6.3 Classical Physics, Energy, Forces, and Motion

6.3 Classical Physics, Energy, Forces, and Motion

Core Principle: Physical science and classical physics constitute approximately 25% to 30% of the CAT-ASVAB General Science subtest. Success requires a solid command of Newtonian mechanics (forces, inertia, acceleration, mass vs. weight), work and power calculations, conservation of energy ($KE$ and $PE$), thermodynamics and heat transfer modes, wave mechanics ($v = f\lambda$), acoustic propagation, the electromagnetic spectrum, and geometric optics (reflection and refraction).

Candidates must understand both qualitative scientific principles and basic quantitative physics equations to solve ASVAB computational problems accurately within the 30-second-per-item timeframe.

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1. Classical Newtonian Mechanics & Laws of Motion

Sir Isaac Newton formulated three foundational laws of motion that govern the mechanical behavior of physical bodies:

+-----------------------------------------------------------------------------------------+
|                               NEWTON'S THREE LAWS OF MOTION                             |
+-------------------+-----------------------------------+---------------------------------+
| Law               | Formal Scientific Principle       | Practical Military Application  |
+-------------------+-----------------------------------+---------------------------------+
| Newton's 1st Law  | Law of Inertia: An object at      | Seatbelts in tactical vehicles  |
| (Inertia)         | rest remains at rest, and an      | restrain passengers when the    |
|                   | object in motion continues at     | vehicle decelerates abruptly;   |
|                   | constant velocity in a straight   | projectiles maintain orbital    |
|                   | line unless acted upon by a net   | trajectories in vacuum.         |
|                   | external unbalanced force.        |                                 |
+-------------------+-----------------------------------+---------------------------------+
| Newton's 2nd Law  | Fundamental Force Law: The        | Firing heavier artillery shells |
| (F = m · a)       | acceleration of an object is      | requires proportionally greater |
|                   | directly proportional to net      | propellant force to achieve the |
|                   | force and inversely proportional  | same muzzle acceleration as     |
|                   | to its mass: F_net = m · a        | lighter rounds.                 |
+-------------------+-----------------------------------+---------------------------------+
| Newton's 3rd Law  | Action-Reaction: For every        | Firearm recoil: expanding gas   |
| (Action/Reaction) | action force exerted on a body,   | exerts forward force on bullet  |
|                   | there is an equal in magnitude    | and an equal rearward force on  |
|                   | and opposite in direction reaction| the weapon bolt/receiver; rocket|
|                   | force: F_A = -F_B                 | exhaust thrusts rocket upward.  |
+-------------------+-----------------------------------+---------------------------------+

Mass vs. Weight Dynamics

• Mass ($m$): The quantitative measure of an object's inertia (resistance to acceleration) and the total amount of matter it contains. Measured in kilograms (kg). Mass is invariant and remains identical anywhere in the universe.
• Weight ($W$): The downward gravitational force exerted on an object's mass by a planetary gravitational field. Measured in Newtons (N) in SI units or pounds-force (lb) in imperial units:

$W = m \cdot g$

Where $g$ is the local acceleration due to gravity ($g \approx 9.8\text{ m/s}^2$ on Earth's surface; $g \approx 1.6\text{ m/s}^2$ on the Moon).

• ASVAB Example: An astronaut with a mass of $100\text{ kg}$ has a mass of $100\text{ kg}$ on both Earth and the Moon. However, their weight on Earth is $W = 100 \times 9.8 = \mathbf{980\text{ N}}$, while their weight on the Moon is $W = 100 \times 1.6 = \mathbf{160\text{ N}}$.

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2. Kinematics, Linear Momentum & Friction

Scalar vs. Vector Physical Quantities

• Scalar Quantities: Described completely by magnitude (numerical value + unit) only. Examples: Distance ($50\text{ m}$), Speed ($25\text{ m/s}$), Mass ($10\text{ kg}$), Time ($12\text{ s}$), Energy ($500\text{ J}$), Temperature ($300\text{ K}$).
• Vector Quantities: Described by both magnitude AND spatial direction. Examples: Displacement ($50\text{ m North}$), Velocity ($25\text{ m/s East}$), Acceleration ($9.8\text{ m/s}^2\text{ downward}$), Force ($100\text{ N forward}$), Momentum ($40\text{ kg}\cdot\text{m/s East}$).

