Lesson–4 : Laws of Motion

Stage–2 : Extended Intermediate Notes

🔹 1. Net Force and Equilibrium

When more than one force acts on a body, the net force is the vector sum of all forces acting on it.

If the net force acting on a body is zero, the body is said to be in equilibrium.

Types of Equilibrium

Static equilibrium: Body at rest
Dynamic equilibrium: Body moving with constant velocity

In both cases, acceleration is zero.

🔹 2. Concept of Unbalanced Force

An unbalanced force is a force or combination of forces that produces a change in the state of motion of a body.

According to Newton’s First Law:

Balanced forces → No change in motion
Unbalanced forces → Change in velocity or direction

Important: Even a small unbalanced force can change motion if it acts for sufficient time.

🔹 3. Detailed Derivation of Newton’s Second Law

According to Newton’s Second Law, force is proportional to the rate of change of momentum.

Let:

Initial velocity = u
Final velocity = v
Time taken = t
Mass of body = m

Initial momentum = mu
Final momentum = mv

Change in momentum = mv − mu = m(v − u)

Rate of change of momentum:

= m(v − u) / t = ma

Hence,

F ∝ ma
F = kma

In SI system, constant k = 1.

F = ma

🔹 4. Force as a Vector Quantity

Force has both magnitude and direction and therefore it is a vector quantity.

When forces act at angles to each other, vector laws must be used to find the resultant force.

In most intermediate problems, forces act either:

Along the same line
Perpendicular to each other

🔹 5. Applications of Newton’s Second Law

(a) Motion of a Lift (Elevator)

When a lift moves upward with acceleration a:

Normal reaction,

N = m(g + a)

When the lift moves downward with acceleration a:

N = m(g − a)

When the lift moves with constant velocity:

N = mg

This concept is frequently asked in board exams.

🔹 6. Impulse – Detailed Understanding

Impulse is the effect of a force acting for a very short time.

Mathematically,

Impulse = F × t = Change in momentum

Impulse is especially useful in:

Collision problems
Stopping a fast-moving object
Safety devices

Increasing the time of impact reduces the force.

🔹 7. Newton’s Third Law – Deeper Analysis

Action and reaction forces:

Are equal in magnitude
Are opposite in direction
Act on different bodies

Because they act on different bodies, they do not cancel each other.

Examples:

Walking: Foot pushes ground backward, ground pushes foot forward
Swimming: Swimmer pushes water backward, water pushes swimmer forward
Rocket motion: Gases pushed backward, rocket moves forward

🔹 8. Common Misconceptions (VERY IMPORTANT)

Force is not required to maintain motion
Action and reaction never act on the same body
Acceleration does not become zero at highest point automatically
Balanced forces do not mean no forces

🔹 9. Importance of Free Body Diagram (FBD)

A Free Body Diagram helps in:

Identifying all forces acting on a body
Applying Newton’s laws correctly
Avoiding sign mistakes

Without a proper FBD, most numerical problems cannot be solved correctly.

🔹 10. Summary of Stage–2

Net force determines acceleration
F = ma is derived from momentum
Impulse changes momentum
Newton’s laws explain all mechanical motion
Free Body Diagrams are essential

Stage–2 Completed ✔
Next: Stage–3 (Intermediate Important Questions & Numericals)

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