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HSSLIVE Plus One Physics Chapter 5: Laws of Motion Notes

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Law of Motion delves into Newton’s revolutionary understanding of force and motion, which forms the cornerstone of classical mechanics. Students explore Newton’s three laws and their applications, from explaining inertia to calculating force, mass, and acceleration relationships. This chapter introduces contact forces like friction and tension alongside gravitational forces, teaching students to create and solve free-body diagrams that predict an object’s motion under multiple forces.

Chapter 5: Laws of Motion

Plus One Physics – SCERT Kerala Board

1. Introduction to Force and Motion

  • Force: An external agent capable of changing the state of rest or motion of a body.
  • Effects of Force:
    • Changes the state of rest or motion (velocity)
    • Changes the shape or size of a body
  • Types of Forces: Contact forces and Non-contact (field) forces
  • Balanced and Unbalanced Forces: When net force is zero vs. non-zero

2. Newton’s First Law of Motion

  • Statement: “A body continues in its state of rest or of uniform motion in a straight line unless compelled to change that state by an external force.”
  • Also known as: Law of Inertia
  • Mathematical expression: If $\vec{F}_{net} = 0$, then $\frac{d\vec{v}}{dt} = 0$
  • Implications:
    • Bodies resist changes in their state of motion
    • Rest and uniform motion in a straight line are equivalent states

2.1 Inertia and Mass

  • Inertia: The inherent property of a body to resist changes in its state of rest or uniform motion.
  • Mass: Measure of inertia of a body; the greater the mass, the greater the inertia.
  • Types of Inertia:
    • Inertia of rest: Resistance to change from rest to motion
    • Inertia of motion: Resistance to change in velocity (speed or direction)
    • Inertia of direction: Resistance to change in direction of motion

2.2 Applications and Examples

  • Objects falling off when a vehicle suddenly starts/stops
  • Dusting a carpet by beating it
  • Athlete’s run before a long jump
  • Satellite’s continued motion in orbit

3. Newton’s Second Law of Motion

  • Statement: “The rate of change of momentum of a body is directly proportional to the applied force and takes place in the direction of the force.”
  • Mathematical expression: $\vec{F} = \frac{d\vec{p}}{dt} = \frac{d(m\vec{v})}{dt}$
  • For constant mass: $\vec{F} = m\vec{a}$ (Force equals mass times acceleration)
  • SI unit of force: Newton (N), 1 N = 1 kg·m/s²
  • Implications:
    • Force causes acceleration
    • Acceleration is directly proportional to force and inversely proportional to mass

3.1 Momentum

  • Definition: Product of mass and velocity of a body.
  • Mathematical expression: $\vec{p} = m\vec{v}$
  • SI unit: kg·m/s
  • Properties: Vector quantity; direction same as velocity

4. Newton’s Third Law of Motion

  • Statement: “To every action, there is an equal and opposite reaction.”
  • Mathematical expression: $\vec{F}{A \text{ on } B} = -\vec{F}{B \text{ on } A}$
  • Implications:
    • Forces always occur in pairs
    • Action and reaction forces act on different bodies
    • Action and reaction forces are simultaneous

4.1 Applications and Examples

  • Recoil of a gun
  • Propulsion of rockets
  • Walking forward
  • Swimming through water

5. Conservation of Momentum

  • Statement: “When no external force acts on a system, the total momentum of the system remains constant.”
  • Mathematical expression: If $\vec{F}{ext} = 0$, then $\vec{p}{initial} = \vec{p}_{final}$
  • Applications:
    • Collisions
    • Recoil of a gun
    • Rocket propulsion
    • Explosion of a bomb

6. Types of Forces

6.1 Friction

  • Definition: Force that opposes relative motion between surfaces in contact.
  • Types:
    • Static friction: Acts when there is no relative motion; $f_s \leq \mu_s N$
    • Kinetic friction: Acts during relative motion; $f_k = \mu_k N$
  • Factors affecting friction:
    • Nature of surfaces in contact
    • Normal reaction between surfaces
    • Area of contact (for rough surfaces)
  • Reducing friction: Lubrication, polishing, use of ball bearings, streamlining

6.2 Tension

  • Definition: Force transmitted through a string, rope, or cable when pulled tight.
  • Properties:
    • Acts along the string
    • Same throughout a massless, inextensible string
    • Always pulls, never pushes (tensile)

6.3 Normal Reaction

  • Definition: Force exerted by a surface on an object in contact with it.
  • Properties:
    • Perpendicular to the contact surface
    • Balances the component of weight perpendicular to the surface

