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The uniform cantilever rod in Fig. P12.8 has torsional stiffness GJ, vertical bending stiffness El, mass per unit length pA, and torsional mass moment of inertia p lp. At end x = L a rigid, weightless bar BC is attached parallel to the y-axis. At C a concentrated mass m is attached to bar BC, and also at C a load P(t) acts parallel to the z-axis. Assume that rod AB bends in the vertical (i.e., x-z) plane with deflection u(x, f) and twists about its axis with angle of twist θ(x,t) Assume all deflections to be small (e.g., m moves approximately vertically if θ is small), and neglect gravity. Use the Extended Hamilton's Principle to derive the equations of motion and the boundary conditions for this system.
two previously undeformed cylindrical specimens of an alloy are to be strain hardened by reducing their cross-sectional
multi-stage flash distillation is used to desalinate seawater so it is fit for human consumption. a flash distillation
the turbocharger of an internal combustion engine consists of a turbine and a compressor. hot exhaust gases flow
The volume flow Q varies with gravity g, weir width b into the paper, and upstream water height H above the weir crest. If it is known that Q is proportional to b, use the pi theorem to find a unique functional relationship Q(g, b, H )
using a 3 flute solid carbide 20mm diameter slot drill. with feed rate of 0.175mmtoothrev at a depth of cut of 12mm and
A perfect crystal of copper is tensile tested. The crystal is oriented so that the direction perpendicular to its slip plane is at 28° relative to the tensile direction. Consider three possible slip directions (relative to the tensile direction) of 8..
a well-insulated piston-cylinder assembly is connected by a valve to an air supply line at 8 bar. initially the air
Determine the tube length L that meets a design requirement that the tube be twice as long as the thermal entrance length associated with the high- est Reynolds number of interest. Evaluate water properties at 305 K.
The rivets are 6 mm in diameter with an ultimate shear strength of 325 MPa. A factor of safety of 8 is to apply.
Determine the force P required to force the 10° wedge under the 90-kg uniform crate which rests against the small stop at A. The coefficient of friction for all surfaces is 0.40.
a 0.86 kg of saturated vapor steam contained within a piston-cylinder. initially the piston face is at x 0 and the
A system consisting initially of 0.5 m3 of air at 35°C, 1 bar, and 70% relative humidity is cooled at constant pressure to 29°C. Determine the work and heat transfer for the process, each in kJ.
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