Name: ______
PHYSICS
UNIT 0
UNIT GOALS
· Design an experiment using independent, dependent and controlled variables.
· Use graphical analysis to analyze data and determine the equation for a physical relationship
· Use dimensional analysis and significant figures to provide appropriate measurements in the lab
SCIENTIFIC METHOD
READING #1
It took a long while to determine how the world is best investigated. One way is to just talk about it (for example Aristotle, the Greek philosopher, stated that males and females have different number of teeth, without bothering to check; he then provided long arguments as to why this is the way things ought to be). This method is unreliable: arguments cannot determine whether a statement is correct, this requires proofs.
A better approach is to do experiments and perform careful observations. The results of this approach are universal in the sense that they can be reproduced by any skeptic. It is from these ideas that the scientific method was developed. Most of science is based on this procedure for studying Nature.
Scientists use an experiment to search for cause and effect relationships in nature. In other words, they design an experiment so that changes to one item cause something else to vary in a predictable way.
These changing quantities are called variables. A variable is any factor, trait, or condition that can exist in differing amounts or types. An experiment usually has three kinds of variables: independent, dependent, and controlled.
The independent variable is the one that is changed by the scientist. To insure a fair test, a good experiment has only one independent variable. As the scientist changes the independent variable, he or she observes what happens.
The scientist focuses his or her observations on the dependent variable to see how it responds to the change made to the independent variable. The new value of the dependent variable is caused by and depends on the value of the independent variable.
For example, if you open a faucet (the independent variable), the quantity of water flowing (dependent variable) changes in response--you observe that the water flow increases. The number of dependent variables in an experiment varies, but there is often more than one.
Experiments also have controlled variables. Controlled variables are quantities that a scientist wants to remain constant, and he must observe them as carefully as the dependent variables. For example, if we want to measure how much water flow increases when we open a faucet, it is important to make sure that the water pressure (the controlled variable) is held constant. That's because both the water pressure and the opening of a faucet have an impact on how much water flows. If we change both of them at the same time, we can't be sure how much of the change in water flow is because of the faucet opening and how much because of the water pressure.
PRACTICE #1
For each of the questions below, write a hypothesis and create an experiment to test the hypothesis. List the independent and dependent variables of your experiment as well as all of the control variables needed to ensure good experimental results.
Question / Hypothesis / Independent Variable (What I change) / Dependent Variables (What I observe) / Controlled Variables (What I keep the same)How much water flows through a faucet at different openings? / If the faucet opening increases then the amount of water flow will increase / Water faucet opening (closed, half open, fully open) / Amount of water flowing measured in liters per minute / .The Faucet .Water pressure( or how much the water is "pushing")
Does fertilizer make a plant grow bigger?
Does heating a cup of water allow it to dissolve more sugar?
Who listens to music the most: teenagers or their parents?
How fast does a candle burn?
WRITING EQUATIONS THROUGH GRAPHICAL ANALYSIS
READING #2
Graphing data
One of the most effective tools for the evaluation of data and formation of conclusions is a graph. The investigator is usually interested in a quantitative graph that shows the relationship between two variables in the form of a curve. The rectangular coordinate system is convenient for graphing data, with the values of the dependent variable y being plotted along the vertical axis and the values of the independent variable x plotted along the horizontal axis. An example of this choice might be as follows. In an experiment where a given amount of gas expands when heated at a constant pressure, the relationship between the variables, Volume (dependent) and Temp (independent), may be graphically represented as follows:
Temp (x axis) / Volume(x axis)30 / 150
40 / 200
50 / 250
60 / 300
70 / 350
Curve Fitting
When checking a law or determining a functional relationship, there is good reason to believe that
a uniform curve or straight line will result. The process of matching an equation to a curve is
called curve fitting. The formula and equation for a relationship can usually be
determined by looking at a graph of the data. When you state the relationship, tell how y depends on x ( e.g., as x increases, y ). Fortunately for us, most all the physical phenomena we can
measure fall into one of the following relationships between variables: none, direct, inverse,
square, and square root. So, there are basically five shapes of graphs we will encounter in
class.
Directly Proportional
If data plotted on rectangular coordinates yields a straight line, the relationship is said to be directly proportional. This means that as the independent variable increases it causes the dependent variable to increase. This relationship can be expressed mathematically by the linear equation slope-intercept form:
y = mx + b or for our use DV = m(IV) + b
where m is the slope and b is y-intercept.
Consider the following graph of velocity vs. time:
The curve is a straight line, indicating that v = f(t) is a
linear relationship. Therefore,
v = mt + b,
The slope gives the constant rate change of v with respect to t
= m = = 0.80 m/s2 .
The curve intercepts the v-axis at v = 2.0 m/s. This indicates that the velocity was 2.0 m/s when
the first measurement was taken; that is, when t = 0. Thus, b = v0 = 2.0 m/s.
The general equation, v = mt + b, can then be rewritten as
v = (0.80 m/s2 )t + 2.0 m/s.
Inversely Proportional
Consider the following graph of pressure vs. volume:
The curve appears to be a hyperbola (inverse function).
Hyperbolic or inverse functions suggest that as the independent
variable increases it causes the dependent variable to decrease.
