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A uniform disk of mass M and radius a can roll along a rough horizontal rail. A particle of mass m is suspended from the centre C of the disk by a light inextensible string of length b. The whole system moves in the vertical plane through the rail.
Take as generalised coordinates x, the horizontal displacement of C, and θ, the angle between the string and the downward vertical. Obtain Lagrange's equations. Show that x is a cyclic coordinate and find the corresponding conserved momentum px .
Is px the horizontal linear momentum of the system? Given that θ remains small in the motion, find the period of small oscillations of the particle.
the piston diameter is dp 3 mm and the piston position is initially s1 5 cm from the bottom of the piston. at this
Calculate the standard deviation of the slope and intercept.
Pulleys C and D are attached to shaft AB, as shown. - Calculate the belt tension P3. - the maximum shear stress in the shaft.
Assuming the tube surface to have a uniform temperature of 55°C and the paraffin to be an infinite, quiescent liquid, determine the convection coefficient associated with the outer surface.
air an ideal gas contained in a rigid insulated tank fitted with a paddle wheel initially at 27 degrees celcius 2 bar
the two small 0.2-kg sliders are connected by a light rigid bar and are constrained to move without friction in the
a rigid tank has a volume of 0.06m3 and initially contains a two-phase liquid-vapour mixture of h2o at a pressure of 15
An ideal vapor-compression refrigeration system operates at steady state with Refrigerant 134a as the working fluid. Superheated vapor enters the compressor at 30 lbf/in2, 20F, and saturated liquid leaves the condenser at 140 lbf/in2. The refriger..
Of a certain soil it is known from previous studies that c = 20 kPa and φ = 30? . An undrained analysis must be made for a case in which the original vertical effective stresses are 80 kPa, and the horizontal effective stresses are estimated to be..
Get on the Internet and search for scholarships and grants for which you may apply. Research the scholarships and grants offered by companies, foundations, and institutions. What pertinent information do these applications request?
A model of an airplane is to be tested at 20°C in a wind tunnel. The model is built to 1/12th scale. In order to match both the Mach number and the Reynolds number of the plane, the wind tunnel is pressurized. To what pressure (in atm) should the air..
Methane gas at 25°C, 1 atm enters a reactor operating at steady state and burns with 80% of theoretical air entering at 227°C, 1 atm. An equilibrium mixture of CO2, CO, H2O(g), H2, and N2 exits at 1427°C, 1 atm. Determine, per kmol of methane ent..
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