Conceptual Physics Final Test Review

Scientific Method

• The Scientific Method is a series of steps used by scientists to answer questions and solve problems; it's the "game plan" or "blueprint" for scientific investigation.
• We use the Scientific Method often in our daily lives, indirectly and unconsciously.
• Galileo Galilei is often referred to as the "father of the scientific method."
• Francis Bacon is another pioneer of the scientific method; he is recognized as one of the architects of the scientific method because he helped organize it.
• Sir Isaac Newton also made valuable contributions, mainly the procedure.
• Variables are essential in an experiment; there can be more than one variable of each type in an experiment.
• independent or manipulated variable - intentionally changed by the experimenter
• In a hypothesis, it is written after "if".
• In a graph, it is plotted on the x-axis.
• dependent or responding variable - measured by the experimenter, depends on and responds to the independent variable
• In a hypothesis, it is written after "then."
• In a graph, it is plotted on the y-axis.
• constants - all the factors that the experimenter attempts to keep the same
• Pi and the speed of light are constants.
• Not all experiments use constants.
• Experiments also require groups to compare.  These groups must be exposed to the same conditions, but on the experimental group the variable will be tested, whilst on the control, it won't be.
• control group ("no treatment" group) - serves as a standard comparison
• experimental group - undergoes the experiment
• The Scientific Method is composed of 9 cyclic and interchangeable steps.

1. Make an observation: Use your 5 senses to make an observation that can be quantitatively proven.
2. Find background information: Do research to understand your observation.
3. Ask a question (Problem): Ask an intelligent question based on your observation.
4. Form a hypothesis: Make an educated prediction of the answer to the problem.  It must be written with if and then; if followed by the independent variable and then followed by the dependent variable (If independent, then dependent).
• hypothesis: An educated guess about the relationship between the independent and dependent variables.
5. Materials for the experiment: The materials and their quantities must be detailed in a list or underlined in the procedure.  In an experiment, materials are divided into substances and equipment.
6. Procedure of the experiment (Devise and execute): Plan the steps you'll use to test your hypothesis and detail your equipment and substances, along with their measures.
• The outcome of the experiment may lead to a modification in your hypothesis and further experimentation.
7. Collect and analyze results: Charts, pictures, drawings, and essays can be used to collect results.
• There are three main types of graph used in when analyzing results: linear graphs, point graphs and bar graphs.
8. Conclusion: Formulate a final statement to accept or reject your hypothesis; it is based on your hypothesis and data.
• In the conclusion, you can make recommendations for further study and possible improvements to the procedure.
9. Communicate the results: Present your project and be ready to answer questions.

• A scientific theory or natural law is a general and reliable explanation of important natural phenomena that has been developed by a scientist through observations and experiments.
• A hypothesis that has been verified by different experiments can be elevated to a theory or law.

Measurements

• The Metric System (International System of Units, or SI) is used everywhere as the main unit of measure except in the United States, where the English System is used.
• Scientists, even those in the United States, use the metric system as a universal language in measurements to be able to communicate them conveniently.
• Scientific notation is used to express very long numbers in a shorter way.

• We slide the decimal point to where the only digit to the left of it is one between 1-9,
• Depending on how many times and to what direction the point was rolled, we put a positive or negative exponent on base 10 and multiply it by the quantity.
• Significant figures, or digits, are those numbers that represent a value in a number, give useful information, and are not just placeholders.
• 3.14169 = six significant digits
• 1,000 = one significant digit (1)
• 1,000.0 = five significant digits
• 0.00350 = three significant figures
• 1,006 = four significant figures
• 560. = three significant figures
• Conversions between units are done by setting up a conversion factor (fraction), the metric system conversions are based on 10, with different prefixes; those between systems and within the English System may be more complex.
• The unit we want to eliminate goes on the bottom and cancels with the original, the one we want goes on top. (Watch video for explanation)
  
  
• Other common conversions are:
• 1g = 9.8m/s²
• 1 N = 0.225 lb
• 1 lb = 4.45 N
• The International System, or SI (after the French title Système International d'Unités), is a separate system of units within the metric system that only associates one measure with each physical quantity for international consistency.
  

