LogoTech

How Big IS A Mountain?

That's a good question to ask if one wants to analyze the physics implications of Jesus' statements here and here.  I tried googling it and got nowhere.  It wasn't until I prayed about it that a picture of Mount Saint Helens before its eruption appeared in my mind.  All accounts state that the northern face was blown out. The flow is estimated here at 3.7 billion cubic yards, and the picture at the site makes it clear that that is not all of the mountain: probably a third of the mass of the top half of the mountain is gone, and the base is still there.  Still, it is a figure that is endorsed, so let's go with that value, which the site says is an estimate derived from looking at the ejecta and not derived from a direct measurement of the mountain itself.  That means that the figures are for crushed and broken rock.

The main problem with using this figure is that people are not used to thinking about the volume of a mountain, but its weight. On the other hand, volume is easier to measure than its weight. To convert from volume to weight, we have to multiply the volume by the density of Saint Helens rock, density being weight per unit volume.

Wikipedia (a source I normally don't quote, but there's no reason to believe this particular page has been hacked) states that Mt. Saint Helens is composed of layers of balsalt and andesite. Here is a site giving the densities of various materials in kilograms per cubic meter. Because the estimate is based on the volume of broken rock, the figure for broken basalt is 1954 kilograms per cubic meter. Solid basalt is 3011 kilograms per cubic meter, and andesite is 2771 kilograms per cubic meter. Let's assume the density loss for broken rock is the same for all kinds of rock in comparison to its unbroken form, and assume a 50/50 mix of basalt and andesite. The density of Mount Saint helens broken rock is therefore (1954/3011) (for density loss) times ((2771+3011)/2) (for average density of 50/50 mix of andesite and balsalt)=1876 kilograms per cubic meter.

Most of my readers are Americans, so I'll have to do some unit conversions.  The first is from cubic meters to cubic yards to handle the change in units for volume, while the second is from kilograms to pounds to handle the change in units for weight.  Google can also detect if a query is for a conversion between units of measure, so it gives a value 0.764554858 cubic meters per cubic yard, and a kilogram is 2.20462262 pounds. 1876 kilograms per cubic meter works out to about 3162 pounds per cubic yard (1876 kg/cubic meter times 2.2 pounds per kilogram times 0.764554858 cubic meters per cubic yard). Multiplying that by 3.7 billion cubic yards gives a value of about 11699 billion pounds, or 5.8 billion tons. (By the way, there are about 3.097 million square yards in a square mile, so the mass that was removed would cover a thousand square miles of land with a layer of rock weighing over 3700 pounds per square yard, or a bit over 420 pounds per square foot!)

Now, 5.8 billion tons is not the weight of the old Mount Saint Helens.  Rather, that's the weight of the blown out part of Mount Saint Helens, which is not the entire mountain. This website has before and after photos of Mount Saint Helens taken from the same location. How much of the mountain is left? A third? A fourth? I very much doubt it was less than a fifth, but I'd be surprised if it was more than a half, so I'd say that a tad less than a third of Mount Saint Helens proper was blown off, so a conservative estimate for this particular mountain (before its explosion) would be about 17.5 billion tons.  Thats 3.5x1013 pounds or 1.59x1013 kilograms.

Ignoring details like air resistance, it would take about 1.1x1018 joules to throw a mountain the size of Mount Saint Helens 10 kilometers if it is thrown at a 45 degree angle from the vertical.  It would hit the ground at about 1300 Kilometers per hour or 800 miles per hour.  The distance figure doubles every time you double the energy and vice versa, but the velocity figure doubles if you quadruple the energy used or the distance to be thrown.  Of course, at some point the promise cannot be fulfilled for technical reasons, such as reaching escape velocity, at which point it could be said that it cannot be set "in yonder place".  The exact figure in joules is left as an exercise for the reader.

A note about that last link: the photo was taken from Johnston Ridge, named after the USGS volcanologist David Johnston, who was the first to notice the actual eruption and radio a message to that effect.

It took 36 seconds for the wall of rock, trees, snow, and water, to travel the five mile distance from the mountain to the ridge.

[[Edit 09/07/2009: I gave this page to a minister who claimed to use quantum physics to justify and motivate faith in some aspects of the doctrines of the word of faith movement.  In reviewing it before giving it to him, I realized the impracticality of actually demonstrating this capability.  If one grants that one can lift a mountain, exactly where could one put it safely?  Dropping it into the ocean would produce a colossal tidal wave.  One has to worry about what would be under the mountain if it is placed back on land.  And the perversity of human nature would deny that anything had been done if the mountain was placed back on land ("Nothing has changed!  See?  It's still where it was!".)

However, while reading John Clowder's "The Ecstacy of Knowing God" and considering his claim of the appearing of jewels from thin air and the appearing of gold foil and oil on the hands of ecstatic preachers, I realized that there is an equivalent method of demonstrating this capability that should have occurred to me as a worker at a nuclear plant: according to Einstein's equation e=mc2, 1.1x1018 joules is the energy equivalent of 12.2 kg.  It should be pointed out that the mass component is independent of that mass' elemental form.  While not as dramatic as moving a mountain, the financial implications of properly chooing the elemental form into which that energy is to be condensed are intriguing...]]