Chapter 4: Laws of Motion - Comprehensive NEET Physics Formulae Guide

1. Fundamental Concepts in Mechanics

1.1 Newton's First Law of Motion (Law of Inertia)

• Formula: N/A
• Explanation: Newton's First Law states that a body at rest stays at rest, and a body in motion continues to move at a constant velocity unless acted upon by an external force. This law introduces the concept of inertia, which is the resistance of any physical object to a change in its state of motion or rest.

Example Application:
If a book is lying on a table, it will remain at rest until someone applies a force to move it.

Common Mistake:
Misinterpreting inertia as a force rather than a property of matter.

1.2 Newton's Second Law of Motion

• Formula: $F=ma$
• Explanation: This law states that the force applied on an object is equal to the mass of the object multiplied by its acceleration. Here, $F$ is the force in newtons (N), m is the mass in kilograms (kg), and $a$ is the acceleration in meters per second squared (m/s²).

Derivation:

1. Momentum, $p=mv$, where $v$ is the velocity.
2. The rate of change of momentum is @$\frac{dp}{dt}=\frac{d(mv)}{dt}=m\frac{dv}{dt}=ma$.
3. Thus, $F=ma$.

Example Application:
If a car of mass 1000 kg accelerates at 2 m/s², the force required is: $F=1000\times 2=2000N$.

Common Mistake:
Forgetting that force and acceleration are vectors, requiring consideration of direction.

1.3 Newton's Third Law of Motion

• Formula: $F_{AB}=-F_{BA}$
• Explanation: For every action, there is an equal and opposite reaction. If body A exerts a force on body B, then body B exerts an equal and opposite force on body A.

Example Application:
When a swimmer pushes against the water, the water pushes back with an equal and opposite force, propelling the swimmer forward.

Common Mistake:
Assuming action and reaction forces act on the same body. They act on different bodies.

1.4 Law of Conservation of Momentum

• Formula: $\text{Total momentum before collision}=\text{Total momentum after collision}$
• Explanation: In an isolated system, the total momentum remains constant if no external forces act on it. This is derived from Newton's Third Law.

Example Application:
In a collision between two cars, the total momentum before and after the collision remains constant.

Common Mistake:
Neglecting external forces that might act on the system.

1.5 Equilibrium of Forces

• Formula: $\sum F=0$
• Explanation: For a particle to be in equilibrium, the vector sum of all forces acting on it must be zero.

Example Application:
A book resting on a table is in equilibrium as the gravitational force is balanced by the normal force from the table.

Common Mistake:
Not considering all forces acting on the system, such as friction or tension.

1.6 Circular Motion and Centripetal Force

• Formula: $F_c=\frac{m{v}^2}{r}$
• Explanation: A force that acts on a body moving in a circular path is directed towards the center of the circle. Here, $m$ is the mass, $v$ is the velocity, and $r$ is the radius of the circular path.

Example Application:
The tension in a string that keeps a ball moving in a circular path.

Common Mistake:
Confusing centripetal force with centrifugal force, which is a pseudo force observed in a rotating reference frame.

2. Additional Concepts

2.1 Frictional Force

• Formula (Static Friction): $f_s\le {\mu }_{s}N$
• Formula (Kinetic Friction): $f_k={\mu }_{k}N$
• Explanation: Friction is the force resisting the relative motion of solid surfaces. Static friction acts when the body is at rest, and kinetic friction acts when the body is in motion. Here, ${\mu }_s$and ${\mu }_k$ are the coefficients of static and kinetic friction respectively, and $N$is the normal force.

Example Application:
A block sliding down an inclined plane experiences kinetic friction opposing its motion.

Common Mistake:
Assuming frictional force is always the same regardless of the situation.

2.2 Impulse

• Formula: $J=F\Delta t=\Delta p$
• Explanation: Impulse is the change in momentum of an object when a force is applied over a period of time. It is useful in situations involving short-duration forces like a bat hitting a ball.

Example Application:
A bat hitting a cricket ball imparts a certain impulse, changing the ball's momentum.

Common Mistake:
Neglecting the time interval over which the force acts.

Quick Recap

• Newton's First Law: Inertia and the need for an external force to change the state of motion.
• Newton's Second Law: Relation between force, mass, and acceleration.
• Newton's Third Law: Action-reaction pairs.
• Conservation of Momentum: Total momentum in an isolated system remains constant.
• Equilibrium: Sum of forces equals zero for a body in equilibrium.
• Circular Motion: Centripetal force maintains circular motion.
• Friction: Opposes relative motion between surfaces.

Concept Connection

Link to Chemistry: The concept of force is essential in understanding atomic bonding, where forces between particles (electrons, protons) are central to chemical interactions.

NEET Problem-Solving Strategy

• Break down problems into smaller parts, analyzing forces acting on individual components.
• Use free-body diagrams to visualize forces.
• Apply Newton's laws methodically, ensuring to consider all forces and directions.

Practice Questions

1. A 5 kg block is pushed with a force of 20 N across a surface with a coefficient of kinetic friction of 0.3. Calculate the acceleration of the block.
2. • Solution: $f_k={\mu }_{k}N=0.3\times 5\times 9.8=14.7N$
     $F_{net}=20-14.7=5.3N$
     $a=\frac{F_{net}}{m}=\frac{5.3}{5}=1.06m/s^2$
2. A car of mass 1200 kg moving at 20 m/s comes to rest in 5 seconds. What is the average force acting on the car?
3. • Solution:$F=\frac{\Delta p}{\Delta t}=\frac{0-1200\times 20}{5}=-4800N$

This guide covers essential formulas and their applications in mechanics, equipping you with the necessary tools for problem-solving in NEET physics.