Fundamental Physics Quantities

• Space, time, and matter are the three basic aspects of the material universe that we must quantify.
• Distance, time, and mass, are the fundamental physical quantities; they're so basic they're hard to define.
• Distance represents a measure of space in one dimension.
• Ex: length, width, height
  
• Time is a measure of periodical phenomena (repeats at a regular rate).
• The rotation of Earth was originally used to establish the second: 1 rotation is equal to 86,400 seconds.
• The Metric and English Systems share units of time.
  
• Mass is a measure of how much matter an object contains; it is also known as inertia and as it increases the object is more difficult to speed up or slow down.
• Mass is not used much in the English system so you may have never heard of the slug.  Weight is used instead, which is similar but not the same,
• Mass depends on the object's size (volume) and its composition.
• Mass is determined by the number of subatomic particles (protons, neutrons, and electrons) that comprise an object.
  
  
• Area and volume are physical quantities closely related to distance, yet they don't form part of the three essential ones.
• Area refers to the size of a surface, it is obtained by multiplying length times width.
• We can see it as how many 1m by 1m squares (or any unit) cover a surface.
• Volume is the space something occupies; it is obtained by multiplying length times height times width.
• We can see it as how many 1m by 1m by 1m cubes (or any other unit) fill a space an object occupies.
  
  
• The variety of units for each of the quantities has been established to work with more manageable numbers for different scale objects.
• If something measures 80,000 meters, you could instead say it measures 80km, which is more convenient and concise.
• A pendulum consists of a mass dangling on the end of a string, clocks often use swinging pendulums to keep time; mechanical wristwatches use an oscillating balance wheel instead and quartz electric clocks and digital watches use vibrations of an electrically stimulated quartz-crystal,
• The period (T) is the time for one complete cycle of a process that repeats.
• It is a measure of time, so the units are seconds, minutes, etc.
• T = 1/f
• The frequency (f) of a pendulum is the number of cycles that occur per unit of time, its unit is hertz (Hz).
• f = 1/T
• f  = # of cycles/time
• An oscillation is a back and forth movement, it is also known as a cycle.

Speed and Velocity

• Speed is the rate of movement; it's a key concept to use when quantifying movement.  The two aspects of speed are:
• Speed is relative.
• The speed of a person running towards the front on the deck of a cruise ship that is going 20mph may be 8mph in relation to the cruise ship, but 28mph in relation to a nearby pier. (The ship and the pier are different reference points)
• Most times speed is measured using the Earth's surface as a reference point.

  

  The person's speed relative to the boat is 8mph, but relative to
  the pier it is 28mph (20 + 8).

  
  
• It is important to distinguish between average speed and instantaneous speed.
• An object's average speed is the total distance it travels within a certain time divided by this total elapsed time.
• A 1,500-mile flight that last 3 hours' average speed is 500mph (1,500-miles/3 hours = total distance/total elapsed time). This does not mean the plane was always traveling at a steady speed of 500mph.
• A runner that finished the 100-meter dash in 10 seconds' average speed is 10m/s, but he was not necessarily always running at this speed.
• Instantaneous speed is an object's speed at an instant in time; it can't be calculated like speed because an "instant" implies that 0 time passes, but to get an estimate we can calculate it using a very short time.
• A car's speedometer reads instantaneous speed, when it says 50mph it's saying that if you travel at the speed you're traveling in that instant for an hour, you'll cover 50 miles.
• We can use this pyramid as a trick to remember the speed, distance and time formulas.  If we cover what we're trying to find, we can get the formula to find it.
  
• To measure the speed of a segment of something that has already moved, we can take the final values (the ones we want to measure) minus the beginning values.  This is using the changes in distance and time to calculate instantaneous or average speed; speed would equal change in distance over change in time.

