1. Structural Geology Basics We need to review fundamental information about physical properties and their units. We need to review fundamental information about physical properties and their units.

2. Exponents a m a n = a m+n a m /a n = a m-n (a m ) n = a mn (ab) m = a m b m (a/b) m = a m /b m a -n = 1/a n Suppose m and n are rational numbers

3. Logarithms Logarithms (Logs) are just exponents if b y = x then y = log b x

4. Scalars and Vectors A scalar is a quantity with a size, for example mass or length A vector has a size (magnitude) and a direction. http://www.engineeringtoolbox.com/average-velocity-d_1392.html

5. Velocity Velocity is the rate and direction of change in position of an object. For example, at the beginning of the Winter Break, our car had an average speed of 61.39 miles per hour, and a direction, South. The combination of these two properties, speed and direction, forms the vector quantity Velocity http://www.engineeringtoolbox.com/average-velocity-d_1392.html

6. Vector Components Vectors can be broken down into components For example in two dimensions, we can define two mutually perpendicular axes in convenient directions, and then calculate the magnitude in each direction Vectors can be added The brown vector plus the blue vector equals the green vector

7. Vectors 2: Acceleration. Acceleration is the change in Velocity during some small time interval. Notice that either speed or direction, or both, may change. For example, falling objects are accelerated by gravitational attraction, g. In English units, the speed of falling objects increases by about g = 32.2 feet/second every second, written g = 32.2 ft/sec 2

8. SI Units: Kilogram, meter, second Most scientists and engineers try to avoid English units, preferring instead SI units. For example, in SI units, the speed of falling objects increases by about 9.81 meters/second every second, written g = 9.81 m/sec 2 In geology, both english and SI units are used. We must learn to use both. http://en.wikipedia.org/wiki/International_System_of_Units Système international d'unités pron dooneetay

9. What’s in it for me? Petroleum Geologists trained in Structural Geology and Stratigraphy make more money than other Geology job centers. http://jobs.bhpbilliton.com/jobDetails.asp The mining industry also employs many Structural Geologists, e.g. http://www.na.srk.com/en/page/na-geology-resource- jobshttp://www.na.srk.com/en/page/na-geology-resource- jobs

10. Data and Conversion Factors In your work as a geologist, you will be scrounging for data from many sources. It won’t always be in the units you want. We convert from one unit to another by using conversion factors. Conversion Factors involve multiplication by one, so nothing changes. 1 foot = 12 inches so 1 foot = 1 12 “

11. Example Rock is flowing at a velocity of 3 x 10 -14 meters per second at a depth of 35km. What is this speed in feet per second? Steps: (1) write down the value you have, then (2) select a conversion factor and write it as a fraction so the unit you want to get rid of is on the opposite side, and cancel. Then calculate. (1) (2) 3 x 10 -14 meters x 3.281 feet = 9.843 x 10 -14 feet second meter second

12. Momentum (plural: momenta) Momentum (p) is the product of velocity and mass, p = mv In a collision between two particles, for example, the total momentum is conserved. Ex: two particles collide and m 1 = m 2, one with initial speed v 1, the other at rest v 2 = 0, m 1 v 1 + m 2 v 2 = constant

13. Force Force is the change in momentum with respect to time. A normal speeds, Force is the product of Mass (kilograms) and Acceleration (meters/sec 2 ), so Force F = ma So Force must have SI units of kg. m sec 2 1 kg. m is called a Newton (N) sec 2

14. Statics If all forces and Torques are balanced, an object doesn’t move, and is said to be static Discussion Torques, See-saw Reference frames F=2 F=1 -1 0 +2 F=3

15. Pressure = Stress Pressure is Force per unit Area So Pressure must have units of kg. m sec 2 m 2 1 kg. m is called a Pascal (Pa) sec 2 m 2 For solid-solid systems, Pressure is called “stress” Pressure (stress) = density x gravity x depth  ρgz

16. Density Density is the mass contained in a unit volume Thus density must have SI units kg/m 3 The symbol for density is  pronounced “rho” Very important  is not a p, it is an r It is NOT the same as pressure

17. Chaining Conversion Factors  Suppose you need the density of water in kg/m 3. You may recall that 1 cubic centimeter (cm 3 ) of water has a mass of 1 gram.  1 gram water x (100 cm) 3 x 1 kilogram = 1000 kg / m 3  (centimeter) 3 (1 meter) 3 1000 grams  water = 1000 kg / m 3 Don’t forget to cube the 100

18. Energy Energy is the ability to do work, and work and energy have the same units Work is the product of Force times distance, W = Fd 1 kg. m 2 is called a N. m or Joule (J) sec 2 Energy in an isolated system is conserved KE + PE + P/v + Heat = constant N. m is pronounced Newton meter, Joule sounds like Jewel. KE is Kinetic Energy, PE is Potential Energy, P/v is Pressure, v is unit volume An isolated system, as contrasted with an open system, is a physical system that does not interact with its surroundings.

19. Kinetic Energy Kinetic Energy (KE) is the energy of motion KE = 1/2 mass. Velocity 2 = 1/2 mV 2 SI units for KE are 1/2. kg. m. m sec 2 Note the use of m both for meters and for mass. The context will tell you which. That’s the reason we study units. Note that the first two units make a Newton (force) and the remaining unit is meters, so the units of KE are indeed Energy

20. Potential Energy Potential energy (PE) is the energy possible if an object is released within an acceleration field, for example above a solid surface in a gravitational field. The PE of an object at height h is PE = mgh Units are kg. m. m sec 2 Note that the first two units make a Newton (force) and the remaining unit is meters, so the units of PE are indeed Energy Note also, these are the same units as for KE

21. KE and PE exchange An object falling under gravity loses Potential Energy and gains Kinetic Energy. A pendulum in a vacuum has potential energy PE = mgh at the highest points, and no kinetic energy because it stops A pendulum in a vacuum has kinetic energy KE = 1/2 mass. V 2 at the lowest point h = 0, and no potential energy. The two energy extremes are equal Stops v=0 at high point, fastest but h = 0 at low point. Without friction, the kinetic energy at the lowest spot (1) equals the potential energy at the highest spot, and the pendulum will run forever.

22. Overburden Stress caused by gravity is called overburden. Pressure (stress) = density x gravity x depth Stress  ρgz  = 2.7 g/cm 3 x 9.81 m/sec 2 x 1000 m ρ = 2.7 g x 100 3 cm 3 x 1 kg = 2700 kg/m 3 cm 3 1 m 3 1000 g  = 2700 kg/m 3 x 9.81 m/sec 2 x 1000 m The normal stress (pressure) at 1 km depth is about 26487000 Pa ~25 MPa in the upper crust. The upper crust has an average density of 2.7 g/cm 3 we need to convert units for density