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Spaghetti Bridge Lab

posted Aug 1, 2017, 10:40 PM by Mark Schober

I love starting the year by asking my new class of students to show me what they can do: take data so that you can predict the number of masses that could be supported by a bridge made of strands of pasta. 

I used to provide a lot of guidance so that the students would get "good" data, but I've found that the less guidance I give, the greater the variety of student approaches (both good and bad) and the richer the post-lab discussion. After all, this lab isn't about developing a critical physical principle, it's about experimental design, communication, and setting a community norm that "answers" are based on patterns in data taken in a justifiable manner -- not on what the teacher says.

This activity provides a great environment for discussing independent, dependent and control of variables. Depending on the level of your students, some might graph their data and write an equation for the graph, and the spaghetti bridge lab is a nice situation to use because the slope and y-intercept have accessible physical meanings.

Materials:
Uncooked long-strand spaghetti, thick and thin
Large plastic cups or small cans.
String to make a handle on the cup/can to attach to the bridge
Unit masses: Marbles, washers, hex nuts, or pennies. I found some decorative squashed glass marbles -- they don't roll far when they hit the floor.

Lab Procedure Notes:
[] Depending on your comfort level, don't be afraid to let the students come up with their own procedures. The important thing is for every group to explain their procedure in the post lab discussion. During this discussion ideas will emerge about how best to collect, display, and interpret the data. 
[] Let the students make mistakes -- but remind them to keep notes on how they collect their data.
[] If you use marbles, have each group assign a "catcher" for the cup, otherwise there will be potentially dangerous marbles scattered all over the floor.

Post Lab Discussion:
Ask the students show their procedure and represent the pattern they found on large whiteboards. Choose one of the groups with a weaker board to go first. Ask the rest of the class to identify well-done elements on each board and to explain why those elements their communicate procedure and results well. As you make it to stronger boards, also ask the class for suggestions for making the data collection and presentation of data even stronger. You might assign a student to record items that the class feels are important to conducting a good experiment and presenting data clearly.

Example whiteboards:

   

    
Example questions:
Experimental procedure questions:
What was your procedure? Is the procedure clearly shown on the whiteboard?
What was your independent variable? 
What was your dependent variable? 
What is meant by control of variables? 
How did you control variables? 
Why did you control variables? 
How is a dependent variable different from an in dependent variable? 
How did you know you had collected enough data? 
What is the advantage of doing multiple trials?

Questions about the presentation of results:
What are the features of a good data table?
How did you convey the pattern you found?
Use your pattern to determine the number of masses that could be supported by 10 (for example) strands of pasta.
The whiteboard is a visual aid. What representations are most helpful in conveying what you did and what you found?

Questions about the graphical analysis of data: (see the graphical analysis discussion below)
What kind of graph best represents your data?
Explain why you graphed this variable on the vertical axis and that variable on the horizontal axis. 
What does the straight-line graph tell you about the bridge? 
What does the y-intercept mean in terms of your bridge? 
How do you determine the units of the slope? 
What does the slope of your graph tell you about your bridge? 
Why do different groups have different values for their slopes? 
What variables affect the size of the slope?
Under what conditions might you get a larger slope? 
What parts of the equation should have units and what parts of the equation do not have units?

Graphical Analysis:
Students graphing their data will find it to be pretty linear. draw a best-fit line, and determine the slope and y-intercept of their line. Students should be asked to write an equation for their graph. You may need to remind them of the general form of the equation for a line, y = mx + b.  
Example equation for load measured in marbles and strength measured in strands:
    (load) = 8 marbles/strand * (strength) - 5 marbles

The slope tells how many marbles are supported by each strand of pasta. If the students use the word “per” or “over” be sure to ask them explain what the slope means without using per and over. For example, students should be able to explain that 8 marbles/strand means each additional pasta strand can support 8 additional marbles. 

The negative y-intercept is interesting and tricky. Students may notice that heavier marble cups result in larger, more negative y-intercepts. Lead students to observing that the strands never supported quite as many marbles as the slope would predict. Asked what else is putting a load on the bridge, students recognize that the weighted cups put a load on the bridge about the same size as their y-intercept. Therefore, the equation can be interpreted to mean that several strands of strength may be needed to support the cup before any marbles can be added. An equally fruitful discussion arises from describing the meaning of the x-intercept.

