Physics Mechanics Quiz

Translational Motion

• Translational motion is the movement of an object from one location to another.
• One-dimensional motion involves movement along a straight line.
• Two-dimensional motion involves movement in a plane.

Outline: Translational Motion

• Motion in 1 Dimension
  • Descriptions of motion
  • Equations of motion
  • Graphs of motion
• Motion in 2 Dimensions
  • Vectors
  • Projectile Motion

Descriptions of Motion

• Definition
  • The laws governing motion include Newton's laws
  • Prediction of motion is possible.

Description of Motion

• Question 1: What are the laws that govern how this object moves and behaves?
• Question 2: Could I somehow predict how it will move and behave?

Describing Motion with an Apple

• Table: Describing Motion with an Apple
  • Name: Position, Velocity, Acceleration
  • Symbol: x, v, a
  • Units: meters, meters per second, meters per second squared
  • Unit abbreviation: m, m/s, m/s²
• Data: x = 1 m, v = 1 m/s, a = 0.5 m/s²

Intervals of Time

• Initial conditions: x = 1 m, v = 0.25 m/s, a = 0.5 m/s²

• Final conditions: x = 4 m, v = 1.75 m/s, a = 0.5 m/s²

• Time: 3 sec

• Displacement = 3 m

• Average velocity = 1 m/s

• Average acceleration = 0.5 m/s²

• Time = 2 sec and Displacement = 1.5 m

• Average velocity = 0.75 m/s.

• Average acceleration = 0.5 m/s^2

Equations of Motion in 1 Dimension

• a is constant
• v = v₀ + at
• x = x₀ + v₀t + 1/2at²
• v² – v₀² = 2a (x – x₀)

Equations of Motion - Solving Problems

• Steps for solving problems:
  • 1. Draw a picture.
  • 2. Catalogue what you know
  • 3. Catalogue what you need
  • 4. Knowns and unknowns.
  • 5. Gather information

Equations of Motion

• Example Problem: dropping a penny from the top of a 1,000-meter building

• Constant gravitational acceleration: 9.8 meters per second squared downwards

• Acceleration due to gravity is -9.8 m/s^2

Graphs of Motion

• Visualization
• Position vs. Time graph, Velocity vs. Time graph, and Acceleration vs. Time graph are examples.

Visualizing Kinematics

• Position: x (m) vs. t (s), Velocity: v (m/s) vs. t (s), and Acceleration: a (m/s²) vs. t (s)

Visualizing Kinematics

• Example: Δx = 4 m, Δt = 2s, v = 2 m/s

Translational Motion

• Two-dimensional Motion

Vectors

• A vector has magnitude and direction.
• Scalars only have magnitude. (examples: Temperature (T), and Speed (S))

Vectors

• Example: velocity = (300, 400) speed = 500 km/h, (0,100)

Projectile Motion

• Two Dimensions
• Horizontal (x), Vertical (y) -ax = 0 -Vx = V₁x -x = x₀ +v₁xt -ay = -g -Vy = V₁y - gt -y = Y₀ + v₁yt-½gt²

Projectile Motion

• Components of Projectile Motion: -"SOH": sin(θ) = opp/hyp -"CAH": cos(θ) = adj/hyp -"TOA": tan(θ) = opp/adj

Projectile Motion

• Horizontal (x): aₓ = 0, Vₓ=V₀ₓ, X = X₀ + V₀ₓ t
• Vertical (y): aᵧ = -g, Vᵧ = V₀ᵧ - gt, Y = Y₀ + V₀ᵧ t - ½ gt²

Projectile Motion

• Example Problem: a cannonball launched at 100 m/s at a 45-degree angle above the horizontal. Find the horizontal distance and maximum height.

Learning Outcomes

• Know x, v, and a.
• Relate x, v, and a graphically.
• Relate x, v, and a through equations of motion.
• Break a vector into perpendicular components.
• Solve projectile problems in 1 and 2 dimensions

Force I

• Newton's Laws of Motion

Force

• Units for mass are kilograms (kg).
• Units for position are meters (m).
• Units for velocity are meters per second (m/s).
• Units for acceleration are meters per second squared (m/s²).

