# Tutor profile: Ari M.

## Questions

### Subject: Earth Science

What are the main factors that determine the style of a volcanic eruption? In specific, what are the magmatic conditions that precipitate a highly explosive Plinian eruption?

Volcanic eruptions are largely controlled by the buildup of pressure in the magma chamber beneath the surface. Different magmas have different chemical compositions, which affect the physical properties of that magma. For instance, felsic magmas are much more silica-rich than mafic magmas, and therefore have a higher viscosity, or resistance to flow. The buildup of pressure in a magma chamber is mostly controlled by the amount of gas that is trapped by the magma itself. Usually, magmas will have some amount of dissolved gas that will exsolve into small bubbles as the magma moves up towards the surface. If the magma is thin and less viscous, these bubbles will be able to migrate upwards through the magma and escape into the atmosphere. This process alleviates the built-up pressure in the magma chamber, and if an eruption occurs, it will usually be small. Highly explosive Plinian eruptions typically occur in felsic magma, where the gas has been trapped because the bubbles cannot rise through the viscous magma above them. These bubbles continue to exsolve and build up pressure inside the magma chamber until a critical point is reached and the magma chamber ruptures, allowing the gas to quickly move upwards into the atmosphere while carrying hot magma and ash along with it.

### Subject: Calculus

If f'(a) exists, lim[f(x)] as x-->a (a) exists, but there is not enough information available to determine the limit (b) f(a) (c) f'(a) (d) may not exist

(b) The limit will be equal to f(a). The definition of a limit is the value that a function approaches as its input (x) approaches another value. In this case, the question doesn't give us any specific numbers to work with. However, the fact that a derivative f'(a) of the function f(x) exists at x = a tells us that the function is continuous at that point, and therefore the limit of the function at x = a will simply be the value of the function there, f(a).

### Subject: Physics

Do heavier objects fall more quickly than lighter objects?

No, in theory all objects will fall at the same rate on Earth. In this case, acceleration (a) measures the rate at which an object will fall. The acceleration due to gravity on Earth is the same for any object, that is approximately a = 9.8 m/s^2. However, the force (F) of gravity will be different depending on an object's mass (m), because force is equal to mass (m) times acceleration, or F = m*a. Thus, while heavier objects will have a greater force due to gravity than lighter objects, they will both fall at the same rate. To illustrate the concept, imagine dropping a bowling ball and a tennis ball off a balcony onto some pavement. Which one is more likely to crack the pavement? The bowling ball, of course, because it is heavier and carries more force than the tennis ball. However, if dropped at the same time, both balls will hit the ground at the same time.

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