Laws of Motion and Friction for JEE & NEET
Laws of Motion
Newton’s laws of motion are fundamental principles in classical mechanics that describe the relationship between a body and the forces acting upon it.
1. Newton’s First Law of Motion (Law of Inertia)
- Statement: An object at rest stays at rest and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced external force.
- Inertia: This is the tendency of an object to resist changes in its state of motion. The more massive an object, the greater its inertia.
- Example: Imagine pushing a heavy box versus a light box. The heavy box has more inertia and requires more force to start moving or to stop.
- Net Force: For an object to change its velocity (either speed or direction), a net force must act upon it. If all forces on an object are balanced, the net force is zero, and the object maintains its state of motion.
2. Newton’s Second Law of Motion
- Statement: The rate of change of momentum of an object is directly proportional to the applied force and takes place in the direction of the force.
- Momentum (p): A measure of an object’s motion, calculated as the product of its mass (m) and velocity (v): p = mv
- Equation: F = ma (where F is the net force, m is mass, and a is acceleration)
- This equation shows that acceleration is directly proportional to the net force and inversely proportional to the mass. A larger force produces a larger acceleration, and a larger mass results in a smaller acceleration for the same force.
- Example: Pushing a car requires more force than pushing a bicycle to achieve the same acceleration because the car has a larger mass.
3. Newton’s Third Law of Motion
- Statement: For every action, there is an equal and opposite reaction.
- Action-Reaction Pairs: Forces always occur in pairs. When object A exerts a force on object B, object B simultaneously exerts an equal and opposite force on object A. These forces act on different objects.
- Example: When you walk, your foot pushes backward on the ground (action). The ground, in turn, pushes forward on your foot with an equal and opposite force (reaction), propelling you forward.
Friction
Friction is a force that opposes motion between two surfaces in contact. It plays a crucial role in everyday life and is an important concept in the JEE syllabus.
Types of Friction
- Static Friction (fs): The force that prevents an object from moving when at rest. It acts in the direction opposite to the applied force.
- Example: The force that keeps a book from sliding down an inclined plane.
- Kinetic Friction (fk): The force that opposes the motion of an object already in motion. It acts in the direction opposite to the direction of motion.
- Example: The force that slows down a sliding puck on an ice rink.
- Rolling Friction: The force that resists the rolling of a wheel or a spherical object on a surface. It is generally much smaller than static or kinetic friction.
- Example: The force that slows down a rolling ball.
Laws of Friction
- Friction is proportional to the normal force: The force of friction (static or kinetic) is directly proportional to the normal force (N) acting perpendicular to the surfaces in contact.
- Friction depends on the nature of the surfaces: The roughness or smoothness of the surfaces in contact affects the force of friction. This is represented by the coefficient of friction (μ).
- Friction is independent of the area of contact (approximately): For most situations, the force of friction is roughly independent of the area of contact between the surfaces.
Important Equations
- Static Friction: fs ≤ μsN (where μs is the coefficient of static friction)
- Kinetic Friction: fk = μkN (where μk is the coefficient of kinetic friction)
Laws of Motion and Friction for JEE & NEET- Key Concepts
- Angle of Friction: The angle between the normal reaction and the resultant of the normal reaction and the limiting friction.
- Angle of Repose: The minimum angle of inclination of a plane with the horizontal such that a body placed on it just begins to slide.
- Motion on Inclined Planes: Analyzing the forces and motion of objects on inclined planes, considering friction.
- Pulley Systems: Solving problems involving friction in pulley systems.
Tips for JEE Preparation:
- Develop a strong conceptual understanding: Don’t just memorize formulas, understand the underlying principles of friction and how it affects motion.
- Practice problem-solving: Solve a wide range of problems involving friction, including those with inclined planes, pulleys, and different types of friction.
- Analyze real-world scenarios: Try to identify and explain the role of friction in everyday situations. This will help you develop a deeper understanding of the concept.