For one of my other classes, we are studying the eruptive styles and general characteristics of volcanoes, specifically five in Southern Chile. I realized while looking them up that pretty simple physics could be applied to the eruptions. During the more explosive eruptions, material expelled from the volcano basically acts as a projectile, going straight up until the negative acceleration due to gravity causes it to stop its upward direction of motion. Since the height of the column of ash is usually recorded as an indicator of the explosivity, I decided to use this to determine the initial speed that the ash must be going as it passes the top rim of the volcano.
On April 5th, 2009, there was a relatively small eruption that created a column that reached 600 meters. Since we know the height, acceleration (due to gravity) and final speed, we can calculate a rough estimate for the initial speed of the erupted material (ignoring buoyancy from the heat that would increase the height reached and air resistance) using the equation:
vf 2= vo2 + 2aΔx
(0 m/s)2 = v02 + 2(-9.8 m/s)(600 m)
v0 = 108 m/s
And that’s from a small eruption. Some eruptions can cause columns that are around 40 km high. So, fun PSA, this is why you really shouldn’t be near volcanoes while they’re erupting. They can cause a fairly alarming amount of damage. You’d think it’s common knowledge, but it’s really not. People still climb erupting volcanoes all the time in unregulated areas.
Nevado del Ruiz eruption column, November 13th, 1985
I also thought it might be interesting to see how much work an eruption does to make the ash go so high. I couldn’t actually find the amount of erupted material for that eruption, but for a volcano in the same subduction zone, Nevado Del Ruiz (in Colombia), with a 35 km column, the erupted mass was 7.0 x 108 kg. (This was an incredibly destructive eruption, by the way.)
W = mgh
W = (7.0 x 108 kg)(9.8 m/s2)(3500m)
W = 2.4 x 1013 J
Which is, unsurprisingly, quite a large amount of energy.