An essential conclusion for students to reach about the graph is that the constants in the graph: slope and y-intercept, have physical interpretations related to the physical experimental setup.

3D-Print Your Own Lab Clamps

posted Jun 3, 2017, 10:42 PM by Mark Schober   [ updated Jun 9, 2017, 9:31 PM ]

Clamps! You can never have too many, and a great table clamp is indispensable when setting up labs in the physics classroom. But table clamps sell for $50-$100 each, so I set out to design a 3D-printable table clamp that was robust, multifunction, and low cost. Along the way, I designed a variety of other clamps as well that I've shared below. You don't have to print out many clamps before you've earned back your investment in a 3D printer. 

A disclaimer right up front: 3D printed plastic clamps will never be as strong and durable as metal clamps. Although I haven't had any of my 3D-printed clamps fail, I haven't let my students go wild with them, either. For most introductory physics lab activities, these clamps are stable, solid, and strong enough to get the job done, as long as you tighten the bolts with attentiveness to the strain you are putting on the plastic. If a clamp fails and your lab apparatus falls down, don't blame me!

If you have a 3D-printer, great! If you don't, here's how you get a 3D printer:
You: Dear person who holds the purse strings, I need 16 table clamps. 
Money Person: How much? 
You: $1600. 
Money Person: Seriously? No.  
You: Okay, here's an alternative: I need a 3D printer that I can use to print all the clamps I could ever need while providing my students with the opportunity to learn how 3D printing works and enable them to print their own designs. 
Money Person: How much?
You: $1600. 
Money Person: Sold!

Basics of 3D Printing

If you're new to 3D printing, here's the workflow: 
  • You start by designing a 3D object using 3D design software such as TinkerCADSketchUp, or OpenSCAD. Alternatively, you can download 3D files, like the ones I've provided below, or those on websites like thingiverse
  • Once you've designed the object and saved it in the program's native format, you need to export the 3D object as an .stl (STereoLithography) file
  • Next, you need slicing software such as Cura that will read the .stl file and turn it into a toolpath for your specific 3D printer. This is where you can adjust the print quality settings as well, determining the thickness of each layer or the percentage fill inside the object, for example.
All of the software I use is free. 

I printed all of these clamps on a Lulzbot Mini 3D printer. At $1250, it is more expensive than many printers on the market, but it works so well. Cheaper printers will get the job done, but they often take more of your time to get them and keep them properly adjusted to work reliably while risking more failed prints. The Lulzbot has a heated platform, it self-levels, and its 8x8x8" print volume is plenty big for all of these lab clamps. 

Printer Settings

experimented with a variety of print settings and I settled on printing layers .25 mm thick, with walls 1 mm thick and a fill of 30%. This gave me good balance between strength and print speed. In my tests, I went from a 20% fill with thick walls (on the left) to a 30% fill with thinner walls (on the right). The latter printed more quickly and was every bit as strong.

I printed everything using PLA filament. ABS plastic would be stronger, but we don't have great ventilation in our 3D printer room, so we've put the ABS on the shelf until we upgrade our ventilation. I experimented with a variety of print settings and I settled on printing layers .25 mm thick, with walls 1 mm thick and a fill of 30%. This gave me good balance between strength and print speed.


I have not yet experimented with annealing the 3D prints, which should make them up to 30% stronger according to what I've read. Annealing involves reheating the prints in an oven above the glass temperature of the plastic, but below the melting temperature of the plastic. This allows the internal stresses in the print to release while strengthening the bonds between print layers.

In addition to the 3D-printed parts, I used 5/16" nuts and bolts to form the clamps. For lab rods, I've gotten some 3/8" solid rods from steel suppliers on eBay. If they have the length you want at a good price, you're set. For me, the low cost winner is 1/2" electrical metallic tubing (EMT conduit). It's inexpensive and easy to cut. I prefer cutting with a pipe cutter, because it leaves a much smoother cut than a hacksaw. I designed all of the clamps to handle this size of pipe, which is pretty large in diameter compared to most lab rods. The teardrop shape of the holes in the clamp is to provide three contact surfaces for any size of lab rod, resulting in a stable clamping configuration.




