Mechanical properties of solids & fluids Flashcards
Elongation due to self weight
ΔL = MgL/2AY
For a suspended body, tension is max at
top
Modulus of rigidity/shear mod
G = Fl/Ax
For most metals G =
Y/3
Bulk modulus
B = -dPV/dV
Compressibility C =
1/B
Poisson’s ratio σ =
(-ΔD/D)/(ΔL/L)
if σ = 0.5, ΔV =
0
Comparison b/w a spring and an elastic rod
x = FL/AY
Elastic PE
U = 1/2YA/L ΔL^2
Elastic energy density
u = 1/2 x stress x strain
Breaking stress σb =
F(b)/A
Breaking stress depends only on
material
Sag in a doubly supported beam δ =
WL^3/4bd^3Y
When liq is acc, ΔP
ρ(g+a)h
When liq is decc, ΔP =
ρ(g-a)h
When liq is in free fall ΔP =
0
For hydraulic lift F2 =
F2 = A2F1/A1
Buoyancy/Buoyant force/Upthrust F =
(P2-P1)A
Archimedes principle
Buoyant force = weight of liq displaced by obj
B = ρ(fluid)V(immersed)g
Under completre immersion, Loss of weight exp by obj B =
ρ(L) mg/ρ(o)
App. weight Wa =
W - B
If ρ > σ, obj
sinks
Flotation
When an obj floats, it exp a buoyant force which is equla to obj weight
ρ<σ