I recently came across a video of tape measures "racing" along a board of wood as they retract. Who doesn't love extending the tape as far as you can and recklessly letting it fly in? It obviously accelerates dramatically. Like any physics-minded person I got to wondering if the force is constant. How might we assess?
I'm home for the summer, a summer I desperately needed, and away from some of my usual tools. No probeware. No students to help. First I put a small bucket with a handle on a food scale from our kitchen. I extended the tape measure and used it to pull up on the scale. The force was somewhat constant, but not as steady as I would like. A force probe would have been handy to average many data points and see the force graphically.
Perhaps it would be simpler to measure acceleration, rather than measuring force directly. We could replicate the original video. But what about friction? I've also noticed that tape measures sometimes stick when used in this position. What if we pulled a cart of known mass and analyzed the video? The toy cars at my disposal were all too light—or had too much friction—to provide a motion that was slow enough and consistent enough to satisfyingly measure with the tools on hand.
But there it was staring me in the face: the air hockey table. I put the tape measure on its side, so that the weight of the extended tape doesn't cause it to rub as much against the tape (tape retracts more smoothly). Lego base plate floats beautifully on table. A few Lego bricks are placed on one end of the plate to hold the hook of the tape measure during retraction.
Sure, you could use it to demonstrate Lenz's law, but that fine aluminum tube seemed pricey, so I was keen to justify the expense. You can tap it with a mallet (or on the ground) while holding it at various places to produce different notes. The Q of aluminum is great for this. You can stand it up on its end in your classroom to demonstrate unstable equilibrium.
But for my notion of classroom theatrics, the best unintended use for the tube was as a blowgun.
For this RT;DL I prepared a tour through the equations of motion with the blowgun acting as my vehicle. it is very much up to the task. I do this in my AP Physics 1 course only. Regular Physics students don't really need the exercise in number puzzles that the equations of motion afford. The year's too short.
In any case, I blow a marker pen through the tube and arrange two photogates near the muzzle to help determine the exit speed. It's over 60 mph!
Once the exit speed is determined, we figure out the acceleration of the marker while it was in the tube. Over 20 g's.
We also figure out how long it took the marker to exit the tube once its motion began. Then we investigate where the marker was when it was at the half way point (in time) along its journey through the tube.
The preso is enhanced with photos and high-speed videos. And an instructive(?) blooper at the end.
I run this demo in AP Physics 1. I don't run it in Physics. Why? Projectiles is not a topic I teach in Physics. We tend to spend more time in kinematics than kinematics is due. It wasn't a big topic in California Science Standards Physics (RIP). It's not that big a deal in AP Physics 1. It's virtually non-existent in NGSS Physics. If you are among the few, the happy few—the band of brothers and sisters—who teach a year-long AP Physics C-Mechanics, have at it!
But physics teachers of all stripes love, embrace, and perhaps cling to our kinematics. Maybe after a decade of NGSS Physics and a generation of retirements, kinematics' star will begin to fade. I have my doubts. Kinematophilia seems to have inordinate inertia. </soapbox>
In any case, we still regard this demo as a classic. [We don't seem to have a universally agreed-upon name for it. Or if we do, I don't know what it is.] So when it came up this year, I spent some time in my empty classroom trying to get some useable high-speed footage.
Here's the student sheet and preso I cobbled together. (The Mythbusters segment is included.) Oh, and where a prediction is called for, Zoom participant reactions are solicited (yes, no, go slower, etc.).
I found the embedded videos in this HTML export to be a bit cantankerous—practice before using in class. Arrow keys to advance. Clicking in a video activates a scrub bar at the bottom and allows you to scrub forward/backward in that video.
Maybe you can get some use out of these; maybe your district won't let you use it. Guns and bullets are discussed, modeled, and used.
If you're not following Frank Noschese (@fnoschese) on Twitter, why even be a physics teacher with a Twitter account?
And if you get useful mileage out of constant velocity buggies (such as these from Arbor Scientific) but wish you had a convenient, reliable way to curb their enthusiasm, Frank tweets this:
These homemade battery spacers are amazing! Better than anything else I've tried (foil, paper clips, etc) to make a slow moving buggy. * One flat-head machine screw (#6-32 x 2")) * Two fender washers (1/8" x 1") * Three #6-32 hex nuts#iteachphysics#modphyspic.twitter.com/r5gCvpSGJw
The long-awaited Motion Playlist of Phyz is now here. Enjoy!
