What happens when physics class is fun?

I’ll admit that I don’t have any evidence to back up my belief that a classroom can be fun-filled and learning-filled, especially if the two are temporally associated. We are learning about conservation of momentum and learning to represent it in the form of an IF (Initial-Final) Momentum Bar Chart. When one of my students started to rap one of the problems in Kelly O’Shea‘s Momentum Transfer Model (MTM) packet, I couldn’t get the phrase/rhythm out of my head, so I’ve completed it for her. What was

A 2 kg melon is balanced on your bald uncle’s head. His son, Throckmorton, shoots a 50 g arrow at it with a speed of 30 m/sec. The arrow passes through the melon and emerges with a speed of 18 m/sec. Find the speed of the melon as it flies off the man’s head.


There’s a 2-kg (read: Kay-Gee) melon on your bald uncle’s head.
Cousin Throckmorton’s crossbow looks to shoot him dead,
but his arrows are true and are 50 g (read: Gees)
and will pierce the right melon if his daddy don’t sneeze.
When he pulls the trigger, all the physics lovers scream,
and the arrow’s speed drops from 30 to 18
meters per second!

watermelon balanced on a bald man's head

from the now defunct www.thingsonyourhead.com

Problem: Marble and tube

My family recently visited Moon Marble Company, where my daughter picked up a bunch of marbles.  We’ve been having fun concocting ways to entertain ourselves, one of which was to roll the marbles down a cardboard tube.

The tube is at an angle theta with the floor.

A marble is rolled down a cardboard tube. What can we calculate?

To calculate how far a marble will roll along the floor after being dropped down a tube leaves the comfortable world of school physics and enters the real world of rolling friction on cardboard and carpet.  If the tube is close to vertical, the marble will be going quite fast as it exits the tube but won’t go very far horizontally.  If the tube is close to horizontal, the marble will be going quite slowly as it exits the tube.  Our intuition tells us that neither will work as well as somewhere in the middle, so we can search for the angle \theta that maximizes the horizontal distance of the marble along the floor.  This is a case for which the rolling resistances in the tube and on the floor will partly “cancel”, and my daughter’s play tests show that we can get pretty good results just by tracking the proportionality of the velocity to a function of the angle \theta.

What physics models do you have to use to solve this problem?