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Final notecard - Fluids o f=(1/2 k/m Tensile stress = F/A...

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Fluids P ( N / m 2 ) = F / A P atm = 1.01e 5 Pa P absolute = P gauge + P atm Density ( ) = ρ m / v Pressure at a depth: o P = P o + ( ) ρ (g)(h) Buoyancy & archimedes principle o Floating object: o Immersed object: o Buoyant force = weight of fluid displaced by object F B = ( ρ L )(v) (g) Flow rate o Q (m 3 / s ) = (velocity) (area) Bernoulli’s equation: o P 1 + (1/2) v ρ 1 2 + gh ρ 1 = P 2 + (1/2) v ρ 2 2 + gh ρ 2 o Flow rate = constant Q 1 = Q 2 V 1 A 1 = v 2 A 2 Harmonic motion & elasticity Frequency = 1 /Period Simple harmonic motion: o Y coordinate = Asin(wt) o X coordinate = Acos(wt) o W = 2 f π Angular displacement: o = wt Ѳ o T = 2 /w π o f = w/2 π springs: o F spring = -kx o Frequency for simple harmonic motion: f = (1/2 ) ( π √ k/m) simple pendulum: o f = (1/2 ) (g/l) π √ Torsional oscillator: o Torque directly proportional to twist angle Ѳ o = -k τ Ѳ o k = torsion constant o f = (1/2 ) (k/ π √ I) stress, strain, Hooke’s law o hooke’s law: F = -kx o Tensile strain and stress: Tensile stress = F/A Tensile strain= L/L Δ o Force perpen dicular to area Tensile stress = young’s modulu s x tensile strain o F/ A = y ( Δ L/ L o ) Shear stress and strain o Shear stress = F/ A o Shear strain = x/ Δ L o o force parallel to area o shear stress = shear modulus x shear strain F/A = S ( x/L Δ o ) Harmonic motion and energy: o Amplitude (A) = max displacemen t o P.E. spring = (1/2)kx 2 If x=x max = A then, P.E. spring = = (1/2)kA 2 o K.E. = (1/2)mv 2 o E total = (1/2)kA 2 o (1/2)mv 2 + (1/2)kx 2 = (1/2)kA 2 Volume stress and strain: o Volume stress = F/A = P
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o Volume strain = v/v Δ o Volume stress = -bulk modulus x volume strain P = -B( v/v) Δ Simple harmonic
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