That rock

Here's an example of a mid-level (~3 points) lab/HW writeup. A 5-pointer will go into much more detail.

On the Mass of That Rock

by: John A. Johnson

Abstract


I can't remember numbers very well, but I like to calculate stuff. Here's an example of how using street fighting mathematics can help people with poor memories make order-of-magnitude calculations.


Introduction

Hey, how much does that rock weigh (see Figure 1)? Let's figure it out on the way to lunch at Chandler.

Figure 1: A rock

Solution

Well, we know the density of the rock will be comparable to the average density of the Earth. The density of the Earth depends on the mass and radius of the Earth. I used to have both of these quantities memorized, but the process of learning all the Ay20 students' names forced these constants out of my cache.

From my most recent frequent flyer statement I know that the distance from LA to NY is about 3000 miles, which is 4800 km =~ 5e8 cm. There are about ~5 United Stateses around the globe (maybe 6), and this distance divided by 2pi =~ 6 is the radius of the Earth, or R =~ 5e8 cm.

The acceleration of an object dropped near the surface of the Earth is about 10 m/s^2 or 1000 cm/s^2 (I can remember 10!).

The density is the mass divided by the volume, or ~7 g/cc. That rock is about a meter cubed, or 10^6 cc, so it must contain 7 million grams, or 7 metric tons. That's a lotta rock!

Epilogue

It turns out that the average density of the Earth is more like 5.5 g/cc, and the density of the rock in Figure 1 is likely less than this average value, unless it's solid lead or some such. This table gives the density of various materials in kg/cc. Most surface rock is around 2.5-3.0 g/cc, so I'm off by a factor of 3. Which means I'm dead-on to an order of magnitude!

Acknowledgements

I extend my gratitude the lady with the stroller (not pictured) for jumping out of the way just before I snapped this picture.