ADAPT Lessons: Physics

Energy in Perspective Laboratory #5: Working with Triangles

Robert Fuller — Thu, 24 Mar 2011 12:50:36 PDT

Dear ADAPT Students,
We think that these plane figures can be organized into groups that share common properties. We went to Pythagoras but he died before he could tell us much. His last words were,
"Take measurements and focus on ratios..."
Beside his death bed we found 27 different pieces of cardboard cut into a variety of right triangles of various sizes and shapes. Please put the triangles into different groups that display at least two common characteristics and be prepared to explain to your instructor how you did it. You may wish to make a table of your measurements and calculations. Thanks and best wishes from Athens,
As always,
Your fellow students from Greece

Energy in Perspective Laboratory #11: Radiation

Robert Fuller — Thu, 24 Mar 2011 12:47:20 PDT

EXPERIMENTS
A) 1st Expt. Distance
1) Plot corrected counts/minute vs corrected distance.
2) Find the mathematical relationship from the graph.
3) Does doubling the distance cut the count rate in half? Check this mathematically.
4) Give a physical explanation of your results.
B) 2nd Expt. Shielding
1) Comment on the absorption of the various objects used in part A. Include count rates.
2) Plot corrected counts/minute vs shielding thickness for paper, aluminum, and lead. Make 1 graph with 3 plots.
3) Find mathematical relationships for each plot and label it clearly.
4) Which material shields the best? Why do you think it is so?
5) Which radiation is most penetrating? Why do you think it is so?
C) 3rd Expt. Lifetimes
1) Determine the radioactive half-life for the data sets given. See half-life data page.

Energy in Perspective Laboratory #10: Investigations in Optics

Robert Fuller — Thu, 24 Mar 2011 12:40:39 PDT

1. In an old-fashion film-developing device, it is common to use an aperture to control the exposure area of a film. The following diagram is a simplified version. There is a point light source on the left side of the diagram. We place an opaque plate with a 1 cm square hole in its center and 10 cm away from the light source. Then we place a screen 20 cm away from the light source. The plate and the screen are facing the light source and all these objects are arranged in a straight line.

2. This Halloween picture was taken by Chris Moore, a famous digital photographer of Lincoln. His daughter Ella was asked to guess whether she could see the image of the pumpkin in position A, Band C. Without any knowledge of optics, she had to go to each position to check. With your knowledge of optics, explain what you can see of the pumpkin in the mirror from each of the positions A, B, and C. Explain your reasoning using words and drawings as appropriate.

Energy in Perspective Laboratory #6: Induction -- Guessing a General Relationship from Specific Numerical Data

Robert G. Fuller — Sat, 19 Feb 2011 11:23:25 PST

Exploration Activity
An ADAPT student used a mechanical device to lift some heavy load. She recorded the following results:
Effort She Exerted Load She Lifted
10 lb. 410 lb.
22 lb. 520 lb.
33 lb. 620 lb.
45 lb. 730 lb.
60 lb. 860 lb.
77 lb. 1000 lb.
97 lb. 1200 lb.

1) Describe a method by which the student could determine the GENERAL relationship between the load she lifted and the effort she exerted. Is there more than one way that she could do it?
2) Decide on a method for your group. Use it to determine the general relationship between load and effort.
3) Use your results to predict the load she could lift if she exerted an effort of 50 lb. What about 115 lb?

Energy in Perspective Laboratory #7: Predictability, Measurements & Uncertainties

Robert G. Fuller — Sat, 19 Feb 2011 11:17:40 PST

Not all repeated measurements of the same physical quantity will give the same numerical value. Consider the following case:
Two groups, morning and afternoon, of students went out on campus and made repeated determinations of the height of Hamilton Hall and Mueller Tower. The six morning teams made a total of 18 different determinations on the height of each structure. The eight afternoon teams obtained 24 values. Shown below:
1. List a variety of ways you can determine a "best" value for each height.
2. Select a method and do it for each height.
3. What is a value for the uncertainty or possible error in your "best" values and how can you determine that.
4. Determine the "best values" for the heights of the 2 buildings from: morning data, afternoon data, all data.
5. Estimate an uncertainty for each group's data and all of the data.

Energy in Perspective Laboratory #9: A Variety of Physical Systems, or Determining Relationships for Four (yes, 4) Experiments

Robert G. Fuller — Thu, 17 Feb 2011 08:12:51 PST

Your task will be to collect data from a variety of physical systems and find the relationships between the manipulated (independent) and responding (dependent) variables using a graphical method. You now know two different ways of analyzing data using two different graphs, either Cartesian or log-log. It will be up to you to decide which to use. Remember: contrastive features, range of variation, and distribution in larger contexts are all necessary to be able to understand something. In physics language that means explore as wide a range of the manipulated variables as seems reasonable. In fact, every physical system is linear if you take a narrow range of values. Thus, to insure that your analysis is appropriate, be sure you double or triple, etc. the values you select for your manipulated variables.

Energy in Perspective Laboratory #8: Finding More of Nature's Rules, or Not Everything in the World is Described by a Straight Line!

