Section 1: Forces, Motion, and Momentum

Collision

An event where two or more objects come into contact and exert forces on each other.

Kinetic Energy (KE)

The energy an object has due to its motion, calculated as 𝐾𝐸=1/2𝑚𝑣^2

Momentum (p)

The product of an object’s mass and velocity; a measure of how hard it is to stop the object.

Elastic Collision

A collision in which both momentum and kinetic energy are conserved; objects bounce off each other.

Example of Elastic Collision

Two marbles colliding on a smooth surface and bouncing apart without losing energy.

Inelastic Collision

A collision in which momentum is conserved but kinetic energy is not; some energy is converted to heat, sound, or deformation.

Example of Inelastic Collision

A hockey puck hitting a goalie’s glove and stopping; momentum is conserved but some kinetic energy is lost.

Perfectly Inelastic Collision

A special case of an inelastic collision where the colliding objects stick together after impact.

Example of Perfectly Inelastic Collision

Two blocks colliding and sticking together on a frictionless surface.

Momentum in Collisions

Total momentum of the system is conserved in all types of collisions.

Kinetic Energy in Collisions

Conserved only in elastic collisions; partially lost in inelastic collisions.

Elastic Collision Real-World Example

Newton’s cradle, where balls transfer momentum and bounce back without energy loss.

Inelastic Collision Real-World Example

Car crashes where cars crumple and sound or heat is produced.

Elastic vs. Inelastic Collisions

Elastic: momentum and kinetic energy conserved; Inelastic: momentum conserved, kinetic energy not conserved.

Total Momentum

The sum of the momenta of all objects in a system before and after a collision; remains constant in isolated systems.

Impulse

The change in momentum caused by a force applied over a period of time.

Impulse Formula

Impulse equals average force multiplied by time: 𝐽=𝐹Δ𝑡

Units of Impulse

Newton-seconds (N·s).

Average Force (F)

The net force applied to an object over a time interval.

Time Interval (Δt)

The length of time during which a force acts on an object.

Impulse–Momentum Theorem

The impulse applied to an object equals its change in momentum.

Change in Momentum (Δp)

The difference between an object’s final momentum and initial momentum.

Impulse and Force Relationship

For a fixed time, increasing force increases impulse.

Impulse and Time Relationship

For a fixed force, increasing time increases impulse.

Solving for Force Using Impulse

Force equals impulse divided by time: 𝐹=𝐽Δ𝑡

Longer Contact Time

Results in a smaller average force for the same impulse.

Shorter Contact Time

Results in a larger average force for the same impulse.

Impulse as a Vector Quantity

Impulse has both magnitude and direction, matching the direction of the applied force.

Impulse in Collisions

Determines how much an object’s momentum changes during an impact.

Impulse and Safety Applications

Impulse and Safety

Increasing the time of impact reduces the force experienced.

Helmets and Pads

Increase stopping time to reduce the force on the body.

Cushioned Shoes

Spread impact forces over a longer time to lower force on feet and joints.

Bending Knees When Landing

Increases stopping time, decreasing the force on the body.

Rolling After a Fall

Reduces injury by increasing the time over which momentum changes.

Parachutes

Extend the time it takes to stop, reducing impact force.

Catching a Ball Softly

Letting your hand move backward increases stopping time and reduces force.

Impulse in Sports

Players reduce injury risk by increasing contact time during impacts.

Momentum

A measure of how hard it is to stop or change the motion of an object; depends on mass and velocity.

Symbol for Momentum (p)

The letter used to represent momentum in equations.

Momentum Formula

Momentum equals mass times velocity: p=m⋅v.

Units of Momentum

Kilogram meters per second (kg·m/s).

Mass (m)

The amount of matter in an object; measured in kilograms.

Velocity (v)

The speed of an object in a given direction; measured in meters per second.

Relationship Between Mass and Momentum

As mass increases, momentum increases if velocity stays the same.

Relationship Between Velocity and Momentum

As velocity increases, momentum increases if mass stays the same.

High Momentum

Objects that are very massive, moving very fast, or both.

Low Momentum

Objects that are light, slow-moving, or both.

Changing Momentum

Momentum changes when an object’s velocity changes due to a force.

Connection to Newton’s Second Law

Newton’s second law can be written as force equals the change in momentum divided by time.