Velocity & Acceleration Formulas

$\text{Speed } (s) = \frac{\text{Distance } (d)}{\text{Time } (t)}, \qquad \text{Velocity } (\vec{v}) = \frac{\text{Displacement } (\Delta \vec{x})}{\text{Time } (\Delta t)}$ $\text{Acceleration } (\vec{a}) = \frac{\text{Change in Velocity } (\Delta \vec{v})}{\text{Time Elapsed } (\Delta t)} = \frac{\vec{v}_f - \vec{v}_i}{\Delta t} \quad (\text{m/s}^2)$

Linear Momentum ($\vec{p}$) & Conservation

Momentum is the quantitative measure of an object's mass in motion:

$\vec{p} = m \cdot \vec{v} \quad (\text{kg}\cdot\text{m/s})$

Law of Conservation of Linear Momentum: In a closed, isolated physical system with no external forces, the total initial momentum before an interaction or collision exactly equals the total final momentum:

$\sum \vec{p}_{\text{initial}} = \sum \vec{p}_{\text{final}} \quad \Longrightarrow \quad m_1 v_{1i} + m_2 v_{2i} = m_1 v_{1f} + m_2 v_{2f}$

Friction Forces

Friction is a resistive contact force opposing relative motion between two surfaces:

1. Static Friction ($f_s$): The resistive force that prevents an object at rest from starting to slide. Static friction is always higher than kinetic friction.
2. Kinetic (Sliding) Friction ($f_k$): The resistive force opposing an object actively sliding across a surface.
3. Rolling Friction: The resistance encountered when a spherical or cylindrical wheel rolls across a surface (significantly lower than sliding friction).
4. Fluid Friction (Drag): The resistance encountered by an object moving through a fluid medium (liquid or air).

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3. Work, Power & Conservation of Mechanical Energy

+-----------------------------------------------------------------------------------------+
|                               MECHANICAL WORK, ENERGY & POWER                           |
+-----------------------+-----------------------------+-----------------------------------+
| Physical Concept      | Governing Physics Equation  | Standard SI Metric Unit           |
+-----------------------+-----------------------------+-----------------------------------+
| Mechanical Work (W)   | W = F · d                   | Joule (1 J = 1 N · m = 1 kg·m²/s²)|
| Kinetic Energy (KE)   | KE = ½ · m · v²             | Joule (J)                         |
| Gravitational PE (PE) | PE = m · g · h              | Joule (J)                         |
| Mechanical Power (P)  | P = W / t = ΔE / t          | Watt (1 W = 1 J/s)                |
|                       |                             | (1 Horsepower = 746 Watts)        |
+-----------------------+-----------------------------+-----------------------------------+

Work Definition in Physics

In physics, Work ($W$) is performed only when an applied force causes a displacement of the object in the direction of the force:

• Pushing against a stationary wall for 10 hours with 500 N of force does zero mechanical work because displacement is zero ($d = 0$).
• Lifting a 20 kg crate vertically by 2 meters requires work against gravity: $W = F \cdot d = (m \cdot g) \cdot d = (20\text{ kg} \times 9.8\text{ m/s}^2) \times 2\text{ m} = \mathbf{392\text{ Joules}}$

Kinetic vs. Potential Energy Mechanics

• Kinetic Energy ($KE = \frac{1}{2}mv^2$): Energy of motion. Because velocity is squared, doubling an object's speed quadruples ($4\times$) its kinetic energy, quadrupling the braking distance required to bring a vehicle to a complete stop!
• Gravitational Potential Energy ($PE = mgh$): Energy stored in an object due to its elevated position within a gravitational field.

Law of Conservation of Mechanical Energy

In an ideal mechanical system without non-conservative frictional dissipation:

$E_{\text{total}} = KE_{\text{initial}} + PE_{\text{initial}} = KE_{\text{final}} + PE_{\text{final}} = \text{Constant}$

• Classic ASVAB Scenario (The Pendulum / Roller Coaster):
  • At the maximum height (apex), $PE$ is maximal and $KE = 0$ (velocity is momentarily zero).
  • As the mass plunges downward, $PE$ converts completely into $KE$.
  • At the lowest point of trajectory ($h = 0$), $KE$ is maximal (maximum velocity) and $PE = 0$.

