A contact force is one where the force is only felt when two objects are in contact with each other, such as friction.
On the other hand, distant forces are felt even though the objects are not in contact with each other, such as gravity and magnetic forces.
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    When you hold a pen with your fingers with pen being vertical. Then friction force is the contact force.   If you keep a pen on your palm then it is the normal force acting on it through the contact.  If you leave the pen, then the pen falls on ground. That is due to the gravity of EARTH. This is a non-contact force.

Contact forces


Friction force : it acts through the contact between two bodies. It acts along the surface in the direction opposite to the relative speed between the surfaces. It is equal to the coefficient of friction multiplied by the normal force between the surfaces.

Normal force: it is the contact force (it is the push between the two bodies). It acts perpendicular to the surface.  If a body is lying on a floor.  The body exerts a force equal to its weight on the floor.  Floor exerts a force on the bottom surface of the body equal to the weight of the body,

Muscular force , push or pull force or applied force :   The force you exert on a door, when you push the door. The applied force can be at any angle.

Spring force, - you have to  pull the string by touching , then only spring force acts. It is proportional to the extension and opposite to the direction of extension.

Tension force: It is the force developed in a string or thread or a thin material, when it is subjected to a push or pull at its ends.  This force is same all along the thread or rope or string.  Tension makes the string or thread tight. It always acts inward from the ends to the center of the string.

Air resistance force or drag force : it is proportional to the velocity and is opposite to the movement of the body.

Buoyancy force in a fluid: it is equal to the weight of the fluid displaced by the body. It acts through the surface of the body immersed in a liquid.  This is how ships float on water.

These are also called fundamental forces. They are acting even if there is not contact betwen bodies and even if bodies are in vacuum.

Gravitational forces :  our weight for example is due to gravity. Earth revolves around Sun due to gravity. Newtons' law gives the formula.   Force = G M1 M2 / d
                 G = universal gravitational constant    M1, M2 are masses   
                     d = distance between the bodies.
    These forces are always attractive.

Electrical forces: These are the forces which act between bodies having electric charges : positive or negative.  The formula is   = F = (1/4 
π ∈ ) Q1 Q2 / d²
∈ = electric permittivity of medium     Q1, Q2 are charges on the body
               d = distance between bodies/charges
      Opposite charges attract and similar charges repel.

Magnetic forces: This is the force of attraction or repulsion between two opposite poles or similar poles, respectively.  Force is  F = (1/4
π μ )  m1 m2 / d²   ,   
       μ = magnetic permeability of the medium    m1 and m2 are pole strengths
       d = distance between the poles

Nuclear forces: These are the forces among the particles at nucleus level. 

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