Consider two plates, A and B, that are each initially isothermal and each of thickness
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- A thin bar of length L = 3 meters is situated along the x axis so that one end is at x = 0 and the other end is at x = 3. The thermal diffusivity of the bar is k = 0.4. The bar's initial temperature f(x) = 300 degrees Celsius. The ends of the bar (x = 0 and x = 3) are then put in an icy bath and kept at a constant O degrees C. Let u(x, t) be the temperature in the bar at x at timet, with t measured in seconds. Find u(x, t) and then u7 (2, 0.1). Put uz (2, 0.1) calculated accurately to the nearest thousandth (3 decimal places) in the answer box.arrow_forwardQ4. Two long rods of the same diameter, one of brass(k= 85 W/mK) and the other of copper (k=375 W/mK) have one of their ends inserted in a furnace and the other ends exposed to the same atmosphere. At a distance of 105mm away from the furnace, the temperature of the brass rod is 120' C. Find the distance from the furnace in which the copper rod have the same temperature.arrow_forwardA rectangular nylon [E = 8 GPa; v = 0.35; d = 29 x 10-6/°C] plate has a circular hole in its center. At an initial temperature of T; = 19°C, the plate width is b = 360 mm, the plate height is h = 190 mm, the diameter of the central hole is d = 55 mm, and the thickness of the plate is t = 21 mm. At a final temperature of T=45°C, determine (a) the diameter d of the central hole. (b) the thickness t of the plate. Answers: (a) df = i (b) t= i b Save for Later d eTextbook and Media mm mm Attempts: 0 of 5 used Submit Answerarrow_forward
- A thin bar of length L = 3 meters is situated along the x axis so that one end is at x = 0 and the other end is at x = 3. The thermal diffusivity of the bar is k = 0.4. The bar's initial temperature f(x) = 50 degrees Celsius. The ends of the bar (x = 0 and x = 3) are then put in an icy bath and kept at a constant 0 degrees C. Let u(x, t) be the temperature in the bar at x at time t, with t measured in seconds. Find u(x, t) and then u4 (2, 0.1). Put u4(2, 0.1) calculated accurately to the nearest thousandth (3 decimal places) in the answer box.arrow_forwardA steel rod with a cross-sectional area of 199 mm2 is stretched between two fixed points. The tensile load at 29°C is 7,100 N. At what temperature will the stress be zero? ? Assume α = 11.7 × 10-6 m/(m·°C) and E = 203 GPa. Answer must be in degree Celsius.arrow_forwardA solid nylon [E = 8 GPa; v = 0.35; a = 29x106/°C] rod is initially unconstrained. The initial length of the rod is L = 600 mm and its diameter is d = 24 mm. If the temperature of the unconstrained rod is increase by 33°C above the initial temperature, determine (a) the change in the rod's length. (b) the change in the rod's diameter. Answers: (a) AL = i (b) Δd = i eTextbook and Media Save for Later mm mm Attempts: 0 of 5 used Submit Answerarrow_forward
- Current Attempt in Progress A solid 72-mm-diameter cold-rolled brass [G-38.5 GPa) shaft that is 1.21 m long extends through and is completely bonded to a hollow aluminum [G=20.3 GPa) tube. Aluminum tube (1) has an outside diameter of 96 mm, an inside diameter of 72 mm, and a length of 0.81 m. Both the brass shaft and the aluminum tube are securely attached to the wall support at A. Assume L-L2-0.81 m, L3-0.4 m. TB-22 kN-m, and Tc-6 kN-m. When the two torques shown are applied to the composite shaft, determine: (a) the maximum shear stress magnitude r, in aluminum tube (1). (b) the maximum shear stress magnitude 2 in brass shaft segment (2). (c) the maximum shear stress magnitude ry in brass shaft segment (3). (d) the rotation angle of joint B. (e) the rotation angle pe of joint C. Answers: (a) T₁ (b) T₂ = (c) T3 = (d) PB (e) pc = S i Mo i 30x i i 1 To MPa. MPa. MPa.arrow_forwardThe head of a grass string trimmer has 100 g of cord wound in a light, cylindrical spool with inside diameter 3.00 cm and outside diameter 18.0 cm as shown in the figure below. The cord has a linear density of 10.0 g/m. A single strand of the cord extends 16.0 cm from the outer edge of the spool. 16.0 cm +3.00 cm 18.0 cm (a) When switched on, the trimmer speeds up from 0 to 2 250 rev/min in 0.230 s. What average power is delivered to the head by the trimmer motor while it is accelerating? W (b) When the trimmer is cutting grass, it spins at 1 940 rev/min and the grass exerts an average tangential force of 8.85 N on the outer end of the cord, which is still at a radial distance of 16.0 cm from the outer edge of the spool. What is the power delivered to the head under load? Warrow_forwardThe pin-connected structure shown in Fig. P5-68 consists of a rigid bar ABCD, a steel [E = 210 GPa, and α = 11.9(10−6)/°C] bar BF, and an aluminum alloy [E = 73 Gpa and α = 22.5(10−6)/°C] bar CE. The cross-sectional areas are 1200 mm2 for bar BF and 900 mm2 for bar CE. The bars are unstressed when the structure is assembled at 40°C. Determine a. The normal stresses in the bars after the temperature is reduced to − 20° C. b. The shearing stresses in the 30-mm-diameter pins at A, B, and C. Pin B is in double shear, and pins A and C are in single shear. c. The vertical component of the displacement of pin D from it original position. Figure P5-68arrow_forward
- An aluminum pipe has a length of 75 m at a temperature of 18°C. An adjacent steel pipe at the same temperature is 5 mm longer than the aluminum pipe. At what temperature (°C) will the aluminum pipe be 15 mm longer than the steel pipe? (Assume that the coefficients of thermal expansion of aluminum and steel are αa = 23 x 10^–6/°C and αs = 12 x 10^–6/°C, respectively.)arrow_forwardIn the diagram below, metal 1 is made of gold and metal 2 is aluminum. Both bars have the same length and area of cross-section but their thermal conductivities are different. The temperature Th is maintained at a constant 88.0°C at the end A while the temperature T, at the end B is maintained at 19.0°C. A. T metal 1 metal 2 T (a) What is the temperature T; at the junction of the two bars? The thermal conductivity of gold is 318 J/(s · m · °C) and that for aluminum is 220 J/(s• m · °C). °C (b) If metals 1 and 2 are now interchanged, but the values of Th and T, are the same as in part (a), what will be the temperature of the junction? °Carrow_forwardTwo composite bars have the following composition. At an initial temperature of 5 degree C, there is an existing gap of 9mm. Bar 1 and 2 have coefficiens of thermal expansion of a1=140x10^-6/°C and a2=67x10^-6/°C, respectively. Determine the temperature at which thr 9mm gap is closed.arrow_forward
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