• The symbol Δ is the capital greek letter delta; it is used to represent a change in a physical quantity.
• When speed is constant, or the object travels at the same speed (the average speed would be the same as the instantaneous speed always), the relationship between the distance traveled and the time that has passed can be expressed as d = st (distance = speed x time).
• This is an example of a proportionality; d is proportional to t (abbreviated d ∝ t) because if we double the time, then the distance will be doubled as well.  Speed (v or s) is called the constant of proportionality; if it is constant because it will always be the same.
• The speed of light in empty space (c) is the universe's absolute speed limit; nothing has been observed traveling faster than c.
• Direction is an important aspect of motion because its change can produce effects that are equivalent to changing the speed; velocity is speed in a particular direction, it uses the same units as speed.
• Velocity changes whenever speed or direction changes; it can change without the speed changing.  If a car is going 15m/s north, and it curves and starts heading 15m/s east, its velocity changed but its speed didn't.
• With a speedometer (speed) and a compass (direction) we can calculate velocity.
• Velocity can be negative regarding another if it is going in the opposite direction (vector addition or subtraction); when a velocity is negative the negative symbol implies opposite direction, the speed does not become negative.  Speed can never be negative.
• If an airplane is said to be heading 200 miles due north; the displacement of the airplane is given.  Displacement is distance in a direction.
• Physical quantities can be classified as scalars or vectors.

• Scalars are quantities that are just made up of a magnitude and a unit; like speed, time, mass, and volume
• Vectors are quantities that include magnitude, a unit, and direction; they are represented by a proportional arrow in drawings.  Velocity, displacement, and momentum are vectors.
• Vector addition is the process through which we obtain the resultant or net velocity of an object.
• Two vectors are added by representing them as arrows and then positioning one arrow so its tip is at the tail of the other.  A new arrow drawn from the tip of the second is the arrow representing the resultant vector (sum of the two vectors).
  
• When the vectors are due the same direction (a) they're added, when they're due opposite directions (b) we subtract to obtain the resultant velocity.
• When two vectors are not along the same line we can't simply add or subtract their magnitudes.  We must draw the two arrows (head to tail) proportionally, to then draw and measure a resultant.  The resultant's direction is a combination of the two given; in the example below the bird is heading north and the wind is heading east, so the resultant velocity's direction would be northeast.

  

  The resultant velocity (10m/s NE) would be the bird's velocity relative to the ground.

• The Pythagorean theorem can also be used to calculate the magnitude of the resultant vector because vectors always form right triangles, and for any right triangle c² = a² + b².  Here, c stands for the resultant (hypotenuse, or longest side) and a and b are the other two legs of the triangle.
• Any vector can be seen as a resultant vector if we deconstruct it into two vectors.

Acceleration

• Acceleration is a vector quantity of the rate of change of velocity (Δv/Δt).  It indicates how rapidly velocity is changing and is expressed in a unit of distance over a unit of time squared.
  
• An object is in acceleration when it is:
• speeding up (+)
• slowing down or decelerating (-)
• An object is NOT accelerating when it:
• stands still
• moves at a constant velocity
• Acceleration has the same relation with velocity that velocity has with displacement.
• Acceleration indicates how rapidly velocity is changing.
• Velocity indicates how rapidly displacement is changing.
• When an object's acceleration is 1m/s² it means the object is going 1m/s faster every second.
• If the object's speed was 1m/s at 1s, at 2s it will be 2m/s, at 3s it will be 3m/s...
• When acceleration is negative it means the acceleration is going in the opposite direction of the positive velocity, the object is decelerating or slowing down.
• Free falling bodies are only acted on by the force of gravity, ignoring air resistance, they accelerate at 9.8m/s².  This quantity (9.8m/s²) is called acceleration due to gravity and is represented with the letter g.
• g is often used as a measure of acceleration.  An acceleration of 19.6m/s² equals 2g.
• To convert from m/s² to g we must divide the magnitude in m/s² by 9.8.  We can do this by setting up the conversion factor ^1g⁄_9.8m/s².
• Centripetal (center-seeking) acceleration is the acceleration of an object moving in a circular path.
• It is always perpendicular to the object's velocity.
• Its magnitude depends on speed (v) and the radius (r) of a curve; we use the formula ^v2⁄_r to determine centripetal acceleration.
• Acceleration is proportional to the square of the speed (a ∝ v²); this means that when the speed is doubled the acceleration becomes four times as large.
• Acceleration is inversely proportional to the radius (a ∝ ¹⁄_r.); this means that if the radius is doubled, the acceleration becomes half as large,
• A large radius means a path hat is not sharply curved, so velocity changes more slowly and the acceleration is smaller.
• Occurs when you're in the car and take a sharp turn; if you have books on your lap they will probably shift towards the outside of the curve due to the center-seeking centripetal acceleration the car is undergoing.
• Changing the direction of motion of a body is the same kind of thing as changing its speed; they can cause similar effects.  We see both changes in centripetal acceleration.
• A car's cornering acceleration is often evaluated and given; this is measured by the maximum centripetal acceleration it can have when it rounds a curve,
• 0.85g or 8.33m/s² would be a typical value of lateral, or cornering acceleration of a sports car.