This playlist is long. You might want to break it up into two smaller playlists for better results. Or you could pare it down. You could also add to it; I'm sure I missed a few gems. Please let me know in the comments.
Click the "playlist" label in the column to the right to see the playlists for Waves, Electricity, Magnetism, and Light.
I'm in the middle of my first year teaching AP Physics C and we ended last semester with rotation. Therefore, I'm looking at any spinning or round thing in a different light. I was at the RAFT San Jose store and saw giant wooden circles with rough edges for cheap. And this is RAFT cheap so I think it was <$4 for 8 of them. I snagged them unsure of what I would do with them and took them home to be inspired.
I ended up sanding down the rough edges to find they were very sturdy and furniture grade plywood. Since they were leftover from some manufacturing process they were perfect circles. I decided to make them into giant tops/ turn tables. I envisioned students playing with them at the onset of this unit to observe changes in rotational quantities, maybe use some slow mo video or accelerometers. Or perhaps we could use them for conservation of angular momentum. The possibilities are endless!
I reviewed some geometry and found how to find the center of the circle. I measured equivalent length chords around the circle and marked halfway across each chord. From this halfway point I drew a line perpendicular to the chord towards the center of the circle. Doing this a few times gave me a point, or at least a small area of the "center" of the circle. Since I was drilling a big hole in the middle I figured close was going to be ok.
We have a drill press in our mini-shop in the Physics prep room. I used a 7/8" drill bit to drill a hole in each disk. This allowed me to fit a 1/2" PVC pipe through the hole with a bit of wiggle room. Going down to a 1/2" bit was too small of a hole for the PVC to fit so the hole had to be a bit bigger. But "wiggle room" meant that if I turned the PVC axle the disk wouldn't rotate at the same speed. Hmm...
I used smooth 1/2" PVC endcaps on the bottom of about a foot of 1/2" PVC for my axle. The endcaps had the manufacturers logo on it so they did not have a perfectly smooth bottom. If it bothers me enough I may go back and file them smooth. I found that wrapping the PVC with a bit of masking tape increased the diameter of the pipe enough to fit in the hole in the disk snugly. Through trial and error I found about 3 times around worked well. Too tight and I was banging the axle against the ground hoping the disk's inertia would drive it down onto the tape, sometimes that worked. I put a second end cap on the other end of the axle for comfort.
In the end I had 8 tops for use. By the time I made them it was towards the end of the rotation unit but they were still helpful. When students were reviewing torque, angular momentum, etc. I left them out with their review sheets. Students would grab them to rotate and discuss vector directions with their partners.
I also played with the Physics Toolbox app's accelerometer by placing it on one of them and giving it a few turns. Next year I'd like students to investigate the acceleration recorded by the phone at different radii as they turn it with the same speed. Below is a quick video of the attempt.
I had considered sharpening down dowels to a point as the axles instead. But, I teach high school and a sharpened dowel through the center of this disk might become a spear with a shield so ... no.
I have noticed a big difference in student comprehension when the problems become real to them. Simple visuals can have a big impact on the students "getting it." I can't count the number of times I've tossed a tennis ball around to make a point. Somehow holding the tennis ball at different heights or just tossing it up to catch it again can lead to "Oooh now I see what's happening!" So I have several simple demos that help students visualize their problems, a block or two hanging from the ceiling with spring scales, a stuffed toy in a bucket, etc.
When we studied springs I found a Pasco spring demo set with five springs all of the same length but different spring constants. The first stage was to hang a 20 g mass from the red spring and see it barely settle above the table. I asked students what would happen if I were to hang a 500 g mass then from the green (which they assumed was identical). They were surprised at its shorter elongation and when I asked why they all said "it has a larger spring constant."
For the next stage I set up two large ring stands with another bar clamped horizontally between them. I dramatically assure students it is level with the springs hanging at their relaxed length. Then I hang a 500 g mass from each and they can see the slight differences in elongation. Then the 500 g masses are switched out for 1 kg and the difference between them becomes more pronounced (left). Applying this to Hooke's Law they could all calculate the spring constant for each spring. But this made it way more interesting than five given forces and elongation lengths to calculate the spring constant from a word problem.
