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Geodesics on a cone Solve the problem of finding a shortest path over the surface of a cone of semi-angle α by the calculus of variations. Take the equation of the path in the form ρ = ρ(θ ), where ρ is distance from the vertex O and θ is the cylindrical polar angle measured around the axis of the cone.
Obtain the general expression for the path length and find the extremal that satisfies the end conditions ρ(-π/2) = ρ(π/2) = a.
Verify that this extremal is the same as the shortest path that would be obtained by developing the cone on to a plane.
A thin ring of radius a is charged so that a uniform line charge density of Pt C/m exists on the ring. Calculate the electric field intensity at a height h above the center of the ring, on its axis.
Calculate the particle displacement amplitudes for a 90-dB tone at 100, 1000, and 10,000 Hz.
a piston-cylinder device contains 5 kg of r134a at 800 kpa and 60 c. the refrigerant is now cooled at constant pressure
These measurement give an open line impedance of -j50 and a shorted line impedance ofj75. Calculate the characteristic impedance of the line.
a quantity of air undergoes a thermodynamic cycle consisting of three internally reversible processes in series process
consider a 100 mw power plant consisting of an adiabatic steam turbine a constant pressure condenser an adiabatic pump
Then the weight of the ring and the dry soil is found to be 380 g. The ring itself (empty and dry) weighs 210 g. What is the water content of the soil?
determine the density specific heat and thermal conductivity of a lightweight aggregate concrete mix that is composed
the work on a system with a mass 100 lbm is known to be 10 btus. if there is no change in potential energy and the
Consider a simply supported beam of length 50ft subjected to a uniformly distributed downward load of 10kips/ft from x=10ft to x=40ft and concentrated downward loads of 100kips at x=10ft and x=40ft.
a material is found to have a tenth-thickness of 2.3 cm for 1.25-mev gamma rays. a what is the linear attenuation
Air flows steadily through a one-inlet, one-exit control volume. At the inlet, which has a flow area of 28 cm2, the air is at 600 kPa, 500 K, and has velocity of 30 m/s. At the exit, the pressure is 300 kPa, the temperature is 456.5 K, and the veloci..
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