Robert G. Fuller — Thu, 17 Feb 2011 08:10:49 PST

Using x as the independent variable, draw one graph plotting: x vs A, x vs B, and x vs C. For each plot, connect the corresponding points with a smooth, best fit line or curve. (One graph of a data set by each person in your group is sufficient for now.)

The mental power of a linear relationship is our ability to use it to predict behaviors that we have not measured! So far we have used Cartesian (named for French mathematician René Descartes) graphs (see lab #3). Most of our labs have consisted of taking data, plotting the data on a Cartesian graph, and then finding the mathematical relationship between the variables by finding the slope and the starting value from the graph. However, not all graphs produce straight lines! The curves at the right are drawn from relationships between y and x called power laws. The general equation would look like y = Ax^m where A and m have numerical values. On Cartesian graph paper we can only make guesses at A and m. To find them we need to use log-log graph paper!

Energy in Perspective Laboratory #4: Finding Relationships

Robert G. Fuller — Thu, 17 Feb 2011 08:07:14 PST

A group of ADAPT students took the Starship Enterprise to the planet Kunzonia. When they arrived, they felt funny. Their heads seemed light and their feet seemed heavy. To try to understand the force of gravity on this planet, they made a simple swinging device fashioned from equipment on the starship. It was a flat bar with a pivot at the top and three equally-spaced holes along its length. Using masses of 200gm, 400gm, and 600gm (which could be attached in the holes) a meter stick, and a timer, the students let the bar swing to and fro and made the following measurements:

Finding Patterns in Numbers (Lesson #3)

Robert G. Fuller — Fri, 26 Jun 2009 13:51:40 PDT

The ADAPT physics labs were arranged to encourage students to develop formal reasoning as explained by Robert Karplus and Jean Piaget. Each lab is organized as a Karplus Learning Cycle. {Reference: R.G. Fuller (editor), "A Love of Discovery: Science Education, The Second Career of Robert Karplus", Kluwer Academic/ Plenum Publishers, New York, © 2002}

A primary function of the labs was to get the students to develop their skills at finding patterns in the data they would get from the laboratory experiments.

This is the beginning of the data collecting laboratories. The students begin with a series of experiments that can give data that will result in a linear relationship between the variables. Then there follow experiments that yield power law relationships that can be shown as linear on log-log graph paper. Finally, the laboratories are experiments that can be exponential relationships which can be shown a linear on semi-log graphs.

Each group of students, in teams of four, are given a set of eight data cards that have numerical data sets on each card. They are asked to sort them into groups by their similarities. The students are encouraged by the instructions to seek the relationship between the two variables. Some students will insist on only looking as the spacing, etc. between the numbers in one set of the numbers.

After the groups have sorted their numbers into batches that are similar, the source of the data sets can be given to the groups to help them evaluate their batching process

A Semester of Physics Laboratories by a variety of physicists

Wed, 17 Jun 2009 09:37:57 PDT

The ADAPT Program for college freshmen was offered at the University of Nebraska Lincoln from 1975 to 1997. The program always included two semesters of three credit hours of physics. The fall semester of laboratories is given in this pdf file. The physics topics were arranged to develop more and more advanced reasoning and data analysis skills, from linear functions to power law functions to exponential functions. These analysis skills required the students to master Cartesian graphs, log-log graphs and semi-log graphs. All of these laboratories were organized according to the Robert Karplus learning cycle. Near the end of the semester the students were introduced to the concepts of Piaget by the use of the Karplus film, Formal Reasoning Patterns.

After 1981 the second semester of ADAPT physics was called Problem Solving Using Computers and involved the students in solving a variety of problems using applications software on Macintosh computers.

The Planet Puzzle (Lesson #2)

Robert G. Fuller — Wed, 17 Jun 2009 09:36:26 PDT

Students were asked to categorize 13 previously collected samples into 4 groups. Ideas on what properties should be used to categorize the samples were left open to the students. It was found that properties dependent upon the method of collection would make more than 4 groups, therefore properties dependent only upon the material were used in the categorization. The central idea of this activity is to confront the student with the requirement to quantify his concrete experience with materials of different densities. Density, since it involves ratios, requires formal operations. This experiment begins with a task that will hopefully induce some disequilibration, followed by the opportunity for self-regulation.

International Trade (Lesson #1)

Robert G. Fuller — Wed, 17 Jun 2009 09:34:56 PDT

This lesson is intended to provide motivation for the students to appreciate the use of an International System of Units.

The students are divided into small groups, around lab tables. The measuring instruments are provided to each group. Each group is treated as a different “country”. Each country is given a different set of measuring instruments: A ruler is a colored strip of paper marked off in ten divisions. Each country is given a different length for its ruler. A liquid volume measuring cup is a colored plastic cup marked off in ten divisions. Each country has a cup with a different volume. A pan balance with ten metal washers as the balancing units. Each country has a different size of washer for its mass unit. The name of a country was based on the color of its “ruler” and same color of its measuring cup.

Each country is given a supply of energy (symbolized by pieces of wire that will need to be measured in length), food (symbolized by pretzels that will need to be measured by mass) and water (which will need to be measured by volume) at the start. Each country has a different kind of pretzel. When setting up the countries at the start, before class starts, the instructor makes sure that the various countries have very different amounts of the natural resources.

Each country is required to trade with every one country at least once.