When my AP Physics C class started center of mass, many could calculate the center of mass with equations but had a hard time visualizing what that actually meant. A common problem involves materials of different densities stuck together, for example a piece of aluminum and a piece of iron. To make a real life version I found a piece of Styrofoam that was the same thickness as a piece of scrap wood. I drilled three holes in the wood, stuck three dowels into the holes and stuck the dowels into the Styrofoam. I wrapped the whole thing in paper to make it appear uniform but I did tell students it was made of two different materials. I showed it to students and asked what information they would need to solve for the center of mass. Of course I play with them a bit and after each response I say, "Ok, now you can solve it right?" to which they predictably respond, "No, we need XYZ too!" Eventually, I give them the dimensions of the whole thing and let them solve for it. The dimensions are listed on the paper below (the "total mass" includes the paper in case they ask).
They are not surprised that the center of mass is closer to the wood side but they are surprised that for this particular arrangement it's actually on the wood. It's a simple practice problem but once they're done I can balance the piece on my hand at (almost) the exact position they predicted, about 5 cm in from the wood side. Students that struggle with this homework problem were successful with this in-class practice problem.
Another simple one my colleague Jessie Chen shared with me can be done by every student in your class on the cheap. Like less than $1 cheap. Most dollar stores sell packs of cards for $1, or even a double pack if you're lucky. Each student will need one plastic playing card (or index card) folded at a right angle along the length of the card. Place it on the corner of the table with one corner hanging off the edge of the table. Place two pennies on the card so that one is on the portion on the table and one is on the portion hanging off the table. You can use a pen or pencil to press on the card so that when it moves it pivots around that point. Flick the vertical part of the card on the side that is hanging off the table. This causes the card to move so that it is no longer supporting the penny hanging off the table and it will fall straight down due to gravity. On the other side the vertical portion of the card will push forward, applying a horizontal velocity to the penny and making it shoot off the table in a half a parabola shape. You can hear (and see) the two pennies hitting the ground at the same time. Many of us have a fancy machine that demos this for us, sometimes called a "Drop/shot" or a Newton's Second Law machine, and those work great, don't get me wrong. But to be able to hand these to my students and have them try it, nothing can be better than that!
I find myself repeating "Longer time, smaller force," throughout my momentum unit. There are so many examples of safety devices that decrease the force one might experience by increasing the time. Bike helmets, car bumpers, crumple zones, air bags, seat belts, etc. All decrease the force experienced by increasing the time of the collision. The sticking point is always that the impulse is the same regardless. Many of my students incorrectly think that by increasing the time they have somehow managed to decrease the impulse. I remind them that the vehicle is going from 60 mph to 0 mph whether they use their brakes or hit a wall. They also seem to struggle with applying this concept to larger objects .... And what's larger than a jumbo jet?
Awhile back I caught a news segment about an airplane crash in which an Engineered Material Arresting System (EMAS) safely stopped a plane. Apparently pilots overshoot the runway sometimes and, well, its hard to stop something as big as a jumbo jet. This Popular Mechanics article gives a good background: "EMAS is essentially a rectangular bed of 2,000 to 4,000 collapsible cubes glued in place at the end of a runway, nearly level with the ground. As a plane careens into the cubes, the cubes break apart. Friction between the cubes and the plane's wheels ultimately slows the plane to a stop."The article continues to say "The system can safely stop a Boeing 737 traveling at 65 miles per hour in fewer than 300 feet."
Oooh, that sounds like a Physics problem! All you need is the average mass of the airplane and students could calculate the size of the force that EMAS applies to stop the plane. According to the FAA Fact Sheet for EMAS all runways need an extra 1000 feet past the end of the runway for emergencies. I would be careful that students don't confuse stopping "slowly" through 1000 feet with airplanes that often crash roughly at the end of a rough, unmaintained dirt patch that happens to be 1000 feet long. The point of the EMAS is stop in a short distance in a long time, compared to stopping quickly by say hitting a wall or a long rough distance over a long time.
Since there are many different possible stopping situations solving problems about this with students should be accompanied by simple diagrams, maybe even descriptions for each. If you don't want to get into practice problems you can at least show students pictures and videos of airplanes stopping with EMAS.
I plan to bring up this material in my Crash Cushions project (original post here, additional information about leveling here). In my initial tests of the project a few years ago I found that small paper cubes were the most successful in minimizing the force, a similar design to EMAS!
