Newton's Laws of Motion

• Course code is PHY 101.
• This course is titled Introductory Mechanics and Properties of Matter.
• Covered topics include the dynamics of particles, forces, linear motions, conservation of momentum, work, energy, power, efficiency, elastic and inelastic collisions, rotational dynamics, gravitation, motion of rigid bodies, fluids at rest, and fluid motion.

Definition of Dynamics in Physics

• Dynamics: The branch of mechanics focusing on the motion of objects and the forces causing that motion
• Unlike kinematics, dynamics explains why objects move the way they do by analyzing the relationships between forces, masses, and accelerations.
• Dynamics is based on Newton's Laws of Motion, which explain the cause-and-effect relationship between force and motion.

Importance of Dynamics in Physics

• Dynamics explains why objects move or stay stationary, providing the reasoning behind acceleration, deceleration, and equilibrium conditions.
• Concepts from dynamics are used in engineering and technology for designing vehicles, bridges, machinery, and robots.
• Engineers apply dynamics to predict the effects of forces on the motion and stability of structures.
• Dynamics allows scientists to predict the movement of celestial bodies (planets, moons, asteroids), and the flow of air and water.
• The study of dynamics enhances critical thinking and analytical skills, which are necessary for problem-solving.
• Dynamics helps design vehicles for safety and efficiency.
• Dynamics explains how forces and motion determine performance in sports (e.g., soccer ball curves).
• Dynamics explains various phenomena, such as why a chair remains stationary unless acted upon by an external force.
• Dynamics is essential for understanding advanced physics topics like electromagnetism, fluid mechanics, and quantum mechanics.

Key Examples of Dynamics in Action

• Acceleration of a car when the driver steps on the gas pedal
• A spacecraft's trajectory under the influence of gravitational forces
• The force required to push a heavy object across a surface

Newton's Laws of Motion

• Definition: Fundamental principles describing the relationship between an object's motion and the forces acting on it, forming the foundation of classical mechanics

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

• An object remains at rest or in uniform motion in a straight line unless acted upon by an external force.
• Inertia is an object's tendency to resist changes in its state of motion.
• Examples include a book on a table remaining stationary until moved, and a passenger feeling a jolt when a car stops suddenly.

Newton's Second Law of Motion

• The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.
• F = ma (Force = mass x acceleration)
  • F is the net force acting on the object (in Newtons, N)
  • m is the mass of the object (in kilograms, kg)
  • a is the acceleration of the object (in meters per second squared, m/s²)
• The equation explains how force causes an object to accelerate, and the acceleration depends on the object's mass.
• Larger forces produce greater accelerations, while heavier objects accelerate less with same force.

Key Concepts Related to Force, Mass, and Acceleration

• Force is a push or pull that can change the motion of an object (speed, direction).
  • The unit of force is the Newton (N), where 1 N = 1 kg⋅m/s².
• Mass is the amount of matter in an object and a measure of its inertia.
  • The unit of mass: Kilogram (kg)
  • Larger mass is harder to accelerate for the same force.
• Acceleration is the rate at which an object's velocity changes with time.
  • It is proportional to the force and inversely proportional to the mass.
  • The unit of acceleration is m/s².

Relationship Between Force, Mass, and Acceleration

• Force is proportional to acceleration: Increasing the force on the same mass increases acceleration.
• Force is proportional to mass: A heavier object requires a larger force for the same acceleration.
• Acceleration is inversely proportional to mass: With constant force, an object with greater mass accelerates less.

Practical Examples

• Driving a car:
  • Pressing gas increases force and acceleration
  • A heavier car needs more force for the same acceleration
• Pushing a grocery cart:
  • An empty cart accelerates quickly with a small push
  • A full cart needs more force to move at the same speed
• Throwing a ball:
  • A tennis ball accelerates more than a basketball with the same force
  • The harder a football is kicked, the greater the acceleration

Applications of F=ma

• Rocket propulsion: Engine produces a large force to accelerate the rocket upward.
• Sports: A harder kick in soccer results in faster ball acceleration.
• Lifting objects: Machines like cranes apply significant force to lift heavy loads.

Newton's Third Law of Motion

• For every action, there is an equal and opposite reaction
• Forces always come in pairs
  • If object A exerts a force on object B, object B exerts an equal force in the opposite direction on object A.
• Examples include a swimmer pushing water backward and the water pushing the swimmer forward, a rocket launching by expelling exhaust gases, and a boat moving backward when someone jumps off.

