Laws of motion: Physics Notes for TS EAMCET

Laws of Motion

Study Notes – TS EAMCET (Physics)

1. Simple Explanation

The laws of motion (Newton’s laws) describe the relationship between a body’s motion and the forces acting upon it. They are the foundation of classical mechanics and allow us to predict how objects will move when forces are applied.

Law	Statement (in plain words)	Key Idea
1st	An object at rest stays at rest, and an object in motion continues with a constant velocity unless acted upon by a net external force.	Inertia – resistance to change in motion.
2nd	The acceleration of an object is directly proportional to the net external force and inversely proportional to its mass: F = m·a.	Quantifies how much a force changes motion.
3rd	For every action there is an equal and opposite reaction.	Forces always come in pairs.

2. Key Points

2.1 First Law (Law of Inertia)

Definition: A body will keep its state of rest or uniform straight‑line motion unless acted upon by a net external force.
Implication:
- If all forces cancel (ΣF = 0), acceleration a = 0.
- On a frictionless surface, a car that has no engine will keep moving forever (ideal case).
Applications:
- Understanding motion of projectiles, free‑fall, satellites, etc.
- Designing safety features (seatbelts) that counteract sudden stops.

2.2 Second Law (Law of Acceleration)

Vector equation: **F_net** = m · **a
- F_net – vector sum of all external forces.
- m – mass of the body (scalar).
- a – acceleration vector.
Forces to consider:
- Weight W = m·g (downward).
- Normal force N (perpendicular to surface).
- Friction f = μ_k N (kinetic) or f ≤ μ_s N (static).
- Tension T in a rope or string.
- Air resistance (often negligible at low speeds).
Important Relationships:
- On an incline of angle θ:
  - Parallel component of weight: W_parallel = m g sinθ
  - Perpendicular component: W_perp = m g cosθ
  - Normal force: N = W_perp (if no vertical acceleration).
- Friction on incline: f = μ_k N = μ_k m g cosθ (if sliding).
- Net force along incline: F_net = W_parallel – f (if the block is sliding downward).

2.3 Third Law (Action‑Reaction)

Forces always appear in pairs: if body A exerts a force F on body B, body B exerts a force –F on body A.
Examples:
- Pulling a rope: you feel the reaction force from the rope.
- Rocket propulsion: exhaust gases push the rocket in the opposite direction.

2.4 Common Situations & Formulas

Situation	Net Force	Acceleration	Notes
Block on horizontal surface (no friction)	`F = m a`	`a = F/m`	`N = mg`, `f = 0`
Block on horizontal surface (kinetic friction)	`F_net = F_applied – f_k`	`a = (F_applied – μ_k mg)/m`	`f_k = μ_k N`
Block on inclined plane (no friction)	`F_net = m g sinθ`	`a = g sinθ`	`N = mg cosθ`
Block on inclined plane (friction)	`F_net = m g sinθ – μ_k mg cosθ`	`a = g (sinθ – μ_k cosθ)`
Hanging mass (pulley)	`F_net = m g – T`	`a = g – T/m`	Tension from rope
Two‑body interaction	`F_AB = –F_BA`	`m_A a_A = F_AB`, `m_B a_B = F_BA`

3. Worked Example

Problem Statement

A 10 kg block is pulled horizontally across a rough floor by a constant horizontal force of 50 N. The coefficient of kinetic friction between the block and the floor is 0.2.

(a) Find the block’s acceleration.
(b) Find the block’s velocity after 5 s, assuming it starts from rest.

Assumptions

The floor is horizontal (θ = 0).

No other forces except weight, normal force, applied force, and kinetic friction.

Gravitational acceleration g = 9.8 m/s².

(a) Acceleration

Normal force
[ N = m g = 10 \times 9.8 = 98 ,\text{