Bringing in real-life examples that students can evaluate and analyze can help them improve their designs which is an aspect of the NGSS Science & Engineering Practices.
Next week I begin my Thermodynamics unit which includes discussing the 0th, 1st and 2nd Laws of Thermodynamics. When I teach the First Law of Thermodynamics, we discuss how it is basically a restatement of the Conservation of Energy. A favorite demo of this is to use large ball bearings that get slammed together on either side of paper. They are often called "colliding spheres" and are a really simple way to show the heat lost in even a simple collision. When you slam the spheres on either side of the paper a small hole is burned into the paper. When I demonstrate this to students I have a volunteer hold a piece of paper straight up vertically and slam the spheres on either side of them several times. It takes students a moment to realize that holes have been made in the paper and then they notice the smell. Only a few holes in the paper is enough to fill the surrounding area with the smell of burning paper. I talk about how hot the paper must have gotten to literally burn at the contact point and that the thermal energy comes from conserving the energy from the initial collision. Dean Baird uses this as an exhibit in his student run Exploratorio, called "Fire Clap."
Even though it seems obvious to me that the burned hole is an example of thermal energy I wanted to show students the collision as viewed through a thermal imaging camera. I tried looking online but I could not finding any such video. I don't own a FLIR camera (yet) but the Exploratorium Museum of San Francisco does! I was there today to help with a Teacher Institute workshop and headed down to the FLIR exhibit with a set of the colliding spheres. Some other teachers and I got some videos:
Our first attempt showed that there was in fact a bit of heat around where the holes were made. You can see the color change around the edge of the hole over time:
While rearranging for another take we noticed that our hands left residual heat lines on the paper so we drew on the paper that way for awhile. Physics teachers are easily distracted by cool stuff. We found that my fingers didn't work well and when everyone held their hands up we saw why. My fingertips showed up black (cold) while everyone else's were white, the same color as the rest of their hands, apparently I have cold hands.
In this video you can see the experiment take place on the right and the projected FLIR video is on the left. Again the holes produced have a bright white that eventually fades to the color of the paper.
At this point we remembered that we were making holes and therefore we could "see" the heat signatures of things behind the holes. We oriented the paper so that a dark color was behind it so that we did not have contrast behind it. A well timed museum visitor passed behind and we can see that the color changes:
Another experiment commonly done with the colliding spheres is to slam them on either side of a piece of foil. This Educational Innovations post explains both aspects of the experiment. When we tried the foil we found that there was no heat seen through the FLIR camera. We could not heat the foil like we did the paper and see the residual lines from our hands.
According to Zeke Kossover of the Exploratorium it is due to the low emissivity of the foil. This FLIR article explains it a bit but basically the foil is so good at reflecting radiation (visible light and heat) that the FLIR camera does not accurately show its temperature. In the picture above the black rectangle on the right and the two spheres in my hand appear black which translates "cold" through the FLIR camera. They are in fact both room temperature or warmer as they have been held for a moment.
So now I have video to show my students that confirms, in more ways than one that thermal energy is produced when the two spheres are slammed together. There's nothing quite as cool as seeing the heat ... *bad dum ching*.
Every year, for as long as I can remember, I've shown a clip from the British show Brainiacthat makes a giant pendulum mirroring the in-class bowling ball demo. My downloaded copy is grainy and pixelated so I decided to try and find a better version. I downloaded one Brainiac episode (Season 1, episode 3) with the intention of editing it down to the 4 minutes or so that I wanted. I ended up watching the whole 40 minute episode and editing out six clips to use in my classroom. Not too shabby for some fun TV time.
Conservation of Energy and a giant pendulum:
Well explained and stands alone well.
Oil Slip & Slide:
Even really slippery surfaces have a coefficient of friction that slows down moving objects. You could have students estimate it using the values given in the clip.
LN2 filled water bottle:
Quick example of pressure, boiling and of course liguid nitrogen.
Does a duck's quack echo?
Sometimes students just won't believe you unless they see it for themselves. Or in this case hear it.
Don't microwave a CD:
#ThingsThatShouldGoWithoutSaying
Playground G forces:
Brainiacs (the volunteers and staff that put on the science of the show) try to get the most G forces possible out of a playground merry-go-round. You could get more but they are limited by human power.