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4. Thermodynamics & Heat Transfer Mechanisms

Temperature is the physical measure of the average kinetic energy of the microscopic particles in a substance. Heat ($Q$) is the thermal energy transferred spontaneously from an object of higher temperature to an object of lower temperature.

+-----------------------------------------------------------------------------------------+
|                                THREE MODES OF HEAT TRANSFER                             |
+--------------------+------------------------------------+-------------------------------+
| Mode               | Physical Mechanism                 | Everyday & Military Examples  |
+--------------------+------------------------------------+-------------------------------+
| 1. Conduction      | Direct physical contact; thermal   | Metal spoon heating up in hot |
|                    | energy transferred via molecular   | soup; aluminum heatsinks on   |
|                    | collisions and free electrons.     | computer microprocessors.     |
+--------------------+------------------------------------+-------------------------------+
| 2. Convection      | Macroscopic bulk circulation of    | Boiling water currents; hot   |
|                    | FLUIDS (liquids or gases) driven   | air balloon rising; atmospheric|
|                    | by thermal density variations.     | thermal updrafts.             |
+--------------------+------------------------------------+-------------------------------+
| 3. Radiation       | Transfer of thermal energy via     | Sunlight warming Earth across |
|                    | ELECTROMAGNETIC INFRARED WAVES.    | the vacuum of space; FLIR     |
|                    | Requires NO physical medium!       | thermal night vision sights.  |
+--------------------+------------------------------------+-------------------------------+

Temperature Scales & Mathematical Conversions

• Celsius to Fahrenheit: $F = \frac{9}{5}C + 32 = 1.8C + 32$
• Fahrenheit to Celsius: $C = \frac{5}{9}(F - 32)$
• Celsius to Kelvin: $K = C + 273.15$
• Absolute Zero ($0\text{ K} = -273.15^\circ\text{C} = -459.67^\circ\text{F}$): The theoretical temperature at which all classical thermodynamic molecular kinetic motion ceases.

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5. Wave Mechanics & Sound Physics

A wave is an energetic disturbance that propagates through space or a physical medium, transmitting energy without transferring permanent physical matter.

Wave Properties & Terminology

• Wavelength ($\lambda$): The physical distance between two consecutive identical points on a wave (e.g., crest-to-crest or compression-to-compression), measured in meters (m).
• Frequency ($f$): The number of complete wave cycles passing a fixed point per second, measured in Hertz ($\text{Hz} = \text{s}^{-1}$).
• Amplitude ($A$): The maximum displacement of a wave from its central equilibrium position (corresponds to wave energy and sound volume/intensity).
• Period ($T$): The time required for one full wave cycle to pass ($T = 1/f$).

The Universal Wave Equation

The velocity ($v$) of any wave is the product of its frequency and wavelength:

$v = f \cdot \lambda$

Because wave speed is constant in any uniform medium, frequency and wavelength are inversely proportional (higher frequency means shorter wavelength).

+-----------------------------------------------------------------------------------------+
|                               TRANSVERSE VS. LONGITUDINAL WAVES                         |
+------------------------------------+----------------------------------------------------+
| TRANSVERSE WAVES                   | LONGITUDINAL (COMPRESSIONAL) WAVES                 |
+------------------------------------+----------------------------------------------------+
| • Particle displacement is         | • Particle displacement is PARALLEL to the         |
|   PERPENDICULAR (90°) to wave      |   direction of wave propagation                    |
|   propagation direction            | • Composed of COMPRESSIONS and RAREFACTIONS        |
| • Composed of CRESTS and TROUGHS   | • Examples: Sound waves, ultrasound, seismic       |
| • Examples: Light, EM waves, radio,|   Primary (P) waves                                |
|   water surface waves, seismic S   |                                                    |
+------------------------------------+----------------------------------------------------+

Acoustic Physics (Sound Dynamics)

