Sample Data & Graph
SLOW Free Fall; One of the toughest things to get across to my fizzix kids is the idea that ALL objects fall at the same rate in the absence of air! This is probably because they simply can't SEE it. The ole "penny & feather" apparatus is cute, but I don't usually like "cute" and the kids usually don't drop feathers. They drop books, T!-83 calculators, and classes, but no feathers. So, I do this as a "teacher-guided" lab activity. I do all the work, they get all the answers. You can do this as a real class lab also, but be forewarned of the mess the kids will make is tremendous and long-lasting. Here's the deal:
1.
Obtain a large beaker; a 500 mL beaker would do or a clear jar with screw-yop lid. Fill it
with CLEAR syrup. I found that Karo works very well. Now, select two identical size, but very different mass metal balls. I use one lead and one aluminum standard 5cm diameter
ball. I have the kids guess (hypothesize) what will happen if I dropped the
balls in the syrup. Almost invariably, they will guess right. Drop them
simultaneously and at the same time into the syrup.
(I accomplish this by already having the balls IN the syrup and just turning the jar upsidedown.) Have the kids observe and
record what happens. They will notice the lead ball sinks faster than the Al
ball. No great surprise here because heavy things fall faster, right? However, this is FIZZIX, DagNabbit! So, we actually TIME the falls. If doing this as a demo, have half the class time the lead and the other half time the aluminum. Average times are accepted as the real data.
Now,
here's where it gets messy. Dump 1/4 of the syrup out
(back into bottles for future NON-EDIBLE uses) and add a like amount of water
to thin the syrup. Repeat. This gives a 3/4 density. Repeat the falls. The kids will notice that the Pb still falls faster,
but the Al ball isn't quite as far behind at the end. It seemed to fall at a
rate closer to the Pb's rate. Now, repeat again with thinner syrup as many
times as you like. The thinner the syrup, the less difference in the falling
rate is noticed. Now, have kids take this progression to it's limit : What will
happen if you drop these balls in a "syrup" that is so thin, it
offers NO RESISTANCE - sorta like a vacuum, eh? Most kids will see the limit of the
progression as the two falling with NO difference between them.
If your kids can handle math data tables and graphing, have them graph the density vs "time difference". Use the y-axis as the 'relative' Density; starting with D=1, then D=3/4, D=9/16 (3/4-3/16=9/19), D=27/64... and the x-axis is the DIFFERENCE in time between the lead and aluminum ball's falls. The graph will end up looking a little like a backwards half-life graph. (Although, a good arguement can be made that it is a linear relationship since the curvature is 'minor' and hard to note without VERY careful measurements.) The kids can visually take this graph out to it's infinite progression and see that at D=0 (a vacuum) the graph will touch the x-axis indicating a ZERO time difference.
It seems to
work well.