# How To Find Height Of Volcanoes

Several volcanoes have been observed erupting on the surface of Jupiter's closest moon, Io.?

The acceleration of gravity near the surface of Io can be computed from Newton's Law of Gravity:

g = G M / r^2

where G is the Newton gravity constant, M the mass of Io, and r the radius of Io.

You can also find g from kinematics using the information given.

2 g h = v^2 - vo^2

g = acceleration of gravity near the surface of Io (unknown)
h = height reached by ejected material (given)
v = final velocity of the ejected material (zero)
vo = initial velocity of ejected material (given)

So solve for g, then use Newton's Law of Gravity to find the mass of Io.

How high can a volcano get?

Pretty high that’s a lot of smoke

How does magma get all the way to the surface to form a volcano?

Magma forms in the lower crust and upper mantle no deeper than 200km. It lives in a state where the surrounding environment is more structured and stable, whereas it is a free flowing, fluid like substance. This is mainly due to the addition of heat and pressure to an area which then melts the pre-existing rock. Once the magma is formed it develops into a magma chamber or a plume with a hot spot. At this point they can take different paths. With a magma chamber, which is traditionally where magma extruding from a volcano comes from, there is plate tectonic influences. Generally there is a subduction plate, most likely oceanic, that sinks below the heavier continental plate causing the magma to rise.So this picture represents the continental plate overriding the oceanic plate. It then interferes with the magma chamber. Thus finally causing the magma to extrude from the volcanic arc.As for those hot spots and magma plumes, they account for 5% of the volcanic activity.Hawaii is an example as well as the super volcano under Yellowstone National Park. These volcanoes are products of Magma Plumes forming. Magma Plumes are essentially a growing pocket of magma that then melt their surrounding rock causing them to grow in size. They then form a hot spot which is a vertical expansion of magma toward the surface. The magma begins to “gently flow” onto the surface which cools rapidly and forms new land. However with Yellowstone, in the past it’s produced massive eruptions from the huge pressure build up and if it were to erupt today it could kill 90,000 people while also producing a mini ice age.

Why are the mountains and volcanoes on Mars so much taller than those on Earth?

Several things contribute to Mars’s huge volcanic peaks. Mercury does not have them, and it’s smaller than Earth, too. Venus’s are smaller than Earth’s, but Venus is lighter and should have higher volcanoes.So what gives?Lower gravity allows volcanoes to grow higher - IF you have them.Mars is large enough to have had volcanoes in its past (though it does not have active volcanoes now).Weathering is very low on Mars, so large volcanoes stay large.Mars probably didn’t have any (or much) plate tectonics in its past. This means that heat from the interior had only a few places to escape from (hot spots) rather than all sorts of places to leak out (like the Ring of Fire).Combine all of this together, and you get a small number of huge eruptions on a low gravity planet with very little weathering.Voila - Olympus Mons.

How do hot spot volcanoes and convergence zone volcanoes differ?

Any kind of volcano is a consequence, and is not causative. They cannot generate without “magmatic support” from somewhere below. The primary lava / magma feed method also has distinct chemical signatures, as mentioned in the sections below.Hot spot volcanosHot spot volcanos can form anywhere a mantle plume / hot spot occurs, and they will remain active for as long as the plume is active. Case in point: the Hawaiian Island chain of volcano islands. The hot spot is currently under Hawaii Island, which is the “home” of five volcanos, two of which are still active, Mauna Loa and Kilauea. As the Pacific plate moves with respect to the hot spot, the volcanos that were “active” now fade and the “next new one” takes over. There is also a new Hawaiian Island forming to the south of Hawaii Island, and it is called Lo’ihi. It’s summit has not yet risen above sea level.The hot spot under Hawaii has been persistent over millions of years. Mauna Loa itself took approximately one million years to build from the ocean floor to the height of 13,800 feet above sea level. Please note that Mauna Loa is 33,000 higher than the seafloor, and, since the weight of Mauna Loa has depressed the seafloor, it stands 56,000 feet above its base. Typically hot spot volcanos have a high mafic / basalt magma, which is very similar in chemical composition to the mantle itself.Convergent volcanosConvergent zone volcanos are built as seafloor dives under a continental plate boundary. As the one plate dives under the other, the diving edge travels into the deep lithosphere and sometimes into the athenosphere. As it dives it heats up and melts which provides the magmatic support for volcanos along the edge of surviving plate (normally continental, but not always). Where the melted magma rises up it also melts the rocks it encounters in the continental plate, and produces a more felsic magma. Felsic magmas contain a lot of entrained gases, and give rise to a more explosive eruption, as well as a stratovolcano cone (layered with cinders and lava (as an example)). The amount of magma is proportional to the subduction amount of plate as it moves and melts. Active movement yields (in its own timescale) magma to support eruptions. More than not, convergent volcanos have eruptive periods, with perhaps long pauses in their activity, especially if the plates have been locked together (neither can move and the pressure is building).This is a brief synopsis of the two different types you asked about.

What are volcanic mountains? How do they form?

All volcanoes are formed when magma from below infiltrates into the upper layers of the crust.You get different kinds of volcano depending on the magma type and the crust type (and these are inseparable from one another under normal circumstances).With “mafic” magmas, those that are dark and have relatively low silica content and hence high melting points, you tend to get very low, wide, gently-sloping volcanoes that aren’t even recognizable as mountains most of the time. This is because mafic magma (technically mafic lava once it hits the surface) is extremely hot and inviscid, so it flows a long way before cooling down. This is the sort of eruption you usually see in Hawaii-type volcanoes, and the end result is basalt. You get these in basaltic crust, which mostly means oceanic crust, though there is a such thing as a “large igneous province” in which massive, continuous eruptions of mafic magma flood areas hundreds of square kilometers in size on land.The other type of magma is “felsic.” This is your sticky, viscous, high-silica type that’s prone to violent explosions because of its trapped gas content. This stuff is what builds your classic cone-shaped volcano. You find it under continents because continental crust tends to be made of more silica-rich minerals than oceanic crust. It doesn’t flow as far or as fast as mafic lava, so it tends to accumulate in mountains.

Volcanic Lava Fountains (Derivatives)?

It's funny, I'm in the Big Island of Hawaii for the summer and I just hiked along the Kilauea Iki (now dormant) a few days ago.

v0 is supposed to be a constant.
It is the exit velocity you are looking for, and you can assume it stays constant if the height of the fountain doesnot change.
The derivative is ds/dt = v0 - 32 * t, as you found out yourself.

Now let's go back to the physics : the lava reaches the apex of the fountain when its velocity is null. That gives you a relation between v0 and ta, time after which the lava reaches the apex :
ds/dt = 0 = v0 - 32*ta (1)
And you also have data about the ultimate height of the fountain, given by :
ha = v0*ta - 16*ta^2 = 1900 ft (2)

With these two equations, you can solve for v0 (and ta) :
(1) => v0 = 32*ta => ta = v0/32
(2) => v0*ta - 16*ta*ta = 1900
By replacing ta you find :
1/32*v0^2 - 1/64*v0^2 = 1900
v0^2 = 1900 * 64
Assuming gravity on Earth is 9.81 meters per second squared and using the equation:$v^2-v_0^2 = 2a\Delta y$,it is clear that the answer is simply the inverse ratio of the two accelerations, i.e.$\frac{9.81}{3.71}H = 2.64H$  Note that on Mars, the actual height would be higher than this because the atmosphere on Mars is much thinner than Earth's.