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A uniform solid cylinder C with mass m and radius a rolls on the rough outer surface of a fixed horizontal cylinder of radius b. In the motion, the axes of the two cylinders remain parallel to each other. Let θ be the angle between the plane containing the cylinder axes and the upward vertical.
Taking θ as generalised coordinate, obtain Lagrange's equation and verify that it is equivalent to the energy conservation equation. Initially the cylinder C is at rest on top of the fixed cylinder when it is given a very small disturbance.
Find, as a function of θ, the normal component of the reaction force exerted on C. Deduce that C will leave the fixed cylinder when θ = cos-1(4/7). Is the assumption that rolling persists up to this moment realistic?
two kg of saturated liquid water at 1 bar is compressed to 25 bar and 100degc in a water pump. determine the change in
An old gas turbine has an efficiency of 21 percent and develops a power output of 6000 kW. Determine the fuel consumption rate of this gas turbine, in L/min, if the fuel has a heating value of 42,000 kJ/kg and a density of 0.8 g/cm3.
Write the velocity pro?le and calculate the torque and the power required to rotate the inner cylinder at 2000 rpm assuming a laminar ?ow.
What is the axial stress in the wall of the tank due to the water pressure?
A double strap butt joint had to carry a load of 17kN. the ultimate shear strength of the rivets used is 260MPa and a factor of safety of 8 is to apply. if the rivet diameters are to be 6mm, determine the total number of rivets required
water flows through a venturi with piezometers attached to the upstream pipe and the minimum area section. the velocity
amonia as a refrigerant enters the expansion valve at a pressure of 1.5 mpa and a temperature of 32 oc its pressure on
two block masses on smooth wheels m1 and m2 are connected to the wall through spring having a spring constant of k2
steam having a specific enthalpy of 160 kjkg and pressure of 1 kpa enters an adiabatic pump. upon leaving the pump the
A compressor is employed to compress gas flowing steadily through it. The gas enters the compressor at a temperature of 16°C, a pressure of 100 kPa, and with an enthalpy of 391.2 kJ/kg. The gas leaves the compressor at a temperature of 245°C, a pre..
Find the capacity of a cylindrical tank that is 250 feet in diameter and 30 feet high? In the above problem, what is the capacity if the tank is 75% full, and what is the capacity in gallons?
la paz bolivia is at an altitude of approximately 12000ft. assume a standard atmosphere. how high would the liquid rise
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