GRAPHING THEORY

1    a] What is an hypothesis?
A statement or set of statements that helps to order or unify a set of facts.  Example:  the Kinetic Theory of Heat explains how heat moves from a hot to cold object & not the reverse, and why rubbing two things together produces heat.
b] What is a law?
   A cause and effect relationship, without an explanation.
c] Give an example of a law.
Ex#1:  Force of Gravity = a attractive force between any two objects.
              Fg =             GxMass 1 x Mass 2                     .
                   (Distance between centers of gravity)² 
d] Define theory:  a tested set of statements that explains and predicts an outcome.
e] State an example of a theory
Ex#1:  Spontaneous Generation:  certain forms of life (flies, worms, mice) can spontaneously grew out of non-living things such as mud or decaying flesh.
Ex#2:  Darwin’s theory of evolution.  Creatures that adapt to changes in their environment will have better chances of survival, and be less likely to become extinct, than those who don’t. 
Ex#3:  Kinetic theory of gases.  All matter is in constant motion, with inelastic collisions, etc.
f] How does a hypothesis become a law?
   If, after many tests, no one can demonstrate the hypothesis incorrect it is accepted as a law.
g] State and example how a law was proven incorrect.
#1:  Caloric theory explained how things became hotter and cooler.
Caloric was a fluid that flowed from hot things to cool.  It could not explain why rubbing two rough surfaces together made them warmer.  Kinetic theory said that heat is a form of energy that is transferred when fast-moving particles hit other. 
#2--The law of gravity once was:  "Whatever goes up must come down."
Newton developed a theory that predicted the measured orbits of the planets which are up and don't come down.  His law is:  Fg = GM1M2/d²

#3:  The Law of Conservation of Mass & Energy once was:  "Matter and energy cannot be created or destroyed."  They investigated nuclear reactions and found the E = mc² , or The energy created in a nuclear reaction = the mass destroyed x speed of light squared.

e] Define and give an example of a theory.
A theory is an explanation for a cause and effect relationship. 
Ex #1:  Kinetic Theory of Gases:  pressure is caused by perfectly elastic collisions of gas molecules with the container walls.
Ex #2: Theory of Evolution:  complex organisms develop from simpler ones.
Ex #3:  Spontaneous Generation:  flies emerge spontaneously (without outside aid) from rotting meat.

2    LABEL AS:  DIRECT, INVERSE, SQUARE, or SQUARE ROOT VARIATION
a] Y = aX² + b     SQUARE
c] Y = a/X + b     INVERSE
b] Y = aX + b      DIRECT
d] Y = a√X + b     SQUARE ROOT

3    SKETCH & LABEL THE GRAPH FOR EACH VARIATION.

4    DESCRIPTIONS:  LABEL AS DIRECT, INVERSE, SQUARE, or SQUARE ROOT
a] IF THE CAUSE (X) DOUBLES (↑ 2x) THEN THE EFFECT (Y) HALVES (↓BY 1/2)
INVERSE

b] IF THE CAUSE (X) TRIPPLES (↑ 3x) THEN THE EFFECT (Y) INCREASES 9x
SQUARE

c] IF THE CAUSE (X) DOUBLES (↑ 2x) THEN THE EFFECT (Y) DOUBLES (↑ 2x)
DIRECT

d] IF THE CAUSE (X) INCREASES 9x THEN THE EFFECT (Y) INCREASES ONLY 3x
SQUARE ROOT

e] IF FORCE INCREASES 2x THEN ACCELERATION INCREASES 2x   DIRECT

f] IF PRESSURE ON A GAS INCREASES 2x THEN ITS VOLUME DECREASES 1/2: INVERSE

g] IF SPEED INCREASES 3x THEN FORCE INCREASES 9x    
SQUARE

5    WRITE AS AN EQUATION:
a] IF PRESSURE ON A GAS INCREASES 3x THEN ITS VOLUME DECREASES 1/3
VOLUME = A/PRESSURE
b] IF SPEED INCREASES 4x THEN FORCE INCREASES 16x        
FORCE = AxSPEED²
c] IF DISTANCE INCREASES 9x THEN TIME INCREASES 3x  
TIME = √DISTANCE
d] IF FORCE INCREASES 3x THEN ACCELERATION INCREASES 3x
ACCEL = AxFORCE

6    USE INVERSELY AND DIRECTLY TO STATE EACH LAW VERBALLY:
Ex:  ___ VARIES DIRECTLY WITH ___
a] VOLUME = k TEMPERATURE   
VOLUME VARIES DIRECTLY WITH TEMPERATURE

b] VOLUME = k/PRESSURE 
VOLUME VARIES INVERSELY WITH TEMPERATURE

c] VELOCITY = √MASS 
VELOCITY VARIES DIRECTLY WITH SQUARE ROOT OF MASS

d] FORCE = k SPEED²    
FORCE VARIES DIRECTLY WITH THE SPEED SQUARED

e] ACCELERATION = FORCE/MASS
ACCELERATION VARIES DIRECTLY WITH FORCE AND INVERSELY WITH MASS
f] FORCE = k MASS/DISTANCE²
FORCE VARIES DIRECTLY WITH MASS AND INVERSELY WITH DISTANCE SQUARED

7    DERIVE THE EQUATION FOR X:  
a] Y = aX + b                     b] Y = a/X + b
   Y – b = aX                        Y – b = a/X
   (Y – b)/a = X                     X(Y – b) = a
                                     X = a/(Y – b)
c] Y = a√X                        d] Y = aX² + b
   Y² = a²X                          Y – b = aX²
   Y²/a² = X                         (Y – b)/a = X²
                                                                    .
   (Y/a)² = X                       √[(Y – b)/a] = X