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Physics: Mechanics

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Physics: Mechanics - Complete Interactive Lesson

Part 1: Kinematics & Motion

Physics: Mechanics for the MCAT

Part 1 of 7 — Kinematics

The Big 5 Kinematic Equations

$v = v_0 + at$ $\Delta x = v_0 t + \tfrac{1}{2}at^2$ $v^2 = v_0^2 + 2a\Delta x$ $\Delta x = \tfrac{1}{2}(v_0 + v)t$ $\Delta x = vt - \tfrac{1}{2}at^2$

Projectile Motion

Horizontal: $a_x = 0$ , $v_x = v_0\cos\theta = \text{constant}$

MCAT Tip: Free Fall

All objects fall at the same rate regardless of mass (ignoring air resistance). $g \approx 10\;\text{m/s}^2$ for quick calculations on the MCAT.

Relative Motion Shortcut

In one-dimensional motion, use relative velocity directly:

$v_{A/B} = v_A - v_B$

This simplifies chase and meeting-time questions.

Kinematics 🎯

Key Takeaways — Part 1

Use $g \approx 10\;\text{m/s}^2$ for MCAT calculations
Projectile motion: separate into x (constant velocity) and y (constant acceleration)
Complementary angles give same range; 45° gives maximum range
Relative velocity questions are often one subtraction when set up correctly.

Part 2: Forces & Newtons Laws

Physics: Mechanics for the MCAT

Part 2 of 7 — Newton's Laws & Forces

Newton's Three Laws

Inertia: An object at rest stays at rest; an object in motion stays in motion (unless acted on by a net force)
$F = ma$ : Net force equals mass times acceleration
Action-Reaction: Every force has an equal and opposite force (on a DIFFERENT object!)

Common MCAT Forces

Force	Formula	Direction
Weight	$W = mg$

Part 3: Work, Energy & Power

Physics: Mechanics for the MCAT

Part 3 of 7 — Work, Energy & Power

Work-Energy Theorem

$W_{net} = \Delta KE = \frac{1}{2}mv^2 - \frac{1}{2}mv_0^2$

Part 4: Momentum & Collisions

Physics: Mechanics for the MCAT

Part 4 of 7 — Momentum & Collisions

Linear Momentum

$\vec{p} = m\vec{v}$

Part 5: Fluids & Pressure

Physics: Mechanics for the MCAT

Part 5 of 7 — Fluids (ULTRA HIGH YIELD)

Density & Pressure

$\rho = \frac{m}{V} \qquad P = \frac{F}{A}$

Part 6: Waves & Sound

Physics: Mechanics for the MCAT

Part 6 of 7 — Torque, Equilibrium & Simple Machines

Torque

$\tau = rF\sin\theta$

$r$ = distance from pivot (lever arm)
Counterclockwise = positive (by convention)

Equilibrium Conditions

For static equilibrium: $\sum F = 0$ AND

Part 7: Review & MCAT Practice

Physics: Mechanics for the MCAT

Part 7 of 7 — Waves & Sound

Wave Properties

$v = f\lambda \qquad T = \frac{1}{f}$

Transverse: oscillation perpendicular to propagation (light, string waves)

Vertical:

a_y = -g = -9.8\;\text{m/s}^2

Time to reach max height:

t = \frac{v_0\sin\theta}{g}

Range:

R = \frac{v_0^2\sin(2\theta)}{g}

(max at 45°)

Inclined Plane (MCAT FAVORITE)

Component along plane: $mg\sin\theta$
Component perpendicular: $mg\cos\theta$ (= Normal force if no other vertical forces)
Friction on incline: $f = \mu mg\cos\theta$

Force-Analysis Workflow

Isolate one object.
Draw every real force (weight, normal, tension, friction, applied).
Choose axes along likely motion.
Write $\sum F = ma$ per axis.

Forces & Newton's Laws 🎯

Key Takeaways — Part 2

$F_{net} = ma$ : always draw a free body diagram first!
Incline: $mg\sin\theta$ along the plane, $mg\cos\theta$ perpendicular
Elevator problems: apparent weight = $m(g \pm a)$
Static friction is a maximum ( $f_s \le \mu_s N$ ); kinetic friction is exact ( $f_k = \mu_k N$ )
If speed is constant, net force is zero even if multiple forces are present.

Conservation of Energy

$KE_i + PE_i = KE_f + PE_f \quad (\text{if no non-conservative forces})$

Kinetic energy: $KE = \frac{1}{2}mv^2$
Gravitational PE: $PE = mgh$
Spring PE: $PE = \frac{1}{2}kx^2$

$P = \frac{W}{t} = Fv$

Units: Watts (W) = J/s

Conservative vs Nonconservative Forces

Conservative (gravity, springs): path-independent work; mechanical energy conserved.
Nonconservative (friction, drag): convert mechanical energy to thermal/internal energy.

When friction is present, include nonconservative work in the energy equation.

Work & Energy 🎯

Key Takeaways — Part 3

$W = Fd\cos\theta$ : only the component of force parallel to displacement does work
Conservation of energy: $KE + PE = \text{constant}$ (no friction/air resistance)
$v = \sqrt{2gh}$ for an object dropped from height $h$ — memorize this shortcut
Power = Work/time = Force $\times$ velocity
Friction does negative work and reduces mechanical energy.

