College Physics I Midterm I Review: Motion, Forces, and Applications

Chapter 1: Representing Motion

Scientific Notation and SI Unit Conversions

Understanding scientific notation and SI unit conversions is fundamental in physics for expressing and manipulating measurements.

• Scientific Notation: Used to express very large or very small numbers concisely. For example, $3.2 \times 10^5$.

• SI Units: The International System of Units (SI) is the standard for physical measurements. Common units include meter (m), kilogram (kg), and second (s).

• Unit Conversion: To convert between units, use conversion factors. For example, $1\,\text{km} = 1000\,\text{m}$.

• Example: Convert $5.0\,\text{km}$ to meters: $5.0\,\text{km} \times 1000\,\text{m}/\text{km} = 5000\,\text{m}$.

Basic Trigonometry (SOH CAH TOA)

Trigonometry is essential for analyzing motion, especially when dealing with vectors.

• SOH CAH TOA: Mnemonic for sine, cosine, and tangent functions:

  • Sine: $\sin\theta = \frac{\text{Opposite}}{\text{Hypotenuse}}$

  • Cosine: $\cos\theta = \frac{\text{Adjacent}}{\text{Hypotenuse}}$

  • Tangent: $\tan\theta = \frac{\text{Opposite}}{\text{Adjacent}}$

• Application: Used to resolve vectors into components.

Vector vs Scalar Quantities

Physical quantities are classified as either vectors or scalars.

• Vector: Has both magnitude and direction (e.g., velocity, force).

• Scalar: Has only magnitude, no direction (e.g., mass, temperature).

• Example: Displacement is a vector; distance is a scalar.

Chapters 2 & 3: Motion in One and Two Dimensions

Displacement, Velocity, and Acceleration vs Time Diagrams

Graphs are powerful tools for visualizing motion.

• Displacement vs Time: The slope gives velocity.

• Velocity vs Time: The slope gives acceleration; the area under the curve gives displacement.

• Acceleration vs Time: The area under the curve gives change in velocity.

• Example: If velocity-time graph shows constant velocity, displacement increases linearly.

Projectile Motion

Projectile motion describes the path of an object launched into the air, subject only to gravity.

• Key Equations:

  • Horizontal motion: $x = v_{0x} t$

  • Vertical motion: $y = v_{0y} t - \frac{1}{2} g t^2$

  • Initial velocity components: $v_{0x} = v_0 \cos\theta$, $v_{0y} = v_0 \sin\theta$

• Trajectory: Parabolic path.

• Example: A ball thrown at $30^\circ$ with speed $10\,\text{m/s}$.

Vector Addition and Subtraction

Vectors can be combined using graphical or analytical methods.

• Graphical Method: Tip-to-tail method.

• Analytical Method: Add components:

  • $\vec{A} + \vec{B} = (A_x + B_x)\hat{i} + (A_y + B_y)\hat{j}$

• Example: Adding displacement vectors to find net displacement.

Chapter 4: Forces & Newton's Laws of Motion

Newton’s Three Laws of Motion

Newton's laws form the foundation of classical mechanics.

• First Law (Law of Inertia): An object at rest remains at rest, and an object in motion remains in motion at constant velocity unless acted upon by a net force.

• Second Law: The net force on an object is equal to the mass times its acceleration.

  • $\vec{F}_{\text{net}} = m \vec{a}$

• Third Law: For every action, there is an equal and opposite reaction.

  • $\vec{F}_{A \text{ on } B} = -\vec{F}_{B \text{ on } A}$

Free Body Diagrams and Vector Sum of Forces

Free body diagrams help visualize all forces acting on an object.

• Steps:

  1. Draw the object as a dot or box.

  2. Draw arrows for each force (label them).

  3. Sum forces to find net force.

• Example: Forces on a block on a ramp include gravity, normal force, and friction.

Motion on a Ramp

Objects on inclined planes experience forces along and perpendicular to the surface.

• Gravity: $mg$ acts downward.

• Component along ramp: $mg \sin\theta$

• Component perpendicular: $mg \cos\theta$

• Example: A block sliding down a $30^\circ$ ramp.

Chapter 5: Applying Newton's Laws

Static vs Kinetic Friction

Friction opposes motion between surfaces.

• Static Friction: Prevents motion; maximum value $f_s \leq \mu_s N$.

• Kinetic Friction: Opposes motion once sliding starts; $f_k = \mu_k N$.

• Coefficient Comparison: $\mu_s > \mu_k$ (static friction is always greater).

• Example: Pushing a box until it starts sliding.

Terminal Speed

Terminal speed is reached when the force of gravity is balanced by air resistance.

• At terminal speed: $F_{\text{gravity}} = F_{\text{drag}}$

• Object stops accelerating and moves at constant speed.

• Example: A skydiver reaches terminal velocity after falling for some time.

Apparent vs Real Weight

Apparent weight is the normal force felt by an object, which can differ from real weight in accelerating systems.

• Real Weight: $W = mg$

• Apparent Weight: Depends on acceleration; in an elevator accelerating upward, $N = mg + ma$

• Example: Standing on a scale in an accelerating elevator.

Tension on Strings & Pulleys

Tension is the force transmitted through a string, rope, or cable when it is pulled tight.

• In a massless, frictionless pulley: Tension is the same throughout the string.

• Multiple objects: Analyze forces and accelerations for each object.

• Example: Two masses connected by a string over a pulley.

Forces Between Objects in Contact

When objects are in contact, they exert equal and opposite forces on each other.

• Action-Reaction Pairs: According to Newton's third law.

• Example: Two blocks pushed together; each block exerts a force on the other.

Summary Table: Static vs Kinetic Friction

Type of Friction	Formula	Coefficient	Motion
Static	$f_s \leq \mu_s N$	$\mu_s$ (greater)	No motion
Kinetic	$f_k = \mu_k N$	$\mu_k$ (smaller)	Sliding motion