Newton's Laws

• 1. Inertia: An object's velocity remains constant unless acted upon by an external force.
• 2. Force and acceleration: The sum of forces on an object equals its mass times its acceleration (F = ma)
• 3. Action-reaction: For every force, there is an equal and opposite reaction force.

Force - working on an apple

• Inertia: v=constant
• Force and acceleration: F=ma
• Action-reaction: F₁ on₂ = -F₂ on₁

Equal and Opposite Forces

• Mass times acceleration of object (M) will equal the negative of the mass times acceleration of object (m). Matruck = -mabug

Force Problems in 2 Dimensions

• Steps for solving problems:
  • Choose a coordinate system.
  • Draw a free body diagram.
  • Break all vectors into perpendicular components.
  • Write Newton's 2nd law for each axis.
  • Solve for acceleration.

Force in 2 Dimensions

• Example problem: A 1000kg spaceship is accelerated with 2N. A leak exerts a force of 1N at a 30-degree angle relative to the ship's direction. What's the velocity and speed after 1 hr.

Kinematics Versus Dynamics

• Kinematics involves movement without concern for the cause (i.e. forces). The equation for distance is a basic example of a kinematics problem.
• Equation of motion involves the cause of movement (i.e. forces)

Force II

• Important Forces
  • Gravity
  • Normal force.
  • Tension.
  • Friction.
  • Air resistance.

Gravity and the Normal Force

• Gravity equation: F = Gm₁m₂/r²
• Normal force definition: The force perpendicular to a surface.

The Inclined Plane

• Setup for inclined plane scenario and problem solving.

The Inclined Plane and Gravity

• Example problem: A 10-kg block slides down a frictionless inclined plane with a 30-degree incline. How long will it take to slide 5 meters down the slope?

Tension

• Definition
• Example: A 10kg mass on a slope with a 30-degree incline is connected to a rope that passes over a pulley to a 15kg mass. Determine how far the 15kg mass will fall during 1 second of motion

Friction

• Definition of friction
• Example problem: A block is at rest on a slope with a coefficient of static friction of 0.5. What's the angle of the ramp at the threshold of movement.

Air Resistance

• Definition of air resistance
• Terminal velocity

Uniform Circular Motion

• Definition of uniform circular motion
• Example Problem: An apple is swinging in a circle at the end of a 1-meter-long string. What's the minimum speed of the spinning apple, and how much tension is in the string at the bottom of the swing, if the apple's mass is 1kg
• Equations for uniform circular motion: a = v²/r, Fc = m v²/r

Center of Mass

• Definition.
• Example Problem: Determining the center of mass for various objects like the earth-sun system.

Optics I

• Reflection and Refraction

Optics in Context

• Reflection, Refraction.
• Mirrors and Lenses.
• Optical Instruments.

Index of Refraction

• Light travels slower through different mediums than in a vacuum.
• n = c/v (Where n is the index of refraction, c is the speed of light in a vacuum, and v is the speed of light in the medium).

Reflection and Refraction

• Refraction: Light bends when entering a medium with a different index of refraction.
• Reflection: The bouncing of light off a surface.

Snell's Law

• n₁ sin θ₁ = n₂ sin θ₂ (Where n₁ and n₂ are the indices of refraction of the two mediums, and θ₁ and θ₂ are the angles of incidence and transmission)

Total Internal Reflection

• Occurs when light travels from a denser medium to a sparser medium and the angle of incidence is greater than a critical angle. The light will reflect back into the denser medium.

Dispersion

• Refraction of light depends on the wavelength. Different wavelengths diffract differently.

Optics II

• Mirrors and Lenses

Mirrors

• Properties of curved circular mirrors
• Concave, Convex

Concave Mirrors

• Parallel rays reflect through the focal point.
• The focal point (f) is half the radius of curvature (r).
• Light from distant objects appears parallel when it reaches the mirror.
• Inverted image can be created at differing distances from the mirror.
• Magnification of concave mirrors: m = -i/o and hi/ho = -i/o

Convex Mirrors

• Rays toward the focal point leave parallel.
• Parallel rays reflects directly away from the focal point.
• The image is virtual.