6.4 Spring Force (Elastic Force)

  • Definition: Force exerted by a stretched or compressed spring.
  • Hooke’s Law: $F = -kx$, where $k$ is the spring constant and $x$ is displacement from equilibrium.
  • Properties:
    • Restoring force (brings back to equilibrium position)
    • Directly proportional to displacement for small deformations

7. Free Body Diagrams

  • Definition: Diagram showing all external forces acting on a body.
  • Steps to draw:
    • Represent the body as a point or simple shape
    • Identify all forces acting on the body
    • Draw arrows representing direction and magnitude of forces
    • Label all forces clearly
  • Importance: Helps in analyzing and solving problems involving forces

8. Dynamics of Circular Motion

8.1 Uniform Circular Motion

  • Centripetal Force: Force acting towards the center of circular path.
  • Mathematical expression: $F_c = \frac{mv^2}{r} = mr\omega^2$
  • Sources of centripetal force:
    • Tension in a string (e.g., stone tied to a string)
    • Gravitational force (e.g., planetary motion)
    • Friction (e.g., vehicle on a flat circular track)
    • Normal reaction (e.g., vehicle on a banked track)

8.2 Banking of Roads

  • Purpose: To provide necessary centripetal force through normal reaction.
  • Angle of banking: $\tan \theta = \frac{v^2}{rg}$
  • Advantages: Reduces dependency on friction, makes turning safer

9. Equilibrium of a Particle

  • Conditions for equilibrium:
    • First condition: Net force must be zero, $\sum \vec{F} = 0$
    • For a particle in 2D: $\sum F_x = 0$ and $\sum F_y = 0$
  • Types of equilibrium:
    • Static equilibrium: Particle at rest
    • Dynamic equilibrium: Particle moving with constant velocity

10. Common Forces in Nature

10.1 Gravitational Force

  • Newton’s Law of Gravitation: $F = G\frac{m_1m_2}{r^2}$
  • Properties:
    • Always attractive
    • Acts along the line joining the centers of mass
    • Central and conservative force

10.2 Electromagnetic Force

  • Coulomb’s Law for electric force: $F = k\frac{q_1q_2}{r^2}$
  • Properties:
    • Can be attractive or repulsive
    • Much stronger than gravitational force
    • Responsible for most everyday forces (except gravity)

10.3 Strong Nuclear Force

  • Properties:
    • Strongest fundamental force
    • Very short range (within nucleus)
    • Holds protons and neutrons together in nucleus

10.4 Weak Nuclear Force

  • Properties:
    • Responsible for radioactive decay
    • Very short range
    • Weaker than electromagnetic force but stronger than gravity

11. Motion on Inclined Planes

  • Components of weight:
    • Parallel to the plane: $mg\sin\theta$ (causes acceleration down the plane)
    • Perpendicular to the plane: $mg\cos\theta$ (balanced by normal reaction)
  • Acceleration down the plane (without friction): $a = g\sin\theta$
  • With friction: $a = g\sin\theta – \mu g\cos\theta$

12. Solving Problems Using Newton’s Laws

  1. Identify the system and draw a free body diagram showing all forces.
  2. Choose a suitable coordinate system (usually with one axis in the direction of acceleration).
  3. Apply Newton’s second law ($\vec{F} = m\vec{a}$) in component form.
  4. Solve the resulting equations for the unknown quantities.
  5. Verify the answer is reasonable and check units.

13. Important Points to Remember

  • Newton’s laws apply in inertial frames of reference.
  • Mass is a scalar quantity, while force and momentum are vector quantities.
  • Action and reaction forces never cancel each other as they act on different bodies.
  • Friction always opposes relative motion or tendency of motion.
  • Centripetal force is not a new type of force, but a role played by forces like tension, friction, etc.
  • The net force in uniform circular motion acts perpendicular to velocity.

14. Summary

  • Newton’s First Law defines inertia and inertial frames of reference.
  • Newton’s Second Law relates force to the rate of change of momentum.
  • Newton’s Third Law states that forces always occur in pairs of equal magnitude and opposite direction.
  • Momentum is conserved when no external force acts on a system.
  • Free body diagrams are essential tools for analyzing forces.
  • Various types of forces in nature include friction, tension, normal reaction, and spring force.
  • In circular motion, a centripetal force directed towards the center is necessary.
  • The application of Newton’s laws allows us to predict and explain a wide range of physical phenomena.

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