Lab 2

Name: Lab #2: Isostasy A) Purpose of the assignment: This lab is meant to get you familiarized with the concept of isostasy, which is invoked to explain how different topographic heights can exist at the surface of the Earth. It is the principle of buoyancy in which an object immersed in a fluid is buoyed with a force equal to the weight of the displaced fluid. Isostasy can be observed if the lithosphere exerts stress on the weaker asthenosphere that flows laterally over geological time such that the load is accommodated by height adjustments. Using the example of an iceberg floating in water that most of you know about, you will then apply the concept to a continent and will able to determine the altitude of a continent knowing the thickness of the continental crust. B) Learning objectives and skills • carefully read instructions • apply basic mathematical skills • provide clear explanation of reasoning and method used • compare your results with what you know about the altitude of continents C) Task: Alfred Wegener argued that the theory that land bridges had once connected the continents and had since sunk into the sea as Earth cooled and compacted was impossible. He compared the continents to icebergs, which equilibrate to float at a given position in the water column. Let’s consider this: Floating iceberg at equilibrium Elevated iceberg (wants to sink) Depressed iceberg (wants to rise) The ice above sea level pushes down just as much as the buoyant ice below sea level pushes up. The push downwards from ice above sea level exceeds the buoyant push upwards from the ice below sea level. The buoyant push upwards from the ice below sea-level exceeds the push downwards from the ice above sea level.

The iceberg is pushed down by the force of gravity. But what pushes it up? Clearly, there is no vertical push happening on its sides, so it must all come from a push on the bottom of the iceberg – the buoyant force exerted by the water. How large is this force? Consider the pressure at points A and B in the figure to the right. The pressure acting at A, which we will call P A , is a result of the weight of the water above it and is given by: P A = d w × H × g (pressure upwards) [1] Where d w is the density of water, H is the depth of the column of water above point A, and g is the gravitational acceleration (9.81 m/s 2 ). Consider an iceberg of total height H + h that has a height h above sea level. The push downward due to the iceberg’s weight creates a pressure at point B ( P B ) that is equal to P B = d ice × ( H + h ) × g (down-directed pressure), [2] where d ice is the density of the ice. If the pressure upwards exceeds the pressure downwards, the iceberg is pushed up. It will be at rest when the two pressures equal one another (i.e., P A = P B ). Using Equations [1] and [2], this can be written as: d w × H × g = d ice × ( H + h ) × g. [3] Removing g on each side of the equation [3], we obtain d w × H = d ice × ( H + h ). [4] Equation [4] says that at the depth of the bottom of the iceberg, the weight of the ice (of height H + h ) equals the weight of the water (of height H ). The density of liquid water is 1,000 kg/m 3 . The density of ice is 900 kg/m 3 .