force system is called parallel force system. 

• Non-coplanar concurrent forces: When all the forces in the system meet at one point but their lines of action don't lie on the same plane that type of system is known as non-coplanar concurrent forces.

• Non-coplanar non-concurrent forces : The forces that are not meet at one point and their lines of actions do not lie on the same plane are called non-coplanar non-concurrent forces.

Resultant force definition

What is the resultant force?

A resultant force is defined as a total force acting on the body along with their directions. 

On the other words, it is the single force obtained by combining a system of forces acting on a rigid body and it has the same effect on the rigid body as the original system of forces.

The resultant force may be determined by the following laws :

Parallelogram law of forces :

By this law, two forces acting simultaneously on a particle and it can be represented in magnitude and direction by two adjacent sides of a parallelogram, then their results may be represented in magnitude and direction by the diagonal of a parallelogram which passes through their point of intersection. 

Similar kind of application applicable for triangle, polygon and for similar types of another shape. 

Resultant of two or more intersecting forces found :

Where two or more intersecting forces are found then for solving resultant of that forces steps given below :

Step -1: First of all resolving all the horizontal forces 
Step -2: Then resolving vertical forces 
Step - 3: Then put all data in the below equation and equate. 
Step - 4: Answer will be the resultant force that what we find. 

R = √ ( ∑horizontal force ) ² + ( ∑vertical force )²

A number of force acting on a particle will be called in equilibrium when :

∑ horizontal force = 0

∑ vertical force = 0

Resultant force for the two forces that are not parallel or any kind of forces :

Step - 1: Draw a free-body diagram of the object.
Step - 2: Draw coordinate axes on the free-body diagram.
Step -3: Decompose the forces acting on the object into x and y components.
Step - 4: Calculate the x and y component of the resultant force by adding the x and y components of all forces.
Step - 5: Find the magnitude and direction of the resultant force by using x and y component. 

Notes :

If the resultant force acting on a stationary object is zero, the object will remain stationary. 

If the resultant force acting on a moving object is zero, the object will carry on moving at the same speed in the same direction.

Force basic definition

Force is a push or a pull that tends to change the state of uniform motion of an object. 

A force can cause an object to accelerate, slow down, remain in original shape or change shape. 

A force while acing on a body may :

• Change the motion of a body 
• Retard the motion of a body 
• Balance the forces already acting on a body 
• Give rise to the internal stresses in a body

In order to determine the effects of a force acting on a body, one must know the following characteristics of the forces. 

• The magnitude of the force
• The line of action of the force  
• The nature of the force 
• The point at which force is acting 

The magnitude of the force is given by in MKS system - kilogram-force ( kgf ) and in SI system - Newton ( N ). 

1 kgf = 9.81 N

There are different types of force. You can check it out below :

• Applied force
• Gravitational force
• Normal force 
• Frictional force 
• Air resistance force 
• Tension force 
• Spring force 

Types of friction

The frictional force is that force responsible for wear and tear of two bodies. 

When two bodies in contact, move relative to each other then there exists a force which has a tendency to oppose that movement which is called frictional force. 

Friction plays an important part in many everyday processes. For instance, when two objects rub together, the friction causes some of the energy of motion to be converted into heat. This is why rubbing two sticks together will eventually produce a fire.

Friction is also responsible for the wear and tear on bike gears and other mechanical parts. That's why lubricants, or liquids, are often used to reduce the friction and wear and tear between moving parts. 

 There are in general  4 different types of friction.

1. Static Friction
2. Kinetic Friction
3. Rolling Friction
4. Fluid Friction

Static Friction :

• When a force is applied to an object but it does not cause it to move

Static friction comes into play when a body is forced to move along a surface but the movement does not start. 
This is the maximum force that must be overcome before a body will just start to move over another body. 
The magnitude of static friction remains equal to the applied external force and the direction is always opposite to the direction of motion. 
The magnitude of static friction depends upon μs (coefficient of static friction) and N (net normal reaction of the body).
 Example: Pushing on a wall

Kinetic Friction :

• Occurs when solid surface sliding over each other

 Kinetic friction denoted as μk comes into play when a body just starts moving along a surface. When the externally applied force is sufficient to move a body along a surface then the force which opposes this motion is called as kinetic frictional force.

This is the maximum force that must be overcome before a body will just be in uniform motion over another body.                                  

Magnitude of kinetic frictional force f_k = μk N

Where μk is coefficient of kinetic frictional force and N is the net normal reaction on the body. The magnitude of kinetic frictional force is always less than magnitude of static frictional force. When value of applied net external force F is more than f_k then body moves with a net acceleration and when these forces are equal then body moves with a constant velocity.

Example : Falling on the pavement

Rolling Friction :

•  Occurs when an object rolls over another 

Rolling frictional force is a force that slows down the motion of a rolling object. Basically it is a combination of various types of frictional forces at point of contact of wheel and ground or surface.When a hard object moves along a hard surface then static and molecular friction force retards its motion. When soft object moves over a hard surface then its distortion makes it slow down. 

Example: Riding a motorcycle, Skateboard 

Fluid Friction :

• Occurs when a object moves through a fluid 

When a body moves in a fluid or in air then there exists a resistive force which slows down the motion of the body, known as fluid frictional force. A freely falling skydiver feels a drag force due to air which acts in the upward direction or in a direction opposite to skydiver’s motion. The magnitude of this drag force increases with increment in the downward velocity of skydiver. At a particular point of time the value of this drag force becomes equal to the driving force and skydiver falls with a constant velocity.

Example : Skydiving, Swimming