Iron in cereal:
This is an easy demo to do in the classroom but it does take some prep, the right cereal, etc. This is a super short clip that demonstrates it if you don't have the time.
Now I want to watch more of it. Besides the energy pendulum the only other clip I have seen prior to this was another all time favorite, "The Electric Fence." It is pretty much all the things you wish you could do in your classroom but couldn't:
Update: For an exhaustive video demo lesson on the Brainiacs: Electric Fence clip, see this old Blog of Phyz post:
I've written about making simple PVC dart gun shooters and how to use them in the classroom with NGSS. I just did this lab with my Physics students, after their projectile unit test because they did not have to calculate projectiles shot at an angle. It was a way to work in a design challenge with my students while letting them explore angled projectiles.
Students were shown how the shooter works and asked to find the largest horizontal range. They were to record their angle, launch height, etc. and discuss the design changes in between each trial. No additional questions, no conclusions, just a quick and fun experiment about experimental designs.
"Can we stand on the tables Mrs. B?" Sure!
"Can we pull the balloon back all the way?" Sure!
"Can we cut the straw?" Sure!
They just had to record how far it went and how they changed their experimental design.
Seven classes did this lab between my partner teacher and I, usually students worked in partners, spread out across the quad of our campus. We had a running record during the day to see who could in fact make it the farthest. The first few classes hit 38 m, later classes had an unconfirmed 53 m but the largest confirmed was about 45 m. Doing the experiment with so many older students we ran into a few new problems I'd like to warn you about:
Use brand name bullets.
A quick Amazon search brings up lots of refill sets for the small Nerf bullets you need. We opted for a knock-off brand and got 200 bullets for $20. We expected to be set for life as I had previously only broken one Nerf bullet out of 20 with three classes of freshmen testing it last year. We were wrong. Bullets would tear after a single firing, the orange tip would come off upon impact and sometimes even just indentations on the side above the straw was enough to get poor results.
Have extra balloons.
Some of my football players decided to get into a "who can pull the balloon the farthest" contest and frequently broke their balloons. Sometimes it just happened in the course of the experiment. Have lots of extra balloons on hand to repair shooters with duct tape. We tried to use the same size and same thickness balloons for consistency. A few students noticed that the replacement balloon wasn't exactly the same length as before and might change their experiment.
Careful with metric tapes.
I have one 50 meter windup tape, nine 10 meter windup tapes and one trundle wheel. By the end of the day I had to completely unwind the 50 m one in order to rewind it correctly and we were down two 10 m tapes. Students did not understand how far 10 m was and would run out the tape with such vigor they broke the internal spindle of the tape. They can not be wound again, if you shake them you can hear all the broken plastic pieces rattle around the inside of the case.
The trundle wheel was far superior for measuring and was easier to reset in between trials. Although I did have one student hole the trundle wheel at arm's length straight out parallel to the ground and asked how it worked. He kind of sighted along it, maybe he thought it was a laser level??
I use my Arbor Scientific Air-Powered Projectile rocket every year. With my Conceptual Physics students we take the data as a class, determine the average time and use that to calculate the maximum height. With my older Physics students this year I decided to open it up. I told students how the rocket worked and asked them to write their own procedure to find the maximum height and initial velocity. Not surprisingly, groups independently determined that the best way to
determine this information was to time the rocket's entire flight and
then use half that flight time to determine the rest. Once students determined how they were going to test it, we went out to an open space and launched the rocket five times with the "low" washer and five times with the "high" washer. Each group collected their own data for their calculations but then I collected their results for each period.
I noticed during three periods of trials that the rocket launched sooner later on in the day. In the morning the rocket consistently launched after 5 pumps with the "low" washer and 7-8 pumps with the "high" washer. By the afternoon it launched after barely 4 pumps with the "low" and 5-6 with the "high." It was a warm day so temperature definitely played a role. Looking at archived temperature data for our area it was about 82 degrees for the first period's data, 90 degrees for the second and 97 degrees for the third. If you look at the consolidated data for all three periods you can see that the maximum heights and initial velocities decrease as the day went on.
My last period did get a chance to try the "super" washer. Now I wish I had tried it in the morning for comparison when it was (relatively) colder.
There are lots and lots of things you can do with this rocket. There is an additional set of wood angled blocks for consistent angled shots you can purchase.
