Impulse and Momentum

Impulse and Momentum

• Momentum measures how hard it is to stop a moving object, it is a vector quantity
• Momentum is also known as "Inertia in Motion"
• Greater mass results in greater momentum
• Greater time results in greater momentum
• Momentum Formula: P = mv, where P is momentum, m is mass, and v is velocity
• Momentum Unit: kg m/s
• Impulse is the force applied over time to stop an object and is a vector quantity
• Impulse Formula: J = Ft, where J is impulse, F is force, and t is time
• Impulse Unit: N.s
• The Impulse-Momentum Theorem states that impulse equals the change in momentum needed to stop an object
• Applying a force for a longer time results in less impact
• Applying a force for a shorter time results in greater impact
• Impulse-Momentum Theorem Formula: Ft = mv
• The Seat Belts Use Act of 1999 (Republic Act No. 8750) mandates seatbelt use for drivers and passengers

Key equations

• Ft = mv is the impulse-momentum theorem
• m = Ft/v calculates mass
• t = mv/F calculates time
• v = Ft/m calculates velocity
• F = mv/t calculates force

Conservation of Momentum

• States that the total momentum in a system of interacting objects remains constant if there are no external forces acting on it
• Total momentum remains the same before and after an interaction
• Two skaters push each other, with one moving forward (positive momentum) and the other backward (negative momentum), the total momentum stays the same

Types of Collisions

• Elastic Collision: Objects lose no energy, deformation is fully restored, and they move separately with different velocities, adhering to the formula m1v1i + m2v2i = m1v1f + m2v2f
• Inelastic Collision: Energy loss and deformation may be permanent, objects move in the same direction with different final velocities, following the formula m1v1i + m2v2i = m1v1f + m2v2f
• Perfectly Inelastic Collision: Two objects stick together and move with the same velocity after colliding, becoming one mass, as described by the formula m1v1i + m2v2i = (m1 + m2) vf

Work

• Work is done when a force causes an object to move
• Work Formula is W = Fd when force and distance are parallel
• Work Formula is W = Fdcosθ when force and distance aren't parallel
• Work Unit is N.m or J

Energy

• Energy is the ability to do work
• Energy can be potential or kinetic
• Potential energy includes gravitational, elastic, and chemical forms
• Kinetic energy is the energy of motion
• Potential energy is stored energy
• Gravitational Potential Energy (GPE) is due to an object's position
• GPE/PE = mgh, where m is mass, g is gravity, and h is height
• Elastic Potential Energy (EPE) relates to compression or expansion
• EPE = (1/2) kx², where k is the spring constant and x is the displacement
• Chemical Potential Energy (CPE) is stored in chemical bonds
• Greater height means more potential energy
• Greater mass means more potential energy
• Kinetic Energy is energy due to motion
• Any moving matter has Kinetic Energy
• KE = (1/2) mv², where m is mass and v is velocity
• Faster objects have more kinetic energy
• More massive objects have more kinetic energy
• Mechanical Energy is due to motion or position
• Mechanical Energy can be kinetic or potential
• ME = PE + KE

Thermodynamics

• James Prescott Joules experimentally determined the mechanical work needed to produce heat in 1945
• Heat can do work
• Heat Engines convert heat energy into work
• Internal Combustion Engines burns fuel inside the engine, e.g., Gasoline and Diesel engines
• External Combustion Engines burn fuel outside the engine, e.g., Steam engines

Laws of Thermodynamics

• Part of the heat transferred to an object does work, the rest changes its internal energy
• Internal Energy is the sum of potential energy in chemical bonds and kinetic energy of molecules
• A heat engine can only convert a limited amount of heat to work
• The Kelvin-Planck statement indicates that no heat engine is 100% efficient
• The Clausius statement says heat flows naturally from hot to cold objects
• The Entropy statement defines entropy as a measure of thermodynamic disorder
• In a reversible process, total entropy remains constant
• In an irreversible process, the universe's total entropy increases
• It is impossible to lower the temperature to 0 K (Kelvin), and ideal efficiency cannot reach 100%
• Ideal Efficiency refers to the efficiency of an ideal heat engine or Carnot Engine

Magnetism

• Is the force of attraction or repulsion due to the arrangement of electrons
• Magnetic forces are strongest at the poles
• Magnets have North and South poles
• Like poles repel, unlike poles attract
• In Unmagnetized materials, spins are unarranged and in opposite directions
• In Magnetized materials, spins are arranged in the same direction

Types of Magnets

• Natural magnets are lodestones, a type of iron ore
• Artificial magnets have artificially produced magnetic properties, such as iron, cobalt, nickel, steel
• Temporary magnets lose their properties easily, e.g., soft iron
• Permanent magnets retain their properties longer, e.g., steel
• Electromagnets produce magnetic effects with electric current, a coil of wire carrying current acts as an electromagnet

Molecular Theory of Magnetism

• Breaking a magnet results in two complete magnets
• Individual molecules act as tiny molecular magnets
• Magnetic properties arise from electron rotation
• In unmagnetized materials, molecular magnets are haphazard and neutralize - losing magnetic properties

Properties of Magnets

• Magnets align in North-South directions
• Like poles repel, unlike poles attract
• Magnetic Field: the area around a magnet where magnetic forces are apparent, flowing from north to south
• The Earth generates its own magnetic field, deflecting solar winds
• Magnets attract magnetizable materials
• Magnets transmit properties through contact or induction

Electricity

• Electricity is the movement of electrons from the outer shell of atoms (valence electrons)
• All matter is made of molecules, which are made of atoms

Types of Electricity

• Static electricity is created by rubbing two materials together, creating charged materials
• Current electricity is the flow of electric charge
• A circuit requires a closed loop for current to flow
• Electrons can only move through the circuit if it's closed
• A switch is used to open or close the circuit

Electricity in Homes

• When turned on, electrons flow and vice versa
• Current measures the rate of electron flow in Amperes
• Power plants generate electricity
• Turbines are turned by burning coal, wind, or moving water
• Generators use large magnets spinning within copper wire coils
• Moving magnets cause electrons to move within the wire, creating electricity
• A step-up transformer increases the pressure to about 756,000 volts for long-distance travel
• Substation transformers lower the pressure to 2000-13000 volts
• Pole transformers further reduce voltage to 120-240 volts
• A meter box is where electricity reaches the home

Projectile Motion

• Projectiles are objects projected and move due to inertia
• Galileo Galilei described projectile motion with horizontal and vertical components
• Horizontal Velocity is constant
• The projectile covers equal displacements in equal time
• Gravity doesn't work to increase or decrease velocity
• Vertical Velocity varies in magnitude and direction
• The projectile does not cover equal displacement in equal time
• Projectile Moves Up, magnitude decreases, direction is upward
• Projectile Moves Down, magnitude increases, direction is downward
• The components produce a parabolic trajectory/path
• Horizontally Launched Projectiles have no upward trajectory or initial vertical velocity
• Vertically Launched Projectiles have initial velocity with two components that operate independently
• Upward velocity undergoes constant downward acceleration
• Horizontal motion is constant