Category Archives: Physics

Physics: Spring Final Study Guide

Test 1

Physics Unit 15: Electrostatics

Physics Unit 15: Electrostatics
question bank

Test 2

Physics Unit 14: Properties of Light

Physics Unit 14: Properties of Light
question bank

Test 3

Physics Unit 13: Optics

Physics Unit 13: Optics
questionbank

Test 4

Physics Unit 12: Waves and Sound

Physics Unit 12: Waves and Sound
question bank

Unit 13: Light – Essential learning goals

Textbook: Glencoe Ch 16
1: You are responsible to read the entire chapter pg 441-437
2: Packet due next monday:
pg 436 practice problems #1-6
pg 447 practice problems# 14-17

Key concepts:

  1. Wave nature of light, E&M fields, E&M spectrum (see post http://math-science-resources.com/physics-unit-12-the-nature-of-light/ )
  2. Luminous flux, illuminance (be able to calculate), illumination
  3. Relativistic Doppler effect

There will be a short quiz next Monday – Tues.

 

Part 2: Chapter 17 – to be assigned later

Learning objectives:

  1. Reflection, Huygen’s principle of wavelets.
    1. Excel project due following monday by email
  2. Specular and Lambertian reflectance, scattering
    1. effect of surface roughness on reflectance

 

Part 3: The peculiar properties of light

  1. Refraction (Huygen’s model)
  2. Diffraction
    1. single slit (drawing and calculating)
    2. double slit
    3. Fraunhofer interference

 

 

 

 

Newton’s Laws

What you need to know:
Newton proposed 3 “Laws”
1] Inertia: An object at rest tends to remain at rest unless acted on by an eternal force. An object in motion tends to remain in motion unless acted on by an external force.
2] Force and Mass: Remember the equation F = ma where F is the force {in units of Newtons – what else could it be?}, a is acceleration and m is an experimentally determined constant of proportionality for an object. m is called the mass.
3] Law of reaction: For every action there is an equal and opposite reaction.

Easy to remember examples:
1] A body in motion, stays in motion…
2] Here’s a joke: A Physicist walks into a bar, and he says…….. “F = ma”
that’s it, pretty funny eh?
3] Push someone and they’ll push back.

Physics Unit 1: Study Guide

What you need to know for the Unit 1 Test (Fri Sept 23 – B, Mon Sept 26 A)

Basic Trigonometry
Sin, Cos, Tan,  (we’ll hold off on arcSin, arcCos, and arcTan till later in the semester)
Pythagorus’ Theorem

The difference between vectors and scalars (velocity and speed)
Converting units
Powers of 10, scientific notation
Significant Figures

How to derive the General Equation of Kinematics and how to derive the ‘time independent’ equation of kinematics using the 2 column derivation method.

The derivations are in this power point

acceleration-part-2

How to solve 1 dimensional motion problems
How to solve gravitational acceleration (free fall) problems
How to solve girlfriend problems (extra credit)
How to solve time independent motion problems

Systems of Units

What are Units of Measure?
What is meant by a System of Units?

Units of measure are names we give to specific items, sizes, lengths, volumes, weights, masses, temperatures, periods of time etc. Most units of measure were developed by scientists and engineers for convenience. The units we use today were agreed on by people across an industry or a science. Some units are related directly to physical phenomenon. These “physical” constants include the speed of light “c”, and the size of an atomic nucleus, the “barn” because scientists were surprised how large the nucleus was when they first  measured it and someone jokingly said “It’s as big as a barn!”

Base units are units which cannot be derived from combinations of other units. Derived units are derived from combinations of base units. Base units include meters {m}, kilograms {kg}, seconds {s}, centimeters {cm}, grams {g}, inches {“}, feet {‘}, slugs {} and others which we will discover later in this course. Some derived units are Newtons {N}, Joules {J}, Watts {W}, dynes {D}, and ergs {e}, pounds {#}, and horsepower {hp}. Notice that I frequently but units in {} brackets when defining them.

A system of units is a group of units which are commonly used together. The three most important systems of units are MKS, CGS, and British or Engineering Units.

In this course, we will be using the MKS system {meters, kilograms, seconds} as the MKS system is best suited to describing large objects such as cars, trains, planets, and people. The MKS system was agreed upon and standardized and named “Système international d’unités” or SI for short. The process of standardizing the MKS system of units began in 1791 and was finally agreed to by an international treaty in 1875 by the Treaty of the Metre. The process continued into the 1950’s with the addition of 3 more base units and a large number of derived units.

The MKS or SI System of Units

Here’s a little history of the “meter”, the “kilogram” and the “second”.

The Meter

huygens-portrait
The idea of the meter as a unit of length started in about 1665 when the Dutch Physicist Christiaan Huygens (arguably one of the greatest minds in the history of science) observed the length of a pendulum which “ticked” with a half period of 1 second (1 second to swing from left to right, another second to swing back), had a length of 39.26 inches. Christian Huygens is also the person who developed the first pendulum clock or “Grandfather Clock” in 1656).
Huygens-clock-2

Huygens-clock

In 1668, Wilkins and Christopher Wren proposed using the length of this pendulum as a standard of length and called the apparatus the “seconds pendulum”. But this definition of the meter did not catch on at the time.

