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Yo-yo with moving support A uniform circular cylinder (a yo-yo) has a light inextensible string wrapped around it so that it does not slip. The free end of the string is fastened to a support and the yo-yo moves in a vertical straight line with the straight part of the string also vertical.
At the same time the support is made to move vertically having upward displacement Z(t) at time t. Take the rotation angle of the yo-yo as generalised coordinate and obtain Lagrange's equation.
Find the acceleration of the yo-yo. What upwards acceleration must the support have so that the centre of the yo-yo can remain at rest? Suppose the whole system starts from rest. Find an expression for the total energy E = T + V at time t.
a 20 bbl influx of 9 lbmgal salt water enters a 10000 ft well containing 10 lbmgal mud. the annular capacity is .0775
consider a heat engine executed using a flow rate of 0.03 kgs of refrigerant-134. the engine operates between two
a gas refrigeration system composed of a turbine a compressor and two heat exchangers is operating at steady state. air
Estimate the viscosity of the fluid. Is the flow laminar? Can you also estimate the density of the fluid?
Compute the reactions and draw the shear and moment curves for the beam in Figure. Also E = 200 GPa and = 120 X 106 mro4 Use symmetry to simplify the analysis.
A 302 in displacement, V8, four-stroke cycle SI engine mounted on a hydraulic dynamometer has an output of 72hp and 4050 RPM. Water absorbs the energy output of the engine as it flows through the dynamometer at a rate of 30 gallons per minute. The dy..
Air flows though the mitered bend shown in Fig. P8.62 at a rate of 5.0 cfs. To help straighten the flow after the bend, a set of 0.25-in.-diameter drinking straws is placed in the pipe as shown. Estimate the extra pressure drop between points (1) ..
a certain indutrial process requires a steady stream of saturated vapor steam at 200 kpa at the rate of 2 kgs. there
a small radiant heater has 25 metal strips each 6 mm wide and a length of 3 m. the surface emissivity of the strips is
A 45 degree strain gage rosette, with each gage having a nominal resistance of 120 W and a gage factor, is attached to an Aluminium structural element of a machine. Each strain gage is inserted into its own dc Wheatstone bridge with all other resisto..
At a given instant, the position of a plane at A and a train at B are measured relative to a radar antenna at O. Determine the distance d between A and B at this instant. To solve the problem, formulate a position vector, directed from A to B, and..
Determine the adiabatic flame temperature for constant pressure combustion of a stoichiometric propane air mixture assuming reactants at 298 k . No dissociation of the products and constant specific heats evaluated at 298 k.
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