Date: Thu, 12 Apr 2001
From: allen.robe@uwlax.edu
Subject: Re: Pennies in cans

I have used the "Pop Can Solar System" described below in teacher workshops. It's from 'Look to the Sky' by Jerry DeBruin (Good Apple Inc., 1988).

He suggests using plaster of Paris to put in the cans. He also warns not to put the stuff in a sink as it will clog the drain.

Fill the Jupiter can and measure its mass after the stuff hardens. Then multiply this by .395 for the Earth, .063 for the Moon, .150 for Mercury, .359 for Venus, .150 for Mars, .420 for Saturn, .364 for Uranus, .466 for Neptune, and .019 for Pluto (you could even use an empty canfor it).

I adapted the "pennies in cans" SPICA activity into a Physics lab after I fell in love with the demo at the Utah IPS meeting in 1992. I like the (recent) idea on DOME-L about using the plaster-of-Paris; it would allow a more continuous tracking of can-masses, but I'd be wary of water evaporation during drying, and shaking cans of pennies sounds intrigues the kids (I tell them that a teacher can't afford to put nickels, dimes or quarters into the cans).

For all age levels, they also seem intrigued that they can "feel" what the can would weigh on the different planets. (We have lots of discussions on the difference between mass and weight.) Penny-weights have varied over time due to specific metal content, so I just calculate the mass of pennies needed per can and adjust the mass with bits of paper thrown in. Then I seal the top with masking tape, whose weight also has to be accounted for.

Be careful about whether you want the gravitational mass of the can or the gravitational PLUS centripetal/ centrifugal weight of the can because each planet is spinning. (I don't account for that in my lab just because it's harder for the kids to calculate, but you may want to account for it if you want to accurately portray the weight of the can on a planet.)

Also, the minimum mass can is Pluto, and for an accurate lab, you have to account for that -- the can is "not just the pennies." A can is typically 15 grams, and that pushes Jupiter over the top in what can be measured on two triple-beam balances (details below).

The activity surrounds giving different groups a set of 10 cans (planets plus our Moon) and two triple-beam balances (initially with me saying, "Use two balances; it will speed up your measurements"), knowing full well that they can mass only half the cans using ONE balance. I ask them which can belongs to which world. A meter stick placed slyly on their lab table eventually allows them to couple two balances together, but then (1) they have to remember to subtract the mass of the ruler and (2) they end up with coupled-oscillators: they have to adjust the mass readings one scale at a time, iteratively getting closer.

It's a challenging exercise because they also have to determine the relative weights of the cans on different planets by using Newton's Law of Gravitation. It usually takes two class periods, and the different groups are labeled by their cans: Diet Pepsi - no caffeine, Regular Coca-Cola, Hansen's drinks, etc.

One problem is that, over the years, our knowledge of how much surface gravity each planet has has varied, and some planets (like Mercury and Mars) are very close. But accurately measured labs still allow discrimination of the two.

--- Steve >>>>
Westridge School, Pasadena Griffith Observatory, Los Angeles

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