This relationship can be expressed mathematically by the linear
equation slope-intercept form:
DV = m ( ) +b or in this case P =( )
If data plotted on rectangular coordinates yields a hyperbola, the relationship is said to be inversely proportional because as the independent variable increases it causes the dependent variable to decrease.
Proportional to the Square
Consider the following graph of distance vs. time:
The curve appears to be a top-opening parabola. This
function shape suggests that as independent
variable increases it causes the dependent variable to
increase at an squared exponential rate.
This relationship can be expressed mathematically by the
quadratic equation form:
DV = (IV)2 +b or in this case d = t2 +b
Proportional to the Square Root
Consider the following graph of distance vs. height:
The curve appears to be a side-opening parabola. This function
suggests that as the independent variable increases, it cause the
dependent variable to increase but at a decreasing squared rate.
This relationship can be expressed mathematically by the
equation form:
DV = Ö(IV) +b or in this case d = Öh +b
Graphical Methods-Summary
PRACTICE #2 WRITING EQUATIONS
For each data set below, determine the mathematical expression. To do this, first graph the
original data. Assume the 1st column in each set of values to be the independent variable and
the 2nd column the dependent variable. Using the shape of the graph write an appropriate mathematical expression for the relationship between the variables then answer the provided questions.
A. As the volume of a gas is increased, its pressure will decrease.
1. Does P increase or decrease as V gets larger? ______
2. Using the graph, estimate what P would be if V was 3 ______
3. Using your equation, what would happen to P if V is doubled? ______
4. What are the units for m? ______
B. As time increases the distance covered by an accelerating object increases at an increasing rate
1. Does x increase or decrease as t gets larger? ______
2. Using the graph, estimate what x would be if t was 0 ______
3. Using your equation, what would happen to x if t is doubled? ______
4. What are the units for m? ______
C. As time increases the weight of a cat eating only twinkies increases at a steady rate
1. Does W increase or decrease as A gets larger? ______
2. Using the graph, estimate what W would be if A was 9 ______
3. Using your equation, what would happen to W if A is doubled? ______
4. What are the units for m? ______
D. As time increases the weight of a dog on a diet stays the same
1. Does W increase or decrease as A gets larger? ______
2. Using the graph, estimate what W would be if A was 20 weeks ______
3. Using your equation, what would happen to W if A is doubled? ______
4. What are the units for m? ______
WRITING EQUATIONS THROUGH PROBLEM ANALYSIS
PRACTICE #3 WRITING EQUATIONS Name ______
Answer the questions below. The stories may seem silly. They are. Make sure to show your work, even on the easy problems. This will help on the harder ones.
1) John and Susan are out picking apples. John can pick 25 apples in one minute. Susan can pick 20 apples in one minute, but she starts with 40 apples in her basket.
a. How many apples does John have after 0 minute? 1 minute? 2 minutes? 15 minutes?
b. How many apples does John have after t minutes?
c. How many apples does Susan have after 0 minute? 1 minute? 2 minutes? 15 minutes?
d. How many apples does Susan have after t minutes?
e. Your answers to parts (b) and (d) are mathematical relationships, also known by that dreaded name “Equations.” What two variables are they relationships between?
f. Write the equations for each above.
g. What is the rate at which John picks apples? Susan?
2) Frank is in a race. He cheats and takes a 3m head start. He can cover 5m in one second.
a. How far is he from the starting line at 0 seconds? 1 second? 3 seconds? t seconds?
b. What two variables is this relationship between?
c. Write the equation for this situation.
d. What is the rate at which Frank travels?
3) A wasteful student leaves a sink on. It drips 0.25 mL every second. There was already 100 mL of water in the sink.
a. How many milliliters of water is in the sink after 0 seconds? 2 seconds? 20 seconds? t seconds?
b. What two variables is this relationship between?
c. Write the equation for this situation.
d. What is the rate at which water drips?
4) Bob eats a banana every day. He started with ten.
a. How many bananas does he have after 0 days? 1 day? Two days? 5 days? t days?
b. What two variables is this relationship between?
c. Write the equation for this situation.
d. What is the rate at which Bob eats bananas?
e. What does the equation say about 12 days after the start? What does this mean? Is this a legitimate is this?
USING EQUATIONS AND UNITS
READING #3
Metric System
The SI is founded on seven SI base units for seven base quantities assumed to be mutually independent, as given below.Base quantity / Name / Symbol
length / meter / m
mass / kilogram / kg
time / second / s
electric current / ampere / A
In our class we will use these base units and no others. Measurements should not be taken in grams, centimeters, minutes, or any other variations of the metric system.
Dimensional Analysis
From the perspective of physical mathematics, the entire universe is constructed from just four simple or fundamental quantities.
These are:
2. / Time. (seconds, hours, etc.)
3. / Mass. (grams, kilograms, etc.)
4. / Electric charge. (coulombs)
All other units of measurement are derived units, constructed from these four fundamental units. Sound unbelievable? Well it's true, and when the physics student masters this profound concept, never again will he/she wonder if a particular physics equation is correct or not. The student who masters dimensional analysis will be able to determine, with nothing more than pencil & paper, the truth of any physics equation.
For example:
1. The equation for the area of a square is area = length * width
If we write this formula out including units we get
So the correct unit for area is meters2
Units may also be checked by examining a graph.
For example:
1. The density of an object can be found by determining the slope of a graph that compares its mass to its volume.