I decided this year that if I was going to continue to take the time to teach students how to interpret kinematics graphs of motion (displacement-time, velocity-time and acceleration-time graphs) I was going to bring them up more often during the year. As we transition in my class from basic kinematics equations to projectiles I was looking for a lab that did just that. This is where it pays to keep more resources than you currently use in your curriculum. I found a pdf I had downloaded from Vernier using motion detectors and a ball. The lab looked simple enough and I tried to reproduce the results myself.
The original instructions had called for a wire basket to be placed over the motion detector to protect it from the ball's return. I tried this with a tennis ball and found it very difficult to get the tennis ball to go up and down directly above the sensor. After lots of attempts (seriously like 50) I was able to get three sets of data to work with:
I wanted students to see what happened at the max height on both the displacement-time and velocity-time graphs and understand what it meant. I wanted them to identify the time that the ball was still being accelerated upwards by their hand (easier on the velocity-time graph by the way). I wanted students to see a constant slope of the velocity-time graph to remember that gravity is constant. I liked how it was coming out but still wanted to make sure that students had an easier time than I did with this lab.
After tweeting to @VernierST I was able to get a few suggestions that made it basically fool proof:
1. Instead of a small tennis ball use a larger basketball (more reflective surface for the sonar).
2. Instead of a wire basket, which I didn't have enough of anyway, try putting two books on either side of the sensor.
Since my books are shorter I had students put two books on either side of the sensor as it was facing up on the table-top (above a picture from their lab). Students got great results and were able to focus more on analyzing the graphs using the tools in LoggerPro. Below is a sample set with the points I asked students to mark in their lab. Overall the lab was actually pretty quick and reliable. I think I could even move up the timing of the lab in my unit as an introduction to gravity rather than a review. Here is the lab I used.
This is an example of a little idea that grew, changed and evolved and I'm still not done with it.
A colleague asked for some ideas about free fall and I remembered an activity often called Tin Pan Alley; here is a video demonstrating it. Usually done as a demonstration, hex nuts are tied to a piece of string and dropped from a tall height on to a pie pan or other metallic plate. The sound is better on a thicker reusable pie pan than the thinner single-use ones. First students are shown a string with the hex nuts equidistant, say 20 or 30 cm. When the string is dropped the sound of each hex nut hitting the pan gets closer to the next hex nut than the last. A second string has hex nuts that are at specific (increasing) distances so that when it is dropped the sounds are equal times apart.
After suggesting this activity to my colleague I began to think about it more and decided to use it in my own kinematics unit. In what felt like a stroke of brilliance I thought of turning this teacher-led demo into a student run inquiry activity. I wanted to hand students ten hex nuts, a pie pan and some string and ask them to determine the distance of hex nuts that would create even interval sounds through experimentation. In the first draft I dashed off I actually titled it "Free Falling Nuts." After remembering I teach in a high school I realized it needed a new title.
But there was a sticking point, how can students be sure that the sounds are in fact even intervals? I decided to try and implement some technology.
I had downloaded the free Physics Toolbox app a few months ago and started to play with its many functions. Its an awesome app I strongly recommend downloading. There is a sound meter on there that records decibel levels over a time axis. I wanted students to use this free app to capture their hex nut hits so that they could compare the intervals between them. I also had Vernier Microphones and wanted to try using them as well. I wrote the whole thing up but before I decided to do it I thought I should try it. Turned out to be a good thing.
My colleague Matt and I decided to try it out before we gave the task to our students. We calculated the distances required for even time intervals with 0.1 s or 0.2 s, etc. and made a few prepared strings. We found that the sounds were so short that neither the Physics Toolbox sound meter nor the Vernier Microphones could pick up the sounds well enough to determine the time intervals. We tried amplifying the sound on a large stool, tried recording and slowing down the recording, etc. Without a 1:1 classroom we didn't want to rely on video analysis. We were forced to abandon the idea of students determine the distances by sound. And given that we wanted to use this as an introduction activity we didn't want students to calculate the distances between the hex nuts yet.
So I was back to the idea of a teacher-led demo. I decided to ask students to predict, discuss and then explain what they were hearing. I wrote this google slide presentation to guide the activity. The background data for calculating the distances for different time intervals is here, first calculated out by Matt. The larger the equal time interval, the longer the string. I was limited to a few meters given my ceiling height, something to keep in mind.