Table Clamp

Editable OpenScad file
Table Clamp
Printable .stl file
Table Clamp 

Scale the thickness of the clamp to 27 mm in your slicer software.
 
  

Table clamp

I had great fun prototyping this clamp, eventually coming up with something that prints well, is strong, clamps to a table as thick as 1.75", and handles rods as large as 1/2" EMT conduit. 

You'll also need to print three bolt handles for 5/16" bolts (file below). The bolts for clamping the rods is 1.5" long, and the bolt for clamping to the table is 3.5" long. I spin a nut two or three twists on to the bolt, apply a dab of hot melt glue to the head of the bolt, and then use a hammer to pound the head of the bolt into the printed bolt handle. The nut protects the threads at end of the bolt which would otherwise be damaged by the hammer.  For each bolt, there is a recessed hexagonal hole to hold the nut in the 3D print. I insert the bolt through the print, spin the nut on, apply some hot glue to the sides of the nut, and then pull the bolt to set the nut into the hexagonal hold. 

The bolt that attaches the clamp to the table needs something attached to the end of the bolt to minimize damage to the surface being clamped to. With the bolt in place through the nut fixed in the 3D print, add a second nut at the end of the long bolt with a couple of twists, add some hot glue to the bolt just under the nut, and then spin the nut down the bolt until it becomes stuck in the hot glue.

Adding a rubber pad for additional friction to the portion of the clamp that sits on the top of the table dramatically increases the clamp's stability.

Here's my prototyping progression:
From left to right, I started with a 1.5" thick version of the clamp that could only attach a lab rod vertically. I printed with different amounts of fill until I found that 30% fill made a big difference in strength while still printing relatively quickly. I next added the ability to clamp a rod horizontally to the table. In the third prototype, I added some angled elements to increase the strength of the clamp, and it made a big difference in the clamps' stiffness. My final design included angles into the horizontal clamp while adding a hole for clamping sideways. In particular, I can use this hole to attach a pulley. I like the functionality and the look of the final design.



Boss Head Clamp/Right Angle Clamp

Editable Open SCAD file 
right angle clamp
Printable .stl file
right angle clamp

scale to 34.9 mm high in slicing software


Boss Head Clamp/Right Angle Clamp
I had initially printed these as the intersection of two cylinders at right angles, but found adding the extra material to form a flat base made the print work much better. You'll also need to print two 5/16" bolt handles for each clamp. The bolts themselves are 1.5" long.

Boss head clamps can be purchased pretty inexpensively on eBay, but printing them is very satisfying. Also, if you want to go with the 1/2" EMT conduit for your lab rods, you'll need to print these, because most boss head clamps are too small to accommodate the conduit.


Tripod Ring Stand Base

Editable OpenSCAD file
ring stand base 
Printable .stl file
ring stand base 

scale to 80.2 mm high in slicer software
  

Tripod Ring Stand Base
Note that there is an inherent weakness in the design of this clamp. Unlike the other clamps I've designed, where tightening the bolt places stress parallel to the 3D printed plastic strands, in this design the bolts that hold the legs place a force on the clamp that tends to pry the layers of the 3D print apart. This print would greatly benefit from being annealed in an oven before being sent to work.

You could cut the legs to whatever length you like. The legs in the picture are 10" long.

Pendulum Clamp

Editable OpenSCAD file
Pendulum clamp 
Printable .stl file

pendulum clamp

scale to 128.6 mm high in slicer software

Pendulum Clamp
You can easily get by without this clamp, but once you get the 3D printing bug (and you've got your printer working smoothly) you'll want to outfit your entire lab with all those crazy clamps you would never normally purchase! 

The advantage of the pendulum clamp is that it is easy to adjust the length of the string for a simple pendulum while having the upper end of the string at a fixed location (which isn't true for a string wrapped around a horizontal rod).

Pulley

Editable OpenSCAD file

pulley 
Printable .stl file

pulley

Scale to a diameter of 50.8 mm in slicing software. 
Pulley
At this point, I've only got the pulley itself, which can be mounted on an R4zz 1/4" x 5/8" x .196" bearing that I've mounted on a quarter inch bolt. I secure the bearing with two nuts. By twisting one nut into the other, they lock each other into place. The bolt can be clamped into the table clamp or the boss head clamp for all kinds of applications. I chose a ten-spoke design, the same as Pasco's smart pulleys, so that you could use it with a photogate and track the rotational motion of the pulley. I have a student designing a yoke to turn this into a pulley clamp. When we get it finished, I'll get it posted.