Lens Properties

• Lenses follow similar logic to mirrors.
• Converging, Diverging lenses
• Similar equation as mirrors, with conventions for f, o, and i

Converging Lenses

• Same geometry as mirrors.
• Image will reverse at certain distances

Diverging Lenses

• Rays parallel to the principal axis diverge away from the focal point.

Learning Outcomes

• You know the basic properties of mirrors and lenses.
• You are able to find the image created by a mirror or lens.
• You can identify an image's location and type.

Optics III

• Optical Instruments

Lens Power

• P = 1/f (Where p is lens power in diopters, and f is the focal length in meters)

Lens Aberration

• Imperfections that cause the geometric ray model to not give accurate results in optics

Optical Instruments and their Features

• Microscopes, Telescopes, Eyes

Visual Angle

• The apparent perspective angle that an object occupies from your vantage point

Angular Magnification

• Magnification is the ratio of two angles, the angular size of the object seen directly and the angular size of the object seen with an optical device. Me = θ₂ / θ₁

Near Point

• Closest point where objects are clearly in focus
• Roughly 25cm for human eyes
• Optical magnification: M₅ = θ₂ / θ₁ = 25cm

Eye Properties

• Light must focus on the retina.
• Things far away from the viewer appear to transmit parallel light rays.
• Muscles in the eye can adjust the shape of the lens to focus on objects at different distances

Magnetism

• Fields and Forces

Magnetic Fields

• Definition
• Magnetic fields are created by moving charges.
• Properties of magnetic fields:
  • B ∝ I/r

Direction of a Magnetic Field

• Right Hand Rule:
  • Thumb is in current flow direction
  • Curl the fingers around the wire to show magnetic field direction.

Linear Magnetic Field

• By twisting a wire, a linear magnetic field can be created
• Add additional magnetic fields to a given wire or coil.

Bar Magnets

• Bar magnets have north and south poles, with field lines running from north to south.
• Magnetic forces apply when magnetic poles are within a magnetic field.

Magnetic Fields

• Example problem: Calculating the magnetic field strength at a given distance from two parallel wires that carry current in opposite but equal directions.

Lorentz Force

• Definition.
• Equation for magnetic force acting on a moving charged particle; |FB| = qvB sin θ
• Direction of force: Right Hand Rule
• In the presence of both electric and magnetic fields: F = FE + FB = qE + q v B sin θ

Cyclotron

• Charged particle moving in a circular path
• Uniform circular motion: F = mv²/r
• Magnetic force: |FB| = qvB
• Cyclotron period: t = 2πm/qB

Learning Outcomes

• Understand the cause and shape of magnetic fields.
• Know the forces acting on a charge in a magnetic field.

Light I

• Wave Phenomena

Light in Context

• Wave phenomena.
• Properties of radiation.
• The light spectrum.

Interference

• Definition

Double-Slit Experiment

• Thomas Young's experiment
• Determine if light is a wave or a particle

Double-Slit Experiment

• Light creates interference bands when directed at two slits

Thin Film Interference

• Light passes through different mediums resulting in a change in speed and altered phase.

Diffraction

• Definition
• The bending/diffraction of waves as they pass a boundary

X-ray Diffraction

• Diffraction of x-rays through a material with an atomic structure
• Materials can be identified using diffraction pattern

Light II

• Properties of Light

Properties of Light

• Light consists of oscillating electric and magnetic fields
• Light travels at constant velocity (c)

Polarization

• Definition of Polarization
• Linear Polarization
• Circular Polarization

Polarization

• Polarization of light can be absorbed

Light III

• The Light Spectrum

Electromagnetic Spectrum

• The full range of wavelengths/frequencies of electromagnetic radiation.

Photons

• Definition of photons.
• Relationship of energy, frequency, and wavelength to photons.

Test your understanding of fundamental concepts in physics mechanics. This quiz covers topics such as gravitational force, normal force, velocity, and acceleration. Perfect for students looking to reinforce their grasp of these principles.