Dynamics: Forces, Energy, & Momentum

A comprehensive overview of the fundamental principles governing motion and interaction in our physical world.

PART 1

Forces & Newton's Laws

Newton's Three Laws of Motion

1. Inertia

An object at rest stays at rest, and an object in motion stays in motion unless acted upon by a net external force.

2. Acceleration

Force equals mass times acceleration. The acceleration is directly proportional to force and inversely proportional to mass.

F = m a

3. Interaction

For every action, there is an equal and opposite reaction. Forces always occur in pairs.

Visualizing Forces: Free Body Diagrams

The Key to Problem Solving

A Free Body Diagram (FBD) is a simplified sketch used to show all the forces acting on a specific object.

Isolate the object of interest.
Represent the object as a dot or box.
Draw vectors (arrows) for each force (Gravity, Normal, Friction, Tension).
Label each vector clearly.

PART 2

Conservation of Energy

Forms of Mechanical Energy

Kinetic Energy (KE)

The energy of motion. Any object with mass that is moving possesses kinetic energy.

KE = \frac{1}{2} m v^{2}

Gravitational Potential Energy (PE)

Stored energy based on an object's position relative to a reference height.

PE = m g h

Principle: Total Mechanical Energy (KE + PE) remains constant in an isolated system.

Example: The Roller Coaster

A roller coaster is the classic example of energy conservation in action.

Top of the Hill: Potential energy is at its maximum, while kinetic energy is nearly zero.

Bottom of the Drop: Potential energy converts to kinetic energy, resulting in maximum speed.

The Loop: A mix of KE and PE keeps the car moving safely through the inversion.

PART 3

Conservation of Momentum

Understanding Momentum

"Mass in Motion"

Momentum (p) is a vector quantity defined as the product of an object's mass and velocity.

p = m v

Conservation Principle

In a closed system with no external forces, the total momentum before an event equals the total momentum after the event.

p_{initial} = p_{final}

Why it matters:

Explains recoil in cannons/rockets.
Critical for analyzing car accidents.
Used in sports (pool, bowling).
Fundamental to particle physics.

Types of Collisions

Elastic vs. Inelastic

Elastic Collision: Both momentum and Kinetic Energy are conserved. Objects bounce off each other perfectly (e.g., ideal gas molecules, billiard balls approx).

Inelastic Collision: Only momentum is conserved. Kinetic Energy is lost to heat, sound, or deformation. Objects may stick together (e.g., car crash, clay hitting floor).

Note: In the real world, perfectly elastic collisions are rare.

Summary: Key Formulas & Units

Concept	Formula	SI Unit	Vector/Scalar
Force	$F = m a$	Newton (N)	Vector
Kinetic Energy	$KE = \frac{1}{2} m v^{2}$	Joule (J)	Scalar
Potential Energy	$PE = m g h$	Joule (J)	Scalar
Momentum	$p = m v$	kg·m/s	Vector
Impulse	$J = F Δ t$	N·s	Vector

Practice Problems

Simple

Newton's Second Law

A 10 kg block is pushed across a frictionless surface with a net force of 50 N.

Calculate the acceleration of the block.

Intermediate

Conservation of Energy

A 2 kg rock falls from a cliff that is 20 m high. Assume air resistance is negligible.

Use energy conservation to find its speed just before impact. (g = 10 m/s²)

Hard

Inelastic Collision

A 2000 kg truck moving at 10 m/s collides with a stationary 1000 kg car. They lock bumpers and move together.

What is their final combined velocity?

Solutions

Simple

Given: m = 10 kg, F = 50 N

Formula: $F = m a$ implies $a = \frac{F}{m}$

Calculation:

a = \frac{50}{10} = 5 m / s^{2}

Intermediate

Given: m=2, h=20, g=10. Start v=0.

Concept: ${PE}_{top} = {KE}_{bottom}$

m g h = \frac{1}{2} m v^{2}

10 (20) = 0.5 v^{2}

200 = 0.5v² → v² = 400

v = 20 m/s

Hard

Given: m1=2000, v1=10; m2=1000, v2=0.

Formula: $p_{i} = p_{f}$

m_{1} v_{1} + m_{2} v_{2} = (m_{1} + m_{2}) v_{f}

2000 (10) + 0 = 3000 v_{f}

20,000 = 3000 vf

vf ≈ 6.67 m/s

PART 4

Interactive Learning

Group Activity: The Egg Drop Challenge

The Mission

Design a container that can protect a raw egg from a fall of 3 meters.

Physics at Play:

Impulse: Increasing the time of impact to reduce force ( $F = \frac{Δ p}{Δ t}$ ).
Air Resistance: Using parachutes to reach terminal velocity.
Energy Absorption: Crumple zones to dissipate kinetic energy.

Physics in the Real World

Rocket Propulsion (Momentum)

Safety Engineering (Impulse)

Sports Dynamics (Energy Transfer)

Questions?

Thank you for exploring dynamics with us.