In the 18th century, there were two approaches to the definition of the standard unit of length. One favored Wilkins approach: to define the meter in terms of the length of a pendulum which produced a half-period of one second. The other approach was to define the meter as one ten-millionth (1/10 000 000) of the length of a quadrant along the Earth’s meridian; that is, the distance from the Equator to the North Pole. This means that the quadrant (a section/distance 1⁄4 of the Earth’s circumference) would have been defined as exactly 10 000 000 metres (10 000 km). In 1791, the French Academy of Sciences selected the meridional definition over the pendular definition because the force of gravity varies slightly over the surface of the Earth, which affects the period of a pendulum.

Question: Calculate the radius of the earth based on the meridional definition of the meter.

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The standard meter today is 40.36 inches, or approximately 1 1/3 yards.

Mass

Now that we have the meter as a standard of length, let’s talk about volume. Volume will lead us to a definition of mass.

There is very little information available about how this started, so I’ll tell what I think happened.

In the 1700’s early chemists wanted a standard of volume and mass so they could compare the results of their research. They figured out how to make a square vessel 1/10th of a meter (10 cm, approximately 4 inches) on each side. They probably made the vessel out of slabs of polished stone or glass, and sealed along each edge with wax. Then they agreed that the amount of water contained in this vessel would be a standard of weight or mass. They called the volume of this vessel 1 liter, and they named the weight or mass of the water contained in this vessel 1 kilogram. In 1889, the CGPM (Conférence Générale des Poids et Mesures) created at standard of mass made from a Platinum – Iridium alloy (a very hard allow which could be accurately machined). kilogram prototype

Later in 1901 the CGPM clarified that this kilogram was the standard unit mass, resolving the confusion created by using weight and mass interchangeably.

Time

Satellite Orbits

Learning Objective: to calculate the orbital period of satellites in various altitude earth orbits.

There are basically 3 major types of satellite orbits, LEO, MEO and GEO.

LEO: Low Earth Orbit
These orbits include;
The International Space Station. The station flies at an average altitude of 248 miles (400 kilometers) above Earth. It circles the globe every 90 minutes at a speed of about 17,500 mph (28,000 kph).
ISS

Using the formulas T = [r^3 / GMe]^1/2 and c= 2 pi* r, use the orbital altitude to confirm the period of the orbit and the orbital speed.

The “A” Train: atmospheric satellites in a sun synchronous orbit.

Kepler’s Laws

Here is all you need to know about Kepler’s Laws.

There are 3 laws.
1] Planets move around the sun in elliptical orbits, not circular orbits.

2] Planets sweep out equal areas in equal time.

3] The ratio of the periods of two orbiting objects can be used to predict the ratio of their orbital radii.

formally: (T1/T2)^2 =(r1/r2)^3

Watch this video to learn about Johannes Kepler’s life (history quiz on Friday).

 

Here’s a really dumb but cute video:

Newton’s Law of Gravitation

Standards:

PH1 m. * Students know how to solve problems involving the forces between two electric charges at a distance (Coulomb’s law) or the forces between two masses at a distance (universal gravitation).

PH1 e. Students know the relationship between the universal law of gravitation and the effect of gravity on an object at the surface of Earth.

Lesson Objective: To be understand the ideas of “Action at a Distance”, the 1/r squared law, and to be able to calculate the gravitational force between two massive objects.

Newton knew that if one object pushes on another or if there was a rope between 2 objects and one pulled the other, the object would experience an acceleration.

Newton was fascinated that the earth could pull on objects without any direct connection. He called this effect “Action at a Distance”.

Newton believed that objects had some internal essence, related to their mass that somehow spread out through space and got weaker as objects were moved farther from each other. He checked his idea by considering the orbital radii and speeds of the moons of Jupiter as compared with the Earth’s moon. This all made sense.

First understand how the surface of a sphere grows as the radius increases:

Sphere-math

Draw this diagram in your notebooks and identify (label)
a] the circumference of the circle
b] the area of the circle
c] the surface area of the sphere
d] the volume of the sphere

Now consider that the gravitational essence of a mass at the center of the sphere spreads out evenly to reach the surface of a sphere 1 meter in radius.

What happens if the radius of the sphere increases to 2 meters? (discuss)

From this Newton realized that the effect of gravity must get smaller by a factor of 1/r^2.

Now let’s use Newton’s 2nd Law to develop a formula for the force of gravity.

F=ma

F=mg

g (the acceleration due to gravity at the earth’s surface) must depend on the mass of the earth (M) and the radius of the earth squared. There also needs to be some constant of proportionality – Newton called this constant “G” The Universal Gravitational Constant.

F= GmM/r^2

The actual value of G remained a mystery until it was determined experimentally by Cavendish 120 years later in 1798.

G = 6.67 x 10^-11 N.m^2/kg^2

 

Circular Motion

Understanding circular motion is a prerequisite for the  Kepler’s Laws of planetary motion, the physics of planetary and satellite orbits as well as Newton’s theory of gravitation.

Angular velocity:
Worksheet:  Please see this link for a worksheet on angular velocity
Angular Velocity

 

Angular Acceleration is the rate of change of angular Velocity with respect to time. It is a vector quantity. It is denoted by α. The Angular Acceleration Formula is given by:
Angular Acceleration Formula
Note: non-calculus version – replace the “d” s  with delta

Where, ω is the angular velocity and t is the time taken.

Formula for Angular Acceleration
Centripetal acceleration:
Centripetal acceleration is the acceleration that keeps objects moving in a circle.  Using the earth – moon system as an example, the centripetal acceleration which keeps the moon moving a round the earth is due to the gravitational field of the earth.

Centrifugal acceleration