I want to share all of these with my classes during kinematics! The NY Times posted these great Olympic moments in composite pictures. Often simple motion is modeled for students by showing the object in successive photos in the same image. By comparing the distances between the object over time students can get a sense of how quickly it is moving.
When viewing the page you will scroll down but will actually be moved to the right in order to see their full width. Some of the images like the one above seems to be taken in even intervals of time and would therefore be easier to compare. So how can you use them? Let's take a look:
Christian Taylor's gold winning triple jump:
Notice that Taylor's body makes a parabola while he's in mid air for the long jump. What might be surprising is that there is also a clear parabola in his bounds before his big jump. You can trace over the image along his center of mass and show students the parabola shape. You can also point out Taylor's change in position at the end during his jump and discuss his center of mass.
"On match point in their semifinal, the Brazilian team of Barbara Seixas
and Agatha Bednarczuk ousted Kerri Walsh-Jennings and April Ross of the
United States."
There are great parabolas to be seen in the projectile motion of this volleyball. The volleyballs are closer together at the top of the parabola because it is moving slower and will not travel as far in between each picture.
Derek Drouin's winning high jump:
This image shows Drouin's change in speed as the distance between each changes. There is a great parabola during his high jump and you can see him change the position of his center of mass.
Laurie Hernandez on the balance beam:
I would use this to show students that even when it seems like she's floating on air her center of mass is always supported by a base underneath her. In the first few images show her feet underneath her. The fourth shows Hernandez supported briefly by her hands. As she dismounts you can see a parabolic shape if you follow her center of mass through her flip.
Anytime you can relate what you're studying to the "real world" for your students is a win.
You've probably seen this video of Luke Aikins jumping out of a plane from 25,000 feet without a parachute. Knowing the physics behind it doesn't make it any less impressive:
There are several videos online but I like this one with the height
gauge at the side. This video shows his top speed at 150 mph but this LiveScience post and a few other sources quote a human's terminal
velocity around 120 mph or 53 m/s. Aikins says both 150 mph and 120 mph
in this NPR interview about how they prepared for the jump. Wired also discussed some of the physics behind Aikins' jump, focusing on air resistance and terminal velocity. The net is 100 feet by 100 feet and held 200 feet above the ground by four cranes at each corner. In the interview Aikins refers to the giant net as his parachute, its just below him instead of above him.
Remind students it Aikins were to go from 120 mph to 0 mph by hitting the ground he (probably) isn't surviving. So how can he go through the same change of speed in the net and survive? Hopefully you hear a chorus of students saying that time is a factor and it has been its extended by the net. If you bring up this example in your motion unit your students will probably refer to the acceleration equation. A smaller time value means a larger acceleration (and a larger force); an extended time will produce a smaller acceleration. Students can practice their unit conversions to find Aikins terminal velocity in kilometers per hour or meters per second.
Aikins flips on to his back, so that he can land without snapping his neck, at 2:30 in the video above. I downloaded the video and edited it down to his landing in the net. In this edited version the first contact with the next is seen at 2:24 seconds. As Aikins falls into the net the edges don't stay taught (another talking point) so its tough to call when he comes to a full stop and when the lowering of the net starts. I called it at 4:00 seconds making the time it takes him to stop in the net 1.76 seconds. If students use 53 m/s they will find a decceleration for Aikins of about -30 m/s^2 or about 3g.
With the same information students can calculate Aikins kinetic energy just before he hits the net. All of that kinetic energy is converted to work done on the net and to elastic potential energy of the net. You will have to make some assumptions about Aikins mass and the stretch of the net. The NPR article includes these two pictures of the net before and after Aikins jumps into it, he's the speck in the top of the left side. I set them side by side and drew a line over to show 200 feet about the ground. The perspective will make it difficult to exactly determine the height of Aikins when he stops completely, you can discuss with students how best to do so.
What else can you discuss? Momentum! This is just like a car traveling at high speed that has to be stopped. It can hit a wall in a short time and be destroyed or it can be stopped over a (relatively) long time and suffer minor damage. Again students can calculate Aikins' change in momentum based on the information they find and making a few simple assumptions.
Obviously the experts that helped build it went into a little more detail but its an interesting piece of Physics not beyond basic mechanics principles we teach our students.