Simple Types of Motion

• There are several types of motion we can graph; when graphing:
• Time is always written in the x-axis (horizontal)
• The slope of a graph is a measure of its steepness attained through the formula ^rise⁄_run.
• Speed or velocity is the slope of a distance vs. time graph.
• Acceleration is the slope of a velocity vs. time graph.

1. Zero Velocity / Stationary Object: No motion occurs; the object sits still.  The distance of the object, from a reference point, is constant.  Velocity and acceleration are 0.  In a distance vs. time graph, the line would go flat.
2. Constant Velocity / Uniform Motion: The body moves at a uniform motion with a constant velocity (constant speed in a fixed direction).  Acceleration is 0 because the object's speed is not increasing nor decreasing, it's staying the same.  In a distance vs. time graph, it would be a straight line; an upward slope would mean positive velocity whilst an old one would not be very good.

   

   The horse, the runner, and the walker all have a constant speed because their lines are straight in a distance vs. time graph.  The horse is going the fastest because it has the steeper slope, the runner is the second fastest and the walker would be the slowest.

3. Constant Acceleration / Uniform Acceleration: Velocity is changing at a fixed rate, a freefalling object is in constant acceleration (g).  When an object starts from rest and has a constant acceleration we can use the formula v = at and their derived ones.  In constant acceleration, d ∝ t².  When acceleration is constant there is a straight line in a velocity vs. time graph, because the slope of a v vs, t graph is a.  A parabolic (curved) line in a distance vs, time graph is formed because the speed (slope of a d vs. t graph) is increasing.

   

   In both of these graphs, there is constant acceleration.  In the first one, velocity vs. time, the slope is acceleration, so if it is constant, the line will be straight.  In the second one, distance vs. time, the slope is speed, since the speed is increasing the slope is also increasing, creating a parabolic line.

• Even though graphs are a very good way of showing relations between physical quantities, math is better because graphs are limited to two (or sometimes 3) variables.  Math is abstract and almost like a language.

• The slope of a distance vs. time graph is velocity.
• The slope of a velocity vs. time graph is acceleration.
• In this distance vs. time graph, velocity is the slope; this graph has a varying slope.

At point A the car accelerates & velocity is increasing.
At point B velocity is constant.
At point C the object is standing still & undergoing no motion the slope is 0.
At point D the car is going in an opposite direction, making velocity negative.

Force

• Sir Isaac Newton was an English scholar who made fundamental discoveries in physics and mathematics; he's called the "father of modern physical sciences."
• Newton began with Galileo's ideas about motion and developed the concept of force, which is a push or pull acting on a body that usually causes distortion of the body and/or a change in velocity.
• Force is the key concept in Newtonian mechanics, and it is a vector.
• Force can be hard to define, and it is sometimes regarded as a fundamental quantity, like time and distance.
  
