# SS Day 11: Power Output

Monday, 30 June 2014

Summer school kids ran stairs and generally got swol in our school weight room in order to calculate the power output for each of their major muscle groups.

Here’s the lab: How Powerful Are You?

# SS Day 10: Accident Analysis

Friday, 27 May 2014

How heavy is my Jeep?

There are days when stuff goes so well — kids are amped up from an activity, you had fun doing it, and everyone learned something cool. Yeah, today was one of those days. Inspired by Frank’s post on Finding the Mass of My Car Using Newton’s Three Laws, we grabbed some bathroom scales, measuring wheels, and the keys to my Jeep.

Like Frank, we set up on a slight incline to cancel out the effects of friction. I tested several downhills on campus to find one where releasing the brake in neutral kept me stationary, but just barely. We found just the spot on the entrance road to campus.

For fun, the kids helped me take the roof down on the Jeep. We all piled in (6 kids plus me!) and drove very slowly to the front of campus. I let the kids take it from there. They had already brainstormed in the classroom what they needed to do outside. While out there, I took their direction. We were outside for about half an hour.

When we got back to the classroom, I locked them in there jury-duty-style and said to come get me when they agreed on a verdict. They brought me in about 10 minutes later and walked me through the explanation shown below (disclosure: I recopied their work because you know the kid who wrote it had the sloppiest handwriting of all time). Conveniently, we were done just in time for lunch.

Student calculations for the mass of my Jeep. Actual mass according to a website: about 2000 kg.

If you think you want to do this with a regular year class, I recommend recruiting teachers so you have more cars per capita. My class of 6 was perfect for one vehicle. Also, if I were to repeat this, I’d definitely include friction rather than finding a downhill area so I could negate friction. Oh, and for those keeping score at home, the kids’ result was about 30% larger than the actual value.

# SS Day 9: Superman and Sidewalks

Thursday, 26 June 2014

Source: Action Comics 1 (June 1938).

Summer school is an odd beast. Sometimes, I’m all crunched for time. Today, I found an extra hour so we talked about my favorite topic, Superman. I asked the kids if Superman’s tall-building-leaping would crack sidewalks. We didn’t think so but how to prove it? Below is our solution, will you check our physics for us? (This was super-scary to solve with the kids because I haven’t solved the problem before.)

How high can Superman leap? According to Action Comics 1 (June 1938), Superman can leap 1/8 of a mile or about 200 meters in the air [1].

What’s his takeoff speed when jumping 200 m in the air? I’m going to assume Superman isn’t experiencing air resistance, so let’s go with my personal favorite of the kinematics equations, $v_{f}^{2}=v_{i}^{2}+2ad$, knowing that $v_{f}=0 m/s$, $a=-9.8 m/s/s$, and $d = 200 m$. You get $v_{i}=63 m/s$.

When Supes crouches down to leap, he has an initial velocity of 0 m/s and must leave the ground at 63 m/s. What acceleration will he give himself in that time? Well, how long do you want to assume that jumping time is? We went with $t=0.1 s$. The definition of acceleration says that $a=\frac{\Delta v}{\Delta t}$. I get an acceleration of 626 m/s/s.

Now, how about that force we promised to find at the start? We know from Newton’s Second Law that $F_{net} = ma$ and from DC Comics that Superman has a mass of 107 kg [2]. I’ve decided on the following free body diagram, with an upward force that his leg muscles generate and Superman’s weight:

Free body diagram of Superman as he’s jumping.

In addition to Newton’s Second Law, I can sum the forces and eventually solve for the jumping force:

$F_{net}=F_{jump}-F_{g}=ma$

$F_{jump}=ma+mg=m(a+g)$

Using the acceleration from above and solving, $F_{jump} = 66,000 N$.

Is that enough force to break concrete? Concrete breaking strength is quoted as a pressure. 20-40 MPa, to be exact [3]. To find pressure, we need the force and area. Assuming Superman’s jumping off the balls of his feet, they occupy a box about 10cm by 20 cm in size. Using $P=\frac{F}{A}$, I get a pressure applied by Superman’s feet to the sidewalk of 3.3 MPa, or about an order of magnitude smaller than concrete’s breaking strength.

You might take issue with some of my assumptions (perhaps his jumping time is not 0.1s or the area of the balls of his feet isn’t right), but I still think we’ll come in under 20 MPa even if you fiddle with them all.

So, good news for the sidewalks of Metropolis — Superman will not break you.

Your homework (in the style of Rhett Allain’s great superhero physics posts): How high would Superman have to jump down from in order to crack a sidewalk?

[1] Action Comics 1, see picture above.

# SS Day 8: 2D Forces

Wednesday, 25 June 2014

Pictured above, I had the kids set up a case of equilibrium on the force tables, take down the numbers, then prove it mathematically. The first part of this lab is to prove equilibrium then set it up on a force table to check your answer. This lab is great because the results are so intuitive.

2D Forces Lab

# SS Day 7: Friction

Tuesday, 24 June 2014

The kids did a decent job with our coefficient of friction lab today. Given our comfort with Logger Pro, I can’t help but wonder if this would’ve been a better lab with the digital force sensors.

I’d love to add a self-checking or self-motivating factor to this lab. The kids calculate a coefficient of friction and turn in the lab. They have no idea if its right or even reasonable. Maybe next time, they’ll need to use the coefficient of friction they find to predict some testable value.

Stuff I wish could’ve or would’ve gone different: Due to the pace of summer school, I didn’t detail the differences between kinetic and static friction, so kids didn’t realize to look for the static force rather than the dynamic force when pulling. There’s a slight difference that makes for a cool discussion during the regular year. We also didn’t get to chat about how surface area is irrelevant in the friction discussion, which is always a great misconception to bust.

If this were a regular school year, we’d be somewhere in February. No wonder we all feel tired and are looking forward to a break next Friday for July 4th.

# SS Day 6: Getting Newton’s 2nd Law

Monday, 23 June 2014

Pulling a cart at constant force is tough!

Tried something new today, based heavily off of labs from Frank and Kelly, which I understand is important in the unbalanced forces model. You need a motion detector, a dynamics cart, a bunch of masses, a spring scale, and some room to run. The result I liked best was seeing position-time graphs like these kids got. Did you see that? Check it:

We struggled with one detail, however: pulling with constant force. How can I get the kids to consistently pull with a constant force? We were just pulling and watching the spring scale.

This lab still needs some work from me but it was a great start, especially for the fourth Monday of summer school.

# SS Day 5: Rocket Range

Friday, 20 June 2014

Big kids show little how to launch air powered rockets.

Today’s plan: review, test, creamsicles, and air rockets! It was quite hot out today, so everyone was happy to see a group of elementary campers using the field space where we intended to continue launching rockets and gathering data. We ditched a competitive part of our plan in favor of showing little kids how to use the rockets. Yay for summer school academic freedom!