Answer: r = 0.8081; s = -0.07071
Explanation:
A = (150i + 270j) mm
B = (300i - 450j) mm
C = (-100i - 250j) mm
R = rA + sB + C = 0i + 0j
R = r(150i + 270j) + s(300i - 450j) + (-100i - 250j) = 0i + 0j
R = (150r + 300s - 100)i + (270r - 450s - 250)j = 0i + 0j
Equating the i and j components;
150r + 300s - 100 = 0
270r - 450s - 250 = 0
150r + 300s = 100
270r - 450s = 250
solving simultaneously,
r = 0.8081 and s = -0.07071
QED!
Answer:
h = 375 KW/m^2K
Explanation:
Given:
Thermo-couple distances: L_1 = 10 mm , L_2 = 20 mm
steel thermal conductivity k = 15 W / mK
Thermo-couple temperature measurements: T_1 = 50 C , T_2 = 40 C
Air Temp T_∞ = 100 C
Assuming there are no other energy sources, energy balance equation is:
E_in = E_out
q"_cond = q"_conv
Since, its a case 1-D steady state conduction, the total heat transfer rate can be found from Fourier's Law for surfaces 1 and 2
q"_cond = k * (T_1 - T_2) / (L_2 - L_1) = 15 * (50 - 40) / (0.02 - 0.01)
=15KW/m^2
Assuming SS is solid, temperature at the surface exposed to air will be 60 C since its gradient is linear in the case of conduction, and there are two temperatures given in the problem. Convection coefficient can be found from Newton's Law of cooling:
q"_conv = h * ( T_∞ - T_s ) ----> h = q"_conv / ( T_∞ - T_s )
h = 15000 W / (100 - 60 ) C = 375 KW/m^2K
Answer
For isotropic material plastic yielding depends upon magnitude of the principle stress not on the direction.
Tresca and Von Mises yield criteria are the yield model which is widely used.
The Tresca yield criterion stated that yielding will occur in a material only when the greatest maximum shear stress reaches a critical value.
max{|σ₁ - σ₂|,|σ₂ - σ₃|,|σ₃ - σ₁|} = σ_f
under plane stress condition
|σ₁ - σ₂| = σ_f
The Von mises yielding criteria stated that the yielding will occur when elastic energy of distortion reaches critical value.
σ₁² - σ₁ σ₂ + σ₂² = σ²_f
Answer:
il(t) = e^(-100t)
Explanation:
The current from the source when the switch is closed is the current through an equivalent load of 15 + 50║50 = 15+25 = 40 ohms. That is, it is 80/40 = 2 amperes. That current is split evenly between the two parallel 50-ohm resistors, so the initial inductor current is 2/2 = 1 ampere.
The time constant is L/R = 0.20/20 = 0.01 seconds. Then the decaying current is described by ...
il(t) = e^(-t/.01)
il(t) = e^(-100t) . . . amperes