5/16" Bolt Handle

 
Editable OpenSCAD file

5/16" Bolt Handle 
  Printable .stl file

5/16" bolt handle

Scale to 12.7 mm high in slicing software

5/16" Bolt Handle
All of the clamps I've designed are for 5/16" bolts. You'll need a lot of these.

3/8" Bolt Handle

Editable OpenSCAD file

3/8" Bolt Handle 
Printable .stl file

3/8" bolt handle

Scale in slicer to 12.7 mm high.
3/8" Bolt Handle 
We had a number of the handles from our Pasco table clamps break for whatever reason. I bought 3/8" bolts from the hardware store and printed handles for the bolts. The clamps are as good as new.

Three-Finger Clamp

 
 
Three-Finger Clamp
I designed this clamp with a 3-axis mount. The rod can come in from the bottom or from either side. The finger (or thumb) articulation requires a series of holes and slots to hold nuts as guides. This clamp is still a work in progress.

Another Approach

I developed a different clamp for the overhead metal racks in our physics labs consisting of an oval anchor and a knob attached to an eye bolt.

 
 
I needed so many copies of the same thing that I printed a few copies of the parts, made a silicone mold of the parts, and then cast resin copies of the parts using materials from Alumilite. 
The polyurethane copies captured all of the detail of the layering in the original 3D print. 



Low-Cost Wave Generator Apparatus

posted Jan 20, 2017, 11:16 AM by Mark Schober   [ updated Jan 20, 2017, 12:49 PM ]

There's something magical about standing waves, resonance, and the tangibility of the nodes and antinodes. Students love working with the waveforms, and they love the direct connection to the musical instruments they play, how harmonics work, and the physical principles behind them. Unfortunately, most science suppliers sell a wave driver apparatus in three parts: 1) the thing that does the shaking, 2) an amplifier, and 3) a function generator. Depending on the supplier, one full setup costs between $500 and $1000. That's a bit steep for me, so here's a homemade version that costs about $30 in parts and takes advantage of the capabilities of your smartphone.

Mechanical Waves Make-n-take Workshop Description

This workshop is based around a low-cost wave-driver and amplifier driven by a free smartphone app for investigating wave propagation in strings. Similarly capable equipment from science suppliers ranges from $500-$1000 per lab setup, while ours costs just $30. We will begin by using the wave driver to examine properties of standing waves on strings, followed by a lab to quantitatively investigate how string tension and string mass per unit length affect the wave speed. You will then build your own wave drivers to use with your students. Not only does this set of labs establish the fundamental properties of mechanical waves, it provides an excellent experimental environment for students to collect and analyze data for a phenomenon that depends upon multiple variables. 
I'm leading a make-and-take workshop to build these for your classroom on March 5th, 2017, from 10 am - 1pm. If you are available to join me at Teacher's College, Columbia University, I'd love to see you there. Registration for the workshop is $20, and wave drivers are $30 each. You can sign up for the workshop here: https://www.eventbrite.com/e/wave-generator-makentake-registration-30285815690

In the workshop we will run the labs you can do with this equipment as well as build the apparatus.



Design Features:

The apparatus consists of a 4-inch speaker, a 50 Watt mono amplifier circuit, a 12-volt power supply, and some laser cut acrylic pieces that tie things together. All parts are mounted to a central acrylic plate that includes notches for cable management when not in use.

You need to supply a ring stand with a flat metal base. The metal rod acts as one anchor for the string and the acrylic pyramid mounted to the speaker cone shakes the string. The magnet in the base of the speaker sticks nicely to the metal base, and a hole in the acrylic plate locks it onto the ring stand rod. This makes the overall apparatus much heavier so that it doesn't go wandering all over the lab table.

There are a variety of smartphone apps that feature tone generators or frequency generators for free. I've been using one called "Function Generator" on an iPhone which works fine, though it's filled with pop-up ads. You want a program that allows you to increase or decrease the frequency by tapping add 1 Hz or add 10 Hz. Interfaces dependent on a slider or having to type in the frequency are difficult to use for this application. I want to give a shout out to the Physics Toolbox app that gives you access to all of the sensors in your phone. (Check it out!) The Physics Toolbox has a tone generator for Android that allows you to change frequency by tapping, but it does not work that way on iOS.


