Physics: Mechanics of Solids
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1
stress
Finternal/A=Fapplied/A
2
two block (mass m and M)conneced by a wire tensile stress is F is applied on M
T.S=Fm/(M+m)A
3
when the mass m is hanging on lift and accelerating upwards with acceleration a tensile stress is
T.S=m(g+a)/A
4
if 3 masses(m,2m,3m) are hanging from rigid end in that order from top to bottom then their tensile stress respectively are
T.S1=6mg/A , T.S2=5mg/A, T.S3 =3mg
5
volume stress
volume Stress =F/A=pressure F=Normal force(thrust)
6
shearing stress
F(tangential force)/A
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strain (longitudinal, volumetric,shearing)
longitudinal strain=∆L/L volumetric strain =∆V/V shearing strain =∆x/L
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hookes law
within elastic limit. stress proportional to strain
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breaking stress also
F1/A1=F2/A2
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breaking of wire under its own weight what is is Lmax
PA=mg ,PA=Vpg=ALmax.p.g Lmax=P/pg
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young modulus (Y) also equation with spring constant
longitudinal stress/longitudinal strain =FL/Ax comparing with force constant (K) k =YA/L
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elastic potential energy
1/2kx^2=F^2/2k=1/2(Fx)=1/2(YA/L)x^2
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potential energy per volume
(1/2)stress*strain ,(1/2)(stress^2/Y),(1/2)Y*strain^2
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stress on heavy rope( x is from bottom to that point) mass per unit length is M/L
stress=Mxg/LA, F=Mxg/L
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elongation due to its own weight
x=MgL/2AY
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elastic potential energy stored due to its in weight
U=M^2g^2L/6AY
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ratio of density immersed in a liquid xa is in air x is in liquid
p/sigma=xa-xb/xa
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ratio of extension (when m' andm" mass are being hanged from top to bottom) l=L1/L2 y=Y1/Y2 d=D1/D2
x1/x2=m'l/m"yd^2
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Bulk modulus
B=∆P/∆V/V (Bisothermal=P Badiabatic=gammaP
20
density of compressed liquid
pf=pi(1+(∆P/B) bulk modulus is possessed by solids liquid and gases
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modulus of rigidity
eta=Fl/(A∆x) (phi=∆x/l)
22
equivalent young modulus in series and parallel
series(keq=k1k2/k1+k2) series(yeq=2Y1Y2/Y1+Y2) parallel (keq=k1+k2) parallel(Yeq=Y1+Y2/2)
23
poisson's ratio(sigma) also theoritical value and practical value
lateral strain/longitudinal strain ((-dr)/dl/l, theoretical value: -1<sigma<0.5 practical value : 0<sigma<0.5
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∆V/V = ?
∆r + ∆l/l ,-2sigma(∆l/l)+∆l/l , ∆l/l(1-2sigma)
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delta(depression of beam)
delta=Wl^3/(4bd^3*Y)
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maximum height of mountain
elastic limit of rock is 3*10^8 Nm^-2 p=3*10^3 kgm^-3 h=10km
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what is the relation b/w shearing modulus (G) and young modulus of most material
G=Y/3
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