Types of Forces

• Force is a push or pull acting on an object, categorized by origin and effect
  • Gravitational Force
    • Attractive force exerted by any object with mass on another, keeping objects grounded and governing planetary motion
    • Fg = Gm1m2/r²
      • Fg is the gravitational force
      • G is the constant (6.674 × 10-11 Nm²/kg²)
      • m1m2 are the masses of two objects
      • r is the distance between their centers
    • Examples include an apple falling and the moon orbiting Earth.
  • Frictional Force
    • Opposes the relative motion between two surfaces in contact, acting parallel to the contact surface.
    • Static friction: prevents motion when stationary
    • Kinetic friction: acts when moving
    • Ff = μFN
      • Ff is frictional force
      • μ is the coefficient of friction
      • FN is normal force
    • Examples include using brake friction to slow down a car and sliding a book across a table.
  • Tension Force
    • The pulling force is exerted by a string, rope, or cable when it is stretched by forces acting at either end.
    • Always directed along the string or rope
    • Acts away from the object attached to the string
    • Examples are a bucket hanging from a rope and a person pulling an object with a rope.
  • Normal Force
    • The support force is exerted by a surface perpendicular to the object resting on it and counteracts gravitational force.
    • FN = Fg = mg (if no other vertical forces)
    • Examples include a book on a table and a person standing on the ground.
  • Applied Force
    • A force applied to an object by a person or another object.
    • Examples include pushing a door open and pulling a suitcase.
  • Air Resistance (Drag Force)
    • Frictional force opposes the motion of an object moving through a fluid (air or liquid).
    • Depends on speed, shape, and surface area
    • Increases with speed
    • Examples are a skydiver falling and a car moving at high speed
  • Spring Force
    • A restoring force exerted by a compressed or stretched spring, attempting to return it to its equilibrium position.
    • Described by Hooke's Law: Fs = -kx
      • Fs is spring force
      • k is spring constant (stiffness)
      • x is displacement from equilibrium
    • Examples include a stretched rubber band and a compressed spring in a toy.
  • Electromagnetic Force
    • Caused by electric charges at rest and in motion, including electric and magnetic forces.
    • Examples include a charged balloon attracting paper and a magnet attracting nails.
  • Buoyant Force
    • The upward force is exerted by a fluid on an immersed object, countering its weight.
    • Archimedes' Principle: The buoyant force equals the weight of the fluid displaced by the object.
    • Examples: boat floating on water, helium balloon rising
  • Centripetal Force -Keeps an object moving in a circular path, directed toward the center of the circle
    • Formula: Fc = mv²/r
      • Fc is centripetal force
      • m is the mass of the object
      • v is the velocity
      • r is the radius of the path
    • Examples: a car turning, a satellite orbiting

Free-Body Diagrams (FBDs)

• FBDs: Simplified graphical representations used to visualize all forces acting on an object, isolating it from its surroundings and showing force direction and magnitude
• FBDs are essential for applying Newton's Laws and solving for unknowns like acceleration.
• FBDs explicitly show directions, which is critical for calculating net force.
• FBDs are used in mechanics, engineering, and real-world applications like structural design and vehicle dynamics.

Steps to Draw a Free-Body Diagram

• Identify the Object: Choose the object of interest
• Isolate the Object: Separate the object from its environment and ignore unnecessary details
• Draw the Object: Represent the object as a point or simple shape at the center
• Show All Forces: Use arrows to represent forces, starting from the object and pointing in the force direction
• Label Each Force: Clearly label forces (e.g., Fg, Ff, FT)
• Consider Directions and Angles: Use axes to indicate directions and break forces into components if needed
• Double-Check: Ensure all forces (contact and non-contact) are included

Common Forces to Include in an FBD

• Gravitational Force (Fg):
  • Acts downward toward Earth's center
  • Fg = mg (where m is mass and g = 9.8 m/s²)
• Normal Force (FN):
  • Perpendicular to the surface
• Frictional Force (Ff):
  • Opposes motion or potential motion
• Applied Force (Fa):
  • Any external force

Tension Force (FT):

• Pulling force via a rope

Air Resistance (Fair):

• Opposes motion through air

Examples of Free-Body Diagrams

• A Book Resting on a Table
  • Forces: Fg (downward), FN (upward) with equal lengths
• A Box Sliding Down an Inclined Plane
  • Forces: Fg (vertically downward), FN (perpendicular to the incline), Ff (opposes motion, parallel to the incline)
  • Fg is split into components: Fg, || = mg sinθ (parallel) and Fg, ⊥ = mg cosθ (perpendicular)
• An Object Hanging by a Rope
  • Forces: Fg (downward), FT (upward)

Examine the consequences of Newton's Laws including friction and constant motion in various directions. The questions cover the application of forces in different scenarios, such as objects on inclined planes, suspended lamps, and boxes at rest.