There isn't anything that complicated here that you couldn't do with a saw and a drill, but once I refine my prototype for the workshop, I'll post the cutting templates and a detailed parts list here to save you some time. I'll also share the curriculum materials that go with the lab and the followup analysis.






Soda Can Photoelectric Effect Demo

posted Apr 8, 2016, 6:55 PM by Mark Schober   [ updated Apr 8, 2016, 8:17 PM ]


The photoelectric effect was at the heart of not just one Nobel Prize, but two! If you can plunk down $175 for a short wave UV source, (or borrow the one your biology teachers might have around for looking at bacteria) you can visit the grocery store to get everything else you need to demonstrate the photoelectric effect.

I'll also tout the soda can electroscope, which, for the low-low cost of dumpster diving, is superior to commercial electroscopes as far as I'm concerned. The pie-plate electrophorus is also as good or better than any commercial one on the market. Just imagine what Ben Franklin might have discovered with access to the wonders of modern take-out containers. As it was, he had to do with pewter and wax -- it was definitely a different time.

Click the image below for instructions on how to assemble the apparatus and do the demo. 

https://drive.google.com/file/d/0B0zTEgmv0I9UNDViRkFrTDlVdXc/view?usp=sharing


LED Photoelectric Effect Apparatus

posted Apr 5, 2016, 5:35 PM by Mark Schober   [ updated Apr 5, 2016, 5:35 PM ]

I first encountered Wayne Garver's low-cost LED photoelectric effect apparatus at a St. Louis Area Physics Teachers workshop in 2005. Since then, I've been involved with building dozens of these. This latest version has some simplifications and additions that make it even more useful. Wayne's insight is that the essence of the commercial apparatus is the vintage phototube at the heart of the device. All the other parts are pretty simple and inexpensive. So for about $100 in materials, you can build an apparatus that will do everything that the $500 version in the science catalog will do.


In the fall of 2015, my engineering classes built 30 photoelectric effect devices as an orientation to using tools and soldering. Some of the solder joints aren't pretty, but they all have been tested and work fine. It was a great mix of practical skill development and service to the school and the science teaching community. At the upcoming workshop, we're selling the apparatus for the cost of the parts.

In April 2016 I am offering a workshop on the photoelectric effect and how to get the best learning impact from the device. If it isn't yet April 9th, sign up to join us! https://www.eventbrite.com/e/photoelectric-effect-make-n-take-workshop-tickets-22946066302


The light source for the device is a set of LED's. Since all of the LED's are clear, it is necessary to label them. I was ready to pull out my model railroad paint when one of my workshop participants in 2014 suggested using fingernail polish. What a brilliant solution!

Here's a close up.

Here are the directions I've written up for constructing the apparatus. Click the image to open the pdf.
https://drive.google.com/file/d/0B0zTEgmv0I9Ub2lOeV9hNlRqV2c/view?usp=sharing

I'll add a few more photos and resources after the April 9 workshop.

Slow Acceleration Apparatus

posted Jul 29, 2015, 12:02 PM by Mark Schober   [ updated Apr 8, 2016, 8:27 PM ]

So that students develop a real kinesthetic sense of accelerated motion, it is ideal for them to investigate the acceleration of an object that speeds up so gradually that the motion can be tracked by hand. Rex Rice, of Clayton HS in St. Louis, developed an elegant solution using a wood disk with an axle made from two golf tees. The wheel and axle rolls down two conduit pipes, and students can mark the position of the axle at equal time intervals, getting 20 to 30 measurements depending on the incline.

After making hundreds of these -- it's no small task cutting 4" disks out of MDF and drilling centering holes in the end of the golf tees so that they align appropriately -- Chris Doscher suggested to me that we could use CD's for the disks by using a faucet washer to attach them to a metal axle. The metal axles are less ideal because they don't have the self-centering feature of the tapered golf tees and the friction between the steel axle and the steel pipes is low enough that they have a tendency to slide on the pipes. One fix we have added is to run a strip of masking tape down each pipe to give a bit better tooth. However, we sometimes found that the disk's acceleration decreased as the wheel approached a terminal velocity with the tape -- be sure to test it ahead of time! I haven't tried it yet, but I want to spray the axle with a clear lacquer to change the friction characteristics.

