federica bianco
astro | data science | data for good
PHYS 207.013
Chapter 12
equilibrium
Instructor: Dr. Bianco
TAs: Joey Betz; Lily Padlow
University of Delaware - Spring 2021
equilibrium
EM = K + U~ \mathrm{is~conserved}
H&R CH12 equilibrium & elasticity
equilibrium
\vec{F}_{net} = 0 => \frac{d\vec{P}}{dt} = 0
translational equilibrium
\vec{\tau}_{net} = 0 => \frac{d\vec{L}}{dt} = 0
rotational equilibrium
must be 0 with respect to any point
H&R CH12 equilibrium & elasticity
equilibrium
\vec{F}_{net} = 0 => \frac{d\vec{P}}{dt} = 0
\vec{\tau}_{net} = 0 => \frac{d\vec{L}}{dt} = 0
H&R CH12 equilibrium & elasticity
key points
\vec{F}_{net} = 0 => \frac{d\vec{P}}{dt} = 0
\vec{\tau}_{net} = 0 => \frac{d\vec{L}}{dt} = 0
equilibrium
H&R CH12 equilibrium & elasticity
elasticity
tensile stress
H&R CH12 equilibrium & elasticity
elasticity
tensile stress
shearing stress
elasticity
tensile stress
shearing stress
hydraulic stress
elasticity
\Delta L = \frac{1}{N} L
H&R CH12 equilibrium & elasticity
elasticity
\Delta L \propto \frac{1}{N}
\Delta L \propto L
H&R CH12 equilibrium & elasticity
elasticity
\Delta L\propto \frac{1}{A}
strain (fractional change in length) is linearly related to the applied stress (force per unit area) by the proper modulus, according to the general relation
stress = modulus x strain
H&R CH12 equilibrium & elasticity
elasticity
\Delta L\propto \frac{1}{A}
\frac{F}{A} = E \frac{\Delta L}{L}
Young's law, Young's modulus
[F][A] = [p] pressure
H&R CH12 equilibrium & elasticity
elasticity
\Delta L\propto \frac{1}{A}
\frac{F}{A} = G \frac{\Delta x}{L}
shear modulus
H&R CH12 equilibrium & elasticity
elasticity
\Delta L\propto \frac{1}{A}
\frac{F}{A} = B \frac{\Delta V}{V}
hydraulic stress
H&R CH12 equilibrium & elasticity
elasticity
H&R CH12 equilibrium & elasticity
elasticity
but its more complicated... https://www.nature.com/articles/nature10739
H&R CH12 equilibrium & elasticity
elasticity
elasticity
elasticity
key points
H&R CH12 equilibrium & elasticity
elasticity
\frac{F}{A} = E \cdot\mathrm{deformation}
- There are 3 types of stress: stretch (acting along the length) shear (acting perpendicular to the length in one direction hydraulic (compressing perpendicularly to the length
- Stress is measure as force per unit area where the area is the area of the cross section following
with e proportionality constant of the material
- Stretch
- Strain
- Hydraulic stress
\frac{F}{A} = E \frac{\Delta L}{L}
\frac{F}{A} = G \frac{\Delta x}{L}
\frac{F}{A} = B \frac{\Delta V}{V}
phys207 equilibrium
By federica bianco
phys207 equilibrium
equilibrium
