Force and Stress I

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# Force and Stress I - PowerPoint PPT Presentation

Force and Stress I. Fundamental Quantities &amp; 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 = d x/ d t Change in distance per time)

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### 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 = dx/dt

• 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 (dv/dt).

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 = S F
• where Fnet represents the net force, and SF 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=Dv/Dt)
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

s = lim dF/dA when dA → 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!

s = [MLT-2] / [L2]=[ML -1T-2]

• In the mks system of the SI system:

s = kg m-1 s-2pascal(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
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