Simple Machine for the win!

Being in California my family takes the drought pretty seriously. We haven't watered our front or back lawn in years. And unfortunately it looks like it. To increase the curb appeal and still keep our water usage low we decide to convert much of our lawn to drought tolerant plants on drip with mulch. As part of the conversion we had to cover 792 square feet with cardboard, overlapping a foot or more at each transition, as a compostable weed block. Even with the start of school I couldn't collect enough cardboard boxes at school to do the job so we ordered a roll of cardboard 6 feet tall and 250 feet long. While it wasn't heavy per se, it was pretty awkward to roll out the 20+ foot lengths I needed.  I had an old diameter wooden closet rod that was over 8 feet long so I shoved that through the middle of the roll and raised it up on two sawhorses.

Since it was above the ground I could easily pull on the end as far as I needed to and the cardboard would roll right off. But then I noticed that the whole roll, well, rolled. In the photo you can see the closet rod was pretty close to the back (right) of the sawhorse. It had started even closer to the front (left). Every few rolls I would have to readjust the rod on the sawhorse and bring it closer to the front. It didn't roll much but every 20 feet or so I would have to adjust it.

That got me thinking. This could be a great example for a Physics class that discusses the Mechanical Advantage of simple machines.  Ask students why the rod rolled, why didn't it roll very much? Usually the "distance in" is the "effort force" which would be the axis in the middle, in this case the closet rod. The "distance out" is the "resistant/ result force" which would be the whole roll acting as a wheel. This may seem backwards for this example since I was moving the wheel and observing the axis roll as a result. Students could calculate the Ideal Mechanical Advantage using the radius of the closet rod (standard 1.25" = 3 cm) and the cardboard "wheel" (2 feet = 30 cm). We would have to assume the machine is 100% to calculate it using distances and not forces.

You could expand the problem for students asking them about the circumference of the closet rod (axis) and how many turns before the rod might fall off the saw horse (assume its 18" wide).