Impulse-Momentum Theorem

$\vec{J} = \vec{F}\Delta t = \Delta\vec{p}$

Conservation of Momentum

$m_1v_{1i} + m_2v_{2i} = m_1v_{1f} + m_2v_{2f}$

Always conserved in the absence of external forces!

Type	Momentum	Kinetic Energy
Elastic	Conserved	Conserved
Inelastic	Conserved	NOT conserved (some lost to heat/deformation)
Perfectly inelastic	Conserved	Maximum KE loss (objects stick together)

For perfectly inelastic: $m_1v_1 + m_2v_2 = (m_1 + m_2)v_f$

Why Increasing Collision Time Matters

From $J = F\Delta t = \Delta p$ , for fixed momentum change, increasing $\Delta t$ lowers average force.

This principle explains airbags, padded helmets, and crumple zones.

Key Takeaways — Part 4

Momentum is ALWAYS conserved in collisions (absent external forces)
KE is ONLY conserved in elastic collisions
Perfectly inelastic = objects stick together = maximum KE loss
Impulse ( $F\Delta t$ ) = change in momentum — explains why airbags work (increase $\Delta t$ )

Hydrostatic Pressure

$P = P_0 + \rho g h$

where $P_0$ = atmospheric pressure (1 atm = 101,325 Pa)

Pressure applied to a confined fluid is transmitted equally: $\frac{F_1}{A_1} = \frac{F_2}{A_2}$

Archimedes' Principle (Buoyancy)

$F_b = \rho_{fluid} \cdot V_{displaced} \cdot g$

Object floats if $\rho_{object} < \rho_{fluid}$

Bernoulli's Equation (Conservation of Energy for Fluids)

$P_1 + \frac{1}{2}\rho v_1^2 + \rho g h_1 = P_2 + \frac{1}{2}\rho v_2^2 + \rho g h_2$

Narrower pipe → faster flow → lower pressure (Venturi effect)

Volume flow rate $Q = Av$ helps connect continuity to units (m $^3$ /s) and physiology passages about blood flow.

Key Takeaways — Part 5

Bernoulli: faster flow → lower pressure (explains aneurysms, airplane lift)
Continuity: $A_1v_1 = A_2v_2$ (incompressible fluid)
Buoyancy: object floats when $\rho_{object} < \rho_{fluid}$
Hydrostatic pressure increases with depth: $P = P_0 + \rho gh$

$x_{cm} = \frac{\sum m_i x_i}{\sum m_i}$

Lever: $F_1 d_1 = F_2 d_2$ (mechanical advantage)
Pulley: redirects force; compound pulleys multiply force
Inclined plane: reduces force needed but increases distance

Key Principle: Machines reduce force but NEVER reduce work ( $W = Fd$ is constant).

Pivot Choice Strategy

Choose a pivot that eliminates unknown forces (often a support point) so torque equations simplify quickly.

Torque & Equilibrium 🎯

Key Takeaways — Part 6

Torque = $rF\sin\theta$ ; maximum when force is perpendicular to lever arm
Equilibrium: $\sum F = 0$ AND $\sum \tau = 0$ (choose any pivot point!)
Simple machines trade force for distance; work is conserved
MCAT loves beam/seesaw problems — practice them!

Longitudinal: oscillation parallel to propagation (sound)

Speed in air: $\approx 340\;\text{m/s}$ (faster in denser media)
Intensity: $I = \frac{P}{4\pi r^2}$ (inverse square law)
Decibels: $\beta = 10\log(I/I_0)$ where $I_0 = 10^{-12}\;\text{W/m}^2$
Every 10 dB increase = 10× intensity

$f' = f\frac{v \pm v_{observer}}{v \mp v_{source}}$

Source approaching → higher frequency (pitch)
Source receding → lower frequency

Both ends fixed: $\lambda_n = \frac{2L}{n}$ , $f_n = n\frac{v}{2L}$
One end open: $\lambda_n = \frac{4L}{n}$ (odd harmonics only: $n = 1, 3, 5...$ )

For a fixed source frequency, wavelength changes with medium because $\lambda = v/f$ and wave speed depends on medium properties.

Waves & Sound 🎯

Physics Mechanics — Complete! ✅

Key formulas: $v = f\lambda$ , Doppler effect, inverse square law for intensity. Sound travels faster in denser media (opposite of light!). Standing wave harmonics depend on boundary conditions.

Physics: Mechanics

Inclined Plane (MCAT FAVORITE)

Force-Analysis Workflow

Key Takeaways — Part 2

Conservation of Energy

Power

Conservative vs Nonconservative Forces

Key Takeaways — Part 3

Impulse-Momentum Theorem

Conservation of Momentum

Collision Types

Why Increasing Collision Time Matters

Key Takeaways — Part 4

Hydrostatic Pressure

Pascal's Principle

Archimedes' Principle (Buoyancy)

Bernoulli's Equation (Conservation of Energy for Fluids)

Continuity Equation

Flow Rate

Key Takeaways — Part 5

Center of Mass

Simple Machines

Pivot Choice Strategy

Key Takeaways — Part 6

Sound

Doppler Effect

Standing Waves

Physics Mechanics — Complete! ✅