• Medium Dependency: Sound is a mechanical longitudinal wave that CANNOT propagate through a vacuum; it requires an elastic physical medium.
• Speed of Sound Across Media: Sound travels fastest in dense, elastic solids and slowest in compressible gases: $v_{\text{solids}} > v_{\text{liquids}} > v_{\text{gases}}$
  • Speed in Air (at 20°C): $\approx 343\text{ m/s}$ ($1,125\text{ ft/s}$ or $767\text{ mph}$ = Mach 1)
  • Speed in Fresh Water: $\approx 1,480\text{ m/s}$
  • Speed in Solid Structural Steel: $\approx 5,960\text{ m/s}$
• The Doppler Effect: The observed shift in wave frequency resulting from relative motion between the wave source and an observer:
  • Approaching Source: Wavefronts compress $\rightarrow$ Observed frequency increases $\rightarrow$ Higher audible pitch.
  • Receding Source: Wavefronts stretch $\rightarrow$ Observed frequency decreases $\rightarrow$ Lower audible pitch.

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6. The Electromagnetic Spectrum & Geometric Optics

Electromagnetic (EM) waves are oscillating transverse electric and magnetic fields that require no physical medium. In a vacuum, all electromagnetic waves travel at the speed of light ($c \approx 3.0 \times 10^8\text{ m/s}$ or $186,000\text{ miles/s}$).

+-----------------------------------------------------------------------------------------+
|                             THE ELECTROMAGNETIC SPECTRUM                                |
+-----------------------------------------------------------------------------------------+
|  LONG WAVELENGTH (λ)                                            SHORT WAVELENGTH (λ)   |
|  LOW FREQUENCY (f)                                               HIGH FREQUENCY (f)    |
|  LOW PHOTON ENERGY (E)                                          HIGH PHOTON ENERGY (E) |
|                                                                                         |
|  [Radio] ---> [Microwave] ---> [Infrared] ---> [VISIBLE] ---> [UV] ---> [X-Ray] ---> [Gamma]|
|                                                   |                                     |
|                       +---------------------------+---------------------------+         |
|                       | Visible Spectrum (ROYGBIV: 700 nm down to 400 nm)     |         |
|                       | Red -> Orange -> Yellow -> Green -> Blue -> Violet   |         |
|                       +-------------------------------------------------------+         |
+-----------------------------------------------------------------------------------------+

Optics: Reflection, Refraction & Lenses

• Law of Reflection: The angle of incidence ($\theta_i$) equals the angle of reflection ($\theta_r$), measured relative to the normal line perpendicular to the reflective surface: $\theta_i = \theta_r$
• Refraction (Snell's Law): The bending of a light ray as it passes from one transparent medium into another with a differing optical density (refractive index $n$):
  • Entering a denser medium (e.g., air to glass): Light slows down and bends TOWARD the normal.
  • Entering a less dense medium (e.g., glass to air): Light speeds up and bends AWAY from the normal.
• Optical Lenses & Mirrors:
  • Convex Lens (Converging): Thicker at center than edges; bends incoming parallel light rays inward to a single focal point. Used in magnifying glasses, cameras, and hyperopia (farsightedness) correction.
  • Concave Lens (Diverging): Thinner at center than edges; spreads incoming parallel light rays outward. Used in myopia (nearsightedness) correction.
  • Convex Mirror (Diverging): Curves outward; produces upright, reduced virtual images with a wide field of view (used in tactical vehicle side mirrors).

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7. Real-World Military & Tactical Applications

1. Ballistics & Trajectory Planning: Projectile range and bullet drop are governed by gravity ($d = \frac{1}{2}gt^2$) and aerodynamic fluid drag forces, requiring snipers and artillery gunners to calculate wind vector components and elevation angles.
2. Infrared Thermal Sights (FLIR): Weapon night sights detect infrared radiation emitted spontaneously by warm biological targets and running engines without requiring external visible illumination.
3. SONAR vs. RADAR Physics: Submarines utilize acoustic longitudinal waves (SONAR) because sound propagates efficiently through dense seawater, whereas aerial defense systems utilize electromagnetic radio waves (RADAR) traveling at light speed through the atmosphere.