Common Forces in Mechanics with FBD Tips and Relationship with Newton's Laws

Common forces in mechanics are of various types that determine how each applies to objects we are familiar with. 

In NCERT Class 11 Physics Chapter 4, section 4.9, you will learn two classifications of forces in classical mechanics, which have further subcategories, applying to the different laws of motion by Newton.

Non-Contact or Pervasive Force 

Gravitational Force - This type of non-contact force acts at a distance without physical interaction or contact, and its force is always directed downwards.

The gravitational force is responsible for the motion of planets, projectile motion, and other phenomena.

Contact Forces

NCERT says, “All the other forces common in mechanics are contact forces. As the name suggests, a contact force on an object arises due to contact with some other object: solid or fluid.”

Contact forces can be of different types. Here is a quick table summary. 

Force Type	Direction of Force	How Objects Respond
Normal (N)	Moves perpendicular to the surface	Reaction to compression from the surface
Friction (f)	Parallel to the surface is its movement	Opposes motion or the tendency of motion. It also involves static and kinetic friction.
Tension (T)	Moves along a string or rope	Always pulls, and it's the same with ideal strings
Spring Force	Movement along a spring	Restores original shape, and is related to Hooke's Law (F= -kx)
Buoyancy	Upward movement in a fluid	Based on displaced fluid

This is the only non-contact force as described in the Laws of Motion chapter. Gravity pulls objects toward Earth through a long-range attractive force.

The force of gravity can be defined as the weight of an object, which is the gravitational pull acting on its mass. 

The weight of an object is a vector quantity. The formula then would be

$\vec{W}=m\vec{g}$ where $m$ is mass (kg) and $\vec{g}=9.8\mathrm{m}/{\mathrm{s}}^2$

Direction of gravitation: Always downward. 

FBD tip to represent gravitation: Keep the force vectors (arrows) pointing downward from the object's centre of mass. 

In addition to that, learn that for CBSE and other exams, gravitation acts in all mechanics problems. This is useful for explaining the equilibrium of a particle, unless specified otherwise.

Relation to Newton’s Law: It relates directly to the Second Law of Motion, which states that force causes vertical acceleration if unbalanced.

 

This is a common contact force that defines its direction as perpendicular to the surface. When you rest a book on a table or a horizontal surface, the normal force acts vertically upward and balances the weight of the object. This type of common force prevents objects from sinking into or breaking the surface. 

FBD Drawing Tip: Always draw it perpendicular to the contact surface and originating from the point of contact.

Newton’s Law and Normal force relation: The Third Law tells us the force reaction to the object's weight on the surface. When the object exerts a downward force, the surface pushes back with an equal and opposite force upwards. 

This is a contact force that opposes relative motion between objects. You can also recall why friction is one of the reasons behind Aristotle’s Fallacy. 

FBD Drawing Tip: Always draw friction arrows parallel to the contact surface and opposite to motion (or intended motion).

There are two important types of frictional force. 

Static Friction

It occurs when the object is at rest or not sliding. Static friction also acts to prevent motion from starting, while adjusting its magnitude to match the applied force (up to its maximum limit)

Maximum value: f_s(max) = μ_s N

Formula for Static Friction f_s ≤ μ_s N

μ_s is typically greater than μ_k, meaning it takes more force to start motion than to keep it going

Example: A book resting on a table, or a car tire gripping the road without slipping.

Kinetic Friction 

When the object is already sliding or moving, there is kinetic friction that acts to oppose the motion that’s already happening. Remember that kinetic friction always has a constant magnitude regardless of speed. 

The formula for kinetic friction is f_k = μ_k N

Example: A sliding box across the floor, or a car tire skidding on the road

Note that there is a key transition point between these two types of frictional forces. 

Static friction becomes kinetic friction when the applied force exceeds the maximum static friction force (μ_s N). Once sliding begins, kinetic friction takes over.

1. Static: f_s ≤ μ_s N
2. Kinetic: f_k = μ_k N

Where:

f_s = static friction force

f_k = kinetic friction force

μ_s = coefficient of static friction

μ_k = coefficient of kinetic friction

N = normal force

 

Tension is a pulling force. It is transmitted through a string, rope, or cable. It moves or pulls away from the object. 

This concept of this type of common contact force is explored more when you learn about Simple Harmonic Motion later, where you analyse pendulum motion and wave propagation through strings. Mostly, in such cases, tension plays an important role in restoring forces and energy transfer. 

For the sake of calculations, there is this assumption of ideal strings that are massless and inextensible, so that tension remains the same throughout. For the pulley-based problems and connected body systems, you have to be aware of these. 

FBD Drawing Tip for Tension: Always draw tension arrows pointing away from the object along the string direction.

Another aspect to note is that tension as a contact force always follows two of Newton’s Laws. Third Law, where you can calculate action-reaction pairs, and the Second Law, F = ma, to calculate mass in pulley systems.

Spring force is a restoring force. As the name suggests, the spring exerts a force to either stretch or compress before returning to its natural (equilibrium) length. Also, it's important to remember that spring force is variable contact force as its magnitude depends on the displacement of the object. 

The spring force always follows Hooke's Law Formula: F = -kx

F = Spring force (in Newtons)

k = Spring constant (stiffness of the spring, in N/m)

x = Displacement from equilibrium position (in meters)

Negative sign = Indicates the force is always opposite to the displacement

Technically, the spring force applies to the Third Law, for reaction from the spring, and the Second Law, which causes the spring to accelerate.
FBD Drawing Tip: Always draw spring force arrows pointing toward the equilibrium position (opposite to displacement). 

As we just learned about the common forces in mechanics, here is a recap with some of their examples you can take note of. Remember these kinds of forces and examples to avoid any misconceptions later. 

Contact Force Types and Examples

Type of Contact Force	Description	Example
Normal Force	Perpendicular reaction from a surface	Book resting on a table
Frictional Force	Opposes relative motion between surfaces	Box sliding on the floor
Tension Force	Pulling force through a rope or string	Tug of war rope
Spring Force	Restoring force in stretched/compressed springs	Mass-spring system

Non-Contact Force Types and Examples 

Type of Non-Contact Force	Description	Example
Gravitational Force	Attraction due to mass	Earth pulling an apple downward
Electrostatic Force	Force between charged particles	Repulsion between like charges
Magnetic Force	Force exerted by magnets	Compass needle deflecting near a magnet