Day Four Conceptual Final Review
Concept 1: some variables are correlated, some are not.
Correlated variables: Circumference and diameter, human weight and age, human height
and weight
Uncorrelated variables: Circumference and height, human height and hair color, housing
prices and wind velocity
Study task: Come up with two sets of three variables, two of which are correlated
and one is not.
Concept 2: A good way to look for correlation is to plot the data and see if it makes a
straight line. If it does, the slope tells you about the correlation.
Concept 3: A graph consists of (7-8 points)
Title (1)
X and Y axes labels (2)
X and Y axes scales (2)
Data points (1)
Curve of best fit (1)
Slope if the curve is a straight line (1)
Study Task: Plot the following three sets of data. Find the slope of the one that forms a
straight line. Which graph is not correlated?
Graph 1
Graph 2
Graph 3
Time (x axis)
Distance (YSpeed (Y-axis)
Height (Y-axis)
axis)
1
0.1
1
5
2
0.2
4
5.208818
3
0.3
9
5.702922
4
0.4
16
3.910136
5
0.5
25
4.943943
6
0.6
36
4.014445
7
0.7
49
5.850812
8
0.8
64
6.459527
Concept 4: Estimation
Sometimes a good estimate provides a way to get started on figuring out how to get an exact
value, or if the exact value is worth getting. The most important thing in estimating is
knowing your assumptions, and documenting them.
Perception and Illusions
Concept 5: Look carefully before you make a decision about something. Optical illusions
can affect your purchases. What is the best way to assess an optical illusion?
Unit pricing is your best approach to evaluating a purchase
Price / unit of measure, such as
$/pound, $/ounce, $/kg, etc.
Find the unit price for the following items:
Item
Unit of
Measurement Price
measure
Cow
Pounds
1000
$1000.00
3
Volleyball
14,819
$10.00
cm
Oatmeal
Ounces
32
$2.00
Price per unit
$1/pound
$0.00067/cm^3
$0.0625/oz
Can you meaningfully ask which of these items is the better buy? Why or why not?__Not a
meaningful question, they are completely different and not interchangeable.__________
Concept 5: Illusions of any kind are best investigated by measurement. Get out a ruler, a
scale, a camera, a volume measure.
Concept 6:
When measuring something using probability or statistics, the more data the better. Any
estimate based on a sample size of less than 30 is unwise.
Study questions: What is the chance of drawing an ace from a deck? _4/52_________
2 aces in a row? (4/52)*(3/51)_3 aces? (4/52)*(3/51)*(2/50)
4 aces? (4/52)*(3/51)*(2/50)*(1/49) __ 5 aces?____0______
What is the chance of rolling a six?___1/6_____ Two in a row?__(1/6)*(1/6)_= 1/36____
Three in a row?__(1/6)*(1/6)*(1/6)__= 1/216___
Flipping a coin once and getting heads?__1/2___________ Twice?____1/4______________
Three times?________1/8_______________
Radioactivity
Concept 7:
Radioactivity is an important natural process that depends on chance. We can predict
with near certainty the amount of material that will decay in one half-life (the time it
takes for half the material to decay). Three types of radioactivity occur
Alpha radiation (does not penetrate far)
Beta radiation (goes farther than alpha, but is stopped by a piece of paper)
Gamma radiation (needs concrete to stop it)
Study task: Which type of radioactivity is most dangerous to be near? Gamma
Which type is safer? Alpha
As an element decays, the amount of material declines in a pattern that looks like this:
Mass of Radioactive Josephium
1200
1000
M
a
s
s
800
600
Mass
400
200
0
0
2
4
6
8
10
12
Time in hours
If there are 1000 grams of Riverium at the start of the clock, how much is left at one hour?
_______500 grams___________________________________________________________
What is the half-life of Riverium?________1 hour________________________________
How much is left after four hours?_____62.5 grams_______________________________
After 6 hours?_____________15.6 grams______________________________________
Potential and Kinetic Energy
Potential Energy is stored energy that can be made available to do work. A simple way to
increase the potential energy of an object is to lift it.
PE = mgh = mass * gravity * height
Increase the mass or the height and you increase the potential energy!
Emily at 50kg is standing on a platform 2m above a pool. If she dives in, she will have
PE = (50kg)(9.8)(2m) = 980 Joules of energy.
If she climbs up to 4m, how does her PE change?_____1960 Joules___________
If she straps on 50kg of ballast, how does her PE change?____Doubles_
If she goes to Jupiter (where gravity is 3 times that of Earth), how does her PE
change?________Increases by 3___________________________________
Kinetic Energy is the energy of motion. Increase the speed or the mass of an object and the
kinetic energy is increased.
KE = ½ mv2
Notice the v2 term. This is why the braking distance goes up with the square of the velocity.
The faster a car is going, the more kinetic energy it has, and it takes longer for the brakes
to get rid of it.
If I double my speed, how does that affect my Kinetic Energy?____Goes up by 4_________
If I double my mass (for the same speed), how does that affect my Kinetic
Energy?_______Doubles______________________________________________
IF I double my speed, how does that affect my braking distance?___Goes up by 4__
If I double my mass (for the same speed), how does that affect my braking
distance?__________Doubles_________________________________________
We measured the effect of kinetic energy by dropping projectiles at flour – the higher the
height, the more PE, which go turned to KE as it fell, and made a bigger splash in the
flour.
Increasing the height of an object from the ground increases what form of energy?__PE______
When an object falls, what gets smaller and what gets bigger?__PE goes down, KE goes up___
In addition to Kinetic Energy, what else increases as the KE increases?__Speed_____________
What are the three major considerations in designing a roller coaster with a loop?__Fast enough,
strong enough, centripetal force greater than gravity (g)_
Mass / Energy (Fusion and Fission)
In the sun, hydrogen is fused into helium and gives off energy. In a nuclear reactor, Uranium
is split and produces energy. In both cases a little mass is converted to energy using
Einstein’s famous equation,
E = mc2.
So mass can be converted to energy and energy into mass. This process (hydrogen to
helium) is the source of essentially all energy on the Earth.
Atoms Concept 18: Rutherford model
The atom is made up of three major particles,
Electrons – carrying negative charge, these hang around the outside of the atom
Protons – these positively charged particles live in the nucleus
Neutrons – these uncharged neutral particles also live in the nucleus
The electrons are available to be moved around. An imbalance of these creates static electricity.
Which of these particles are free to move around in a metal?__Electrons____________________
Nuclear energy is typically discussed in terms of
Fusion: light elements fusing to make heavier elements and releasing energy (due to the
mass defect of the missing mass )
Fission: Heavy elements are split apart into light elements, also releasing energy
Which form of nuclear energy is used in the Indian Point reactor?____Fission___________
Other forms of energy discussed include
Light, Chemical, Thermal (this is really kinetic energy),
Electrical