Slow Acceleration Apparatus Instructions

https://drive.google.com/file/d/0B0zTEgmv0I9UUkduSFhBR2Y5UGs/view?usp=sharing
Click to download a .pdf of the directions to build the apparatus.

The teacher's notes for the Uniformly Accelerated Particle Model on the AMTA site spell out the details, but here is an outline of how you could use this apparatus in an instructional sequence:

1. Introduce the activity in terms of prior explorations in constant velocity. Our goal is to quantitatively describe the motion of an object that has a changing velocity. Students will recognize that they can use the same data collection procedure that they used in the constant velocity lab.

2. Students collect data for the moving disk.

3. Students make a position-time graph. Since it's curved, guide them to the idea of finding velocities at different times of the motion by drawing tangents to the curve and finding the slope.

4. Students make a velocity-time graph. In the discussion, acceleration is quantitatively defined.

5. Students are challenged to make and analyze additional graphs: "Linearize" the position-time graph by making and analyzing a position-time squared graph. Graph velocity vs. position and linearize the graph. By the time the analysis is done, all of the accelerated motion equations have been developed from the data.

Mega Can-Crush

posted Jul 13, 2015, 9:42 PM by Mark Schober   [ updated Jul 13, 2015, 9:55 PM ]

I've done the can crush lab with my students for years, but only crushing soda cans. I find this image of a crushed railroad tank car fascinating and I wrote a quiz based on it for use in Modeling Chemistry Unit 3. By the way -- the steel that makes up the tank on a DOT-111 tank car is 7/16" thick and has a capacity of 34,500 gallons. Because the DOT-111 design has been involved in several recent oil train accidents, the DOT-117 design will replace it, with 9/16" thick tank steel and full end shields. As a railfan, I follow all kinds of information about trains, and I also came across this on Trains.com news feed:

From trains.com on July 7, 2015:
Kelso Technologies Inc. obtained approval from the Association of American Railroads to begin commercial field trial testing on the company’s new Vacuum Relief Valve. The low-pressure device is specifically designed to protect tank cars from the effect of an excessive vacuum, preventing the implosion of the tank car. The patent-pending valve design is a result of customer demand for a better performing product due to the failure rate of products currently in use. The device meets the new DOT-117 tank car specifications to be implemented later this year. Kelso is a railway equipment supplier that designs, produces and sells proprietary tank car service equipment. For more information, go to www.kelsotech.com.

Upgrading an old website

posted Jun 27, 2015, 6:46 AM by Mark Schober   [ updated Jul 16, 2015, 8:50 PM ]

Dear friends, I started this website over 15 years ago as a resource for my students and, as it turns out, for the wider Modeling community.

I have had the opportunity to teach physics in grades 9-12 in public and private schools, and implementing the Modeling Instruction philosophy with each combination of variables required customized curricular approaches to best fit my students. I'm now at a school that has its own password-protected web system and maintaining multiple web platforms has been too much to keep up with. Therefore, some upgrades are needed.

This site is now designed specifically for teachers. My students can get what they need through my school site. This tighter focus will make the site easier to use.

Most of the physics materials I've created and the resources I've assembled are available through the American Modeling Teachers Association website. They have a great platform for exchange of ideas that compiles the resources and brains of hundreds of teachers throughout the Modeling Instruction community.

Many bloggers have done an excellent job of addressing questions and providing excellent resources for teachers. I will add to the blogosphere when I have something to say, but I will also happily refer you to the excellent thinkers out there who have stated things beautifully. My own writing has also appeared on the AMTA site and on the STEMteachersNYC site.

I've branched out beyond physics. I've now taught Modeling chemistry, environmental science, astronomy and modern physics, and engineering. I also have a dozen years of experience with middle school astronomy and meteorology teaching. Along the way I've learned a lot and have generated some resources that may be worth sharing.

I've also thought a lot about developing storylines that connect the entire science sequences together by considering what is central to the scientific subdisciplines and what will set students up for subsequent studies and science. When considered in a holistic way, the physics first sequence makes perfect sense and Modeling approaches in physics makes it doable.

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