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 3Time (x axis) / Distance (Y-axis) / Speed (Y-axis) / Height (Y-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 measure / Measurement / Price / Price per unitCow / Pounds / 1000 / $1000.00 / $1/pound
Volleyball / cm3 / 14,819 / $10.00 / $0.00067/cm^3
Oatmeal / Ounces / 32 / $2.00 / $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:
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