  
• The number of Newtons will always be greater than the number of pounds for the same force.
• 1 lb = 4.45 N
• 1 N = 0.225 lb
• Spring scales use distortion acting on the spring to measure forces.
• Weight (W) is the most common force in our lives; it's the force of gravity acting on a body.
• The weight of an object depends on the amount of matter it has (its mass) and the environment with which the object interacts gravitationally (where it is).
• The weight of an object on the Moon is 1/6 its weight on Earth because the Moon's gravitational pull is weaker than Earth's,
• Weight varies in Earth too: A 190-pound person would weigh about 1 pound less at the equator than at the North or South Pole.
• The direction of the force of gravity determines our concepts of "up" and "down."
• Friction is a force of resistance relative to motion between two bodies or substances in physical contact.
• Static friction occurs when there is no relative motion between two objects, it is a force that opposes gravity (upward).
• Kinetic friction acts when there is relative motion between two substances in contact, in opposite direction to where the object is going.
• Brakes are a use of kinetic friction.
• Net force (or resultant force) is the vector sum of all external forces acting on the body.
• If two equal forces act on opposite directions there is 0 net force.
• Forces that cancel each other out, or have no net force, make an object move at a constant velocity or stay stationary, and are referred to as balanced forces.
• If two forces act towards the same direction, the net force is their sum.
• If two unequal forces act on opposite directions the net force is their difference towards where the largest force went.
• Forces that have a net force are referred to as unbalanced forces; they cause acceleration or deceleration.
• Centripetal force is the force of an object traveling a circular path, undergoing centripetal acceleration.
• It points to the center, the rope it is tied to prevents it from keeping traveling in the same line, as Newton's first law of motion states.
• Certain types of forces result in specific motion patterns, for example:
• 0 net force = object in equilibrium (stationary or at constant velocity)
• a constant net force = constant acceleration
• A freely falling body travels with a constant force (weight).
• a net force opposite to the direction of motion = slow down, eventually to a stop, and then accelerating towards the direction of the force
• This happens when a ball is thrown upwards: it starts slowing down, has 0 velocity in the peak of motion, and then begins accelerating downward (towards the force, gravity).
  
• When an object is thrown upward at an angle to Earth's surface there is projectile motion, a composite of horizontal and vertical motion, that takes the shape of a parabola.
• The key to understanding projectile motion is realizing the vertical force of gravity has no effect on the horizontal motion.
• A restoring force acts to restore a system to the original configuration.
• An object that falls with air resistance eventually comes to a terminal speed, when the kinetic friction of air with the object and gravity balance each other out.

Newton's Laws of Motion

• Newton's first law of motion deals with inertia; it states that "An object will remain at rest or in uniform motion with constant velocity unless acted on by a net external force."
• An external force is one caused by some agent outside the object in question.
• Weight is an external force.
• Aristotle had a flawed concept of motion; he thought a force was required to maintain an object's motion, whilst Newton's first law implies a force is required only to change the state of motion.
• To apply this law, we must understand the concept of mass and its difference with weight.
• Mass is an inertial property of matter that doe snot depend on an external phenomenon, so it's always the same.
• Weight is the force of gravity acting on an object; it can vary with where the object is and is based on the mass of an object.
• Newton's second law of motion is our most important tool for applying mechanics in the real world; it states that "An object is accelerated whenever a net external force acts on it.  The net force equals the object's mass times acceleration (F = ma or a = F/m)."
• The larger an object's mass is, the more force will be required to move it.
• Weight = mg (mass times acceleration due to gravity, 9.8m/s²)
• a = v²/r
• F = mv²/r (centripetal force formula)
• For a force unit to be Newtons, kilograms and m/s² must be multiplied.
• Newton's third law of motion states that "Forces always come in pairs: when one object exerts a force on a second object, the second exerts an equal and oppositely directed force on the first."
• Lift is the equal and opposite upward force on an airplane or a bird's wings.
  
• The Law of Universal Gravitation is not a law of motion, it's a law relating to gravity.
• It states that "Every object exerts a gravitational pull on every other object."
• According to Newton, this gravitational pull depended on the size of the object (greater size = greater pull) and the distance between the object's centers (less distance = greater pull).

THE REVIEW MAY BE MISSING SOME INFORMATION.  YOU SHOULD READ THE BOOK AND POWER POINTS TO ASSURE A GOOD GRADE.