Change in Momentum (Δp)

The difference between an object’s final momentum and initial momentum.

Force and Momentum Equation

Net force equals change in momentum divided by time: 𝐹=Δ𝑝/Δ𝑡

Stopping an Object

Requires removing all of its momentum using external forces.

Impulse

The effect of a force acting over a period of time that changes momentum (related to Δp).

Example: Runner Stopping

A runner must lose all of their momentum to come to a stop, requiring a force over time.

Acceleration and Momentum

Acceleration is a change in velocity, which also means a change in momentum.

Vector Quantity

A quantity that has both magnitude and direction (momentum is a vector).

Law of Conservation of Momentum

In an isolated system, the total momentum remains constant.

Isolated System

A system where no external forces act and no mass enters or leaves.

Total Momentum

The sum of the momenta of all objects in a system.

Before-and-After Collisions

The total momentum before a collision equals the total momentum after the collision.

Collision

An interaction where objects exert forces on each other, changing individual momenta.

Momentum Transfer

When one object loses momentum and another gains the same amount.

Equal and Opposite Momentum Changes

In a collision, momentum lost by one object equals momentum gained by another.

Frictionless Surface

An ideal surface with no external forces, allowing momentum to be conserved.

Elastic Collision

Objects bounce off each other and momentum is conserved.

Inelastic Collision

Objects stick together after colliding, but total momentum is still conserved.

External Forces

Forces from outside a system that can change total momentum.

Why Momentum Is Useful

It helps analyze collisions and interactions without needing to track complex forces.

Atom

The basic building block of matter, made of a nucleus surrounded by electrons.

Nucleus

The dense center of an atom that contains protons and neutrons and most of the atom’s mass.

Proton

A positively charged particle found in the atomic nucleus.

Neutron

A neutral particle found in the atomic nucleus with no electric charge.

Electron

A negatively charged particle that exists in energy levels around the nucleus.

Electron Shells (Energy Levels)

Regions around the nucleus where electrons are likely to be found.

Electrostatic Repulsion

The force that causes positively charged protons to repel each other.

Nuclear Forces

Forces that act inside the atomic nucleus to hold protons and neutrons together.

Strong Nuclear Force

The strongest of the four fundamental forces; binds quarks together and holds protons and neutrons in the nucleus.

Purpose of the Strong Nuclear Force

Prevents the nucleus from flying apart due to electrostatic repulsion between protons.

Range of the Strong Nuclear Force

Extremely short; only works at very small (nuclear) distances.

Quarks

Fundamental particles that make up protons and neutrons.

Up Quark

A type of quark found in protons and neutrons.

Down Quark

A type of quark found in protons and neutrons.

Proton Quark Composition

Two up quarks and one down quark.

Neutron Quark Composition

Two down quarks and one up quark.

Gluons

Particles that carry the strong nuclear force and “glue” quarks together.

Weak Nuclear Force

A fundamental force responsible for radioactive decay and particle transformations.

Purpose of the Weak Nuclear Force

Allows quarks to change type, such as turning a proton into a neutron.

Radioactive Decay

A process in which unstable atoms release energy or particles due to the weak nuclear force.

Element Transformation

When an atom changes into a different element due to particle changes caused by the weak force.

Relative Strength of Forces

Strong nuclear force > electromagnetic force > weak nuclear force > gravitational force.

Why We Don’t Feel Nuclear Forces

They act only at extremely short distances inside atoms.

Nuclear Fusion

A process where light atomic nuclei combine to form a heavier nucleus, releasing large amounts of energy.

Fusion in Stars

Occurs when the strong nuclear force overcomes electromagnetic repulsion between nuclei.

Role of Gravity in Star Formation

Pulls gas and dust together to form a dense core.

Role of Electromagnetic Force in Stars

Helps atoms form and electrons stay bound to nuclei.

Role of Strong Nuclear Force in Stars

Allows nuclei to fuse, releasing energy that makes stars shine.

Role of Weak Nuclear Force in Stars

Enables particle changes that keep fusion reactions going.

Four Fundamental Forces

Gravitational force, electromagnetic force, strong nuclear force, and weak nuclear force.

Why Stars Shine

Energy released from nuclear fusion powered by the strong and weak nuclear forces.