Force and Stress I

Fundamental Quantities & Units of Rocks Mass: Dimension: [M] Unit: g or kg Length: Dimension: [L] Unit: cm or m Time: Dimension: [T] Unit: s

Velocity, v = distance/time = x/t Change in distance per time)

v =[L/T] or [LT-1] units: m/s or cm/s

Acceleration (due to gravity): g = velocity/time Acceleration is change in velocity per time (v/t).

g = [LT-1 ]/[T] = LT-2, units: m s -2

Force: F = mass . acceleration F = mg F = [M][LT-2] units: newton: N = kg m s-2

Newton’s 1st Law Law 1. An object continues in its initial state of

rest or motion with uniform velocity unless it is acted on by an unbalanced, or net external, force. The net force acting on an object, also called

the resultant force, is the vector sum of all the forces acting on it.

Mathematically, Law 1 is expressed as Fnet = F

where Fnet represents the net force, and F represents

the vector sum of all of the forces acting on a given object.

Newton’s 2nd Law The acceleration of an object is inversely

proportional to its mass and directly proportional to the net force acting on it.

Mathematically, Law 2 can be expressed as:

a = Fnet/m or Fnet = ma

where a = acceleration and m = the mass of the object upon which the force is acting.

Physicists define mass as an intrinsic property of an object that is a measure of its resistance to acceleration while acceleration is simply the change in velocity over a change in time (i.e. a=v/t)

Force A property or action that changes or

tends to change the state of rest or velocity or direction of an object in a straight line

In the absence of force, a body moves at constant velocity, or it stays at rest

Force is a vector quantity; i.e., has magnitude, direction

Units of Force Two of the more common units of force are the dyne (d)

and newton (N) The units of a newton are kgm/s2 while those for a dyne are

gcm/s2

A newton is the force required to impart an acceleration of one meter per second per second to a body of one kilogram mass

A dyne is the force required to accelerate one gram of mass at one centimeter per second per second

F = (mass)(acceleration) or

F = ma or F = mg F = [M][ LT-2]

newton: N = kg m s –2

dyne: gr cm s -2 1 N = 105 dyne

Natural Forces Gravitational force

Acts over large distances and is always attractive Ocean tides are due to attraction between Moon & Earth

Thermally-induced forces e.g., due to convection cells in the mantle. Produce horizontal forces (move the plates)

The other three forces act only over short ranges (atomic scales). May be attractive or repulsive Electromagnetic force

Interaction between charged particles (electrons)

Nuclear or strong force Holds the nucleus of an atom together.

Weak force Is responsible for radioactivity

Body Forces Any part of material experiences two types of

forces: surface & body

Body Force: Results from action of a field at every point within the body Is always present Could be due to gravity or inertia

e.g., gravity, magnetic, centrifugal Its magnitude is proportional to the mass of the body

Surface Forces

Act on a specific surface area in a body Are proportional to the magnitude of the area Reflect pull or push of the atoms on one side of

a surface against the atoms on the other side

e.g., force of a cue stick that hits a pool ball force of the jaws of a vice

Body forces give rise to spatial variations or gradients on surface forces

Stress is Great! Forces applied on a body do either or both of the

following: Change the velocity of the body Result in a shape change of the body

A given force applied by a sharp object (e.g., needle) has a different effect than a similar force applied by a dull object (e.g., peg). Why?

We need another measure called stress which reflect these effects

Traction Traction is force per unit area It is the intensity of the force, i.e., how concentrated the force is= lim F/A when A → 0

A force acting on a small area such as the tip of a sharp nail or base of high heel shoe, has a greater intensity than a flat-headed nail or a snow shoe!

= [MLT-2] / [L2]=[ML -1T-2] In the mks system of the SI system: = kg m-1 s-2 pascal (Pa) = N/m2

1 bar (non-SI) = 105 Pa ~ 1 atmosphere = 0.1 MPa 1 kb = 1000 bar = 108 Pa = 100 Mpa 1Gpa = 109 Pa = 1000 Mpa = 10 kb 1 Mpa is equivalent to 1 N/mm2

P at core-mantle boundary is ~ 136 Gpa (at 2900 km) P at the center of Earth (6371 km) is 364 Gpa

Ten common units geologists use to describe stress equivalent to 1 megapascal (MPa)

Units MPa Equivalent

megapascal (Mpa) 1

gigapascal (Gpa) 0.001

pascal (Pa) = N/m2 1,000,000

kg/cm2 10.197

d/cm2 100,000,000.000

bar (b) 10

kilobar (kb) 0.010

pounds per square inch (psi) 145.030

atmosphere (atm) ~ bar 9.869

Types of Stress Tension: Stress acts _|_ to and away from a plane

pulls the rock apart forms special fractures called joint may lead to increase in volume

Compression: stress acts _|_ to and toward a plane squeezes rocks may decrease volume

Shear: acts parallel to a surface leads to change in shape