18.2 Two major divisions of Mechanics:
1. kinematics
- study of motion without reference to the forces causing the motion
2. kinetics
- relates forces to motion
- relates forces to motion
Newton's Laws of Motion:
1st law:
A body in motion tends to stay in motion.
A body at rest wants to stay at rest.
ie - things want to keep doing what they are doing, you have to apply a force if you want it to change what it is doing.
Inertia = the resistance of any physical object to any change in its motion
2nd law: Force = Mass * acceleration
The acceleration of a particle is proportional to the force acting on it and inversely proportional to the particle mass; the direction of acceleration is the same as the force direction.
Large m, Large F.... small F, small m
F = ma
Constant acceleration3rd law:
The forces of action and reaction between contacting bodies are equal in magnitude, opposite in direction, and co-linear.
Law of gravitation:
The force of attraction between two bodies is proportional to the product of their masses and inversely proportional to the square of the distance between their centers.
Many STEM classes revolve around Newton's laws, and understanding how best to control and use forces.
Free-Body Diagrams
A sketch or picture of the problem
Free Body Diagram, FBD
A sketch showing the forces on point "A" in the above problem:
Free Body Diagram, FBD
A sketch showing the forces on point "A" in the above problem:
Forces are represented by arrows. Notice this arrow, or vector, has two important pieces of information:
1. The direction
2. The magnitude (length).
Rectangular Components of a Force: Unit Vectors
rectangular vector components
..
unit vectors
scalar components Fx and Fy
- the ability of a structure to support a designed load without bending, collapsing, or breaking
Structural failure:
Common types of failure:
1. Fracture:
Brittle vs. Ductile
(a) Very ductile, soft metals (e.g. Pb, Au) at room temperature, other metals, polymers, glasses at high temperature.
(b) Moderately ductile fracture, typical metals
(c) Brittle fracture, cold metals and ceramics.
*brittle fracture → rapid run of cracks through stressed material.
*very little plastic deformation
*No warning → worst type of fracture
*Amorphous microstructures (glass) produce shiny brittle fracture surfaces
In crystalline materials:
transgranular fracture - travels through the grain of the material
intergranular fracture - crack traveling along the grain boundaries
(b) Moderately ductile fracture, typical metals
(c) Brittle fracture, cold metals and ceramics.
*brittle fracture → rapid run of cracks through stressed material.
*very little plastic deformation
*No warning → worst type of fracture
*Amorphous microstructures (glass) produce shiny brittle fracture surfaces
In crystalline materials:
transgranular fracture - travels through the grain of the material
intergranular fracture - crack traveling along the grain boundaries
2. deformation
- object returns to its original shape
- Not permanent
Plastic Deformation:
Plastic Deformation:
- object becomes permanently deformed
3. Fatigue
The weakening of a material caused by repeatedly applied loads.
* microscopic cracks form around small discontinuities at the surface & near grain boundaries.
* cracks eventually reaches a critical size, then suddenly propagates through the remainder of the solid.
Fatigue life depends on:
- Temperature
- surface finish
- atomic micro-structure
Ductility, strength, hardness, thermal expansion, thermal conductivity, electrical conductivity, corrosion properties, melting point, density, etc.
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Shear Modulus (or Modulus of Rigidity)
elasticity for a shearing force.
"the ratio of shear stress to the displacement per unit sample length (shear strain)"
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Shear Modulus for common materials:
http://www.engineeringtoolbox.com/modulus-rigidity-d_946.html
