My colleague is obsessed with ninjas in the same way I’m obsessed with superheroes. Whenever she gives her kids a challenging problem, she calls it a Ninja Problem. Students who gain ninja status in her class basically earn bragging rights. My first Ninja Problem went like this: “Is it possible to knock the goalie back into the net with a hockey puck? If no, what would it take?” (Hint: you can do most of the work using conservation of momentum.) Mad props to xkcd what-if for the inspiration.

H’s Hockey Puck Analysis

My student, H. took this Ninja Problem on with a vengeance.

After about 24 hours of thinking time, I shared a video with him that a Twitter pal shared with me. Fun and inspiration ensued.

Here’s his response:

Whoa! That’s crazy. I figured out that in order for a hockey player weighing 151 lbs (126 lbs for average 15 year old and 25 pounds roughly for average hockey gear (68.4924479 kg)) to be pushed .5 meters into a hockey goal in one second, a hockey puck must be launched at the average of the average velocity of a hockey puck (80-90 mph which I chose 85 mph (37.9984 m/s)) and after I calculated the volume of the hockey puck and its required mass, I found that the hockey puck must weigh 4.05729254 grams per cm^3 or .469969705 kg [ed: which is about 5 times heavier than a typical puck]. This means that it closer to Krypton and between Krypton and Yytrium. And in that video I think that guy was moving a little more than .5 meters per second haha. Thanks!

And 5 minutes later:

Whoops I have made a mistake! I multiplied took half of something while multiplying the other side by 2. The real answer is a hockey puck is needed to be made out of samarium or iron.

We talked through the effect of the goalie bracing against the ice (which H ultimately discarded because he didn’t know how to calculate for it), which made me wonder if he’d read the xkcd what-if answer. He hadn’t! When you get rid of bracing, it becomes much simpler to push the goalie back into the net.

N, K, and J’s Solution

This group of students, who elected one to be the star of the video, did a great job of separating the realistic scenario (which they quickly dismissed as implausible) from the hypothetical.

Implications for Physics Teaching

Mythbusters has made asking “what would it take?” fairly normal. A lot of my students understand the general approach of “ok, this thing is impossible as we’ve constrained it, so how could we reframe the situation so it’s plausible?” xkcd’s what-if extends on that. In fact, the hockey puck answer starts off with this gem:

This can’t really happen.

It’s not just a problem of hitting it hard enough. This blog isn’t concerned with that kind of limitation. Humans with sticks can’t make a puck go much faster than about 50 meters per second, so we’ll assume this puck is launched by a hockey robot or an electric sled or a hypersonic light gas gun.

Because high school physics often includes oversimplification to the point of absurdity, the “what would it take?” mechanism helps kids latch on to real problems in meaningful ways.

Points going forward:

1. Teach the kids estimation & rounding skills back-of-the envelope calculations, which don’t require such precision.
2. Find or write more of these questions!
3. Figure out how to engage more kids with Ninja Problems. This problem seriously engaged 5% of my students. I’d be thrilled if the number were closer to 20%. In Doing Whatever a Spider Can, I promised to get kids describing their assumptions more regularly. So far, I haven’t. Ninja Problems may be a nice way to engage kids in this process.

[Earlier this week, Tina asked me my blog's name. Truth is, I never named it. Sure, I bought a domain but I never got around to branding the blog with the same name. So, what's up with the domain name? Kalamity Kat was my grandfather's WWII aircraft, a PBY-5A Catalina flying boat. He and his crew were shot down while rescuing downed fighter pilots out of Tokyo Bay.]

Physics class. The topic is forces and my kids were struggling to solve problems like this:

A student of mass 63.1 kg decides to test Newton’s laws of motion by standing on a bathroom scale placed on the floor of an elevator. Assume that the scale reads in newtons. Determine the scale reading when the elevator is accelerating upward at 0.7 m/s2.

or this:

A basketball with a mass of 0.4 kg is being pushed across a gym floor with a horizontal force of 2.2 Newtons. The coefficient of kinetic friction between the basketball and the floor is 0.2. What is the acceleration of the ball?

Struggling, that is, until I hit upon a way to organize their thinking with a “force table”.

Students fill in the table like it’s a Sudoku puzzle. I think the hardest part now is getting the free body diagram correct. Ooh, just to be sure they know what’s up, I’ve been stressing the importance of completing the last column with justifications.

I like to imagine that all the physics teachers out there trained in physics education went to grad school classes with titles like “How to Teach Kinematics” and “Methods for Helping Kids Who Suck at Math”. In these imaginary courses, y’all received the keys to helping kids past the hurdles of difficult math or “there’s no formula for this, it’s a problem-solving process”. Wait. What? You didn’t have these classes? Then how the heck do you help kids problem-solve? Please share your own organization routines, I’d like to learn from you.

a scientific paper on the most unscientific of topics

Do you remember this scene from Spider-Man 2 (2004)? A NYC subway train hurtles toward imminent doom, unless Spidey can stop it. Is it plausible for spider silk to stop a moving subway train?

Suppose a man bitten by a genetically enhanced (or irradiated, depending on the origin you like better) spider can acquire the strengths of a spider proportional to his size. Next, suppose the scene depicted in a popular Hollywood film can give you some clues about the physics scenario afoot. Do that and you have ”Doing whatever a spider can” by M Bryan, J Forster, and A Stone.  The paper was published 31 Oct 2012 in University of Leicester’s Journal of Physics Special Topics Journal. This stuff is golden¹:

Here’s a top view from the movie:

I want to teach my own students to describe their assumptions as well as these students(?) did in building their model². What’s a good way to go about doing that work?

• Demonstrate it in my own work? Build my own examples and walk through my assumptions.
• Learn from pros? By getting kids reading papers like this one, even if we stop after the model parameters section.
• Practice it? Have the kids analyze situations within their own level of physics. This I’ve tried and found to be incredibly painful. I’m willing, here and in public on my blog to commit to having my kids practice assumption-describing daily for 3 weeks. I’ll report back with results.

h/t to Leah Kazantzis, with whom I have the pleasure of teaching!

¹ What’s that you say? You don’t teach physics using superhero examples? Oh, you’re missing out.
² Enough of my friends teach using Modeling Physics that I expect to hear that idea thrown out here. That’s ok, but I’m looking for other stuff, too.