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Show that, when a particle is projected from the origin in a medium that exerts linear resistance, its position vector at time t has the general form
r = -α(t)k + β(t)u'
where k is the vertically upwards unit vector and u is the velocity of projection. Deduce the following results:
(i) A number of particles are projected simultaneously from the same point, with the same speed, but in different directions. Show that, at each later time, the particles all lie on the surface of a sphere.
(ii) A number of particles are projected simultaneously from the same point, in the same direction, but with different speeds. Show that, at each later time, the particles all lie on a straight line.
(iii) Three particles are projected simultaneously in a completely general manner. Show that the plane containing the three particles remains parallel to some fixed plane.
the density of air is to be determined by measuring its pressure and temperature for insertion in the ideal gas
Compare the ideal COP of R-134a and R-22 at an evaporating temperature of 40 F and 20 F superheat and condensing temperature of 120 F with 15 F sub cooling with the actual compressor COPs calculated from the manufacturer's performance tables.
For the continuous beam shown in Fig. 4.37, find the magnitude and direction of the centerline deflection of the right half of the structure. Assume a uniform EI.
Calculate the heat supplied and change of entropy and show the process on a T-s diagram, indicating the area which represents the heat flow.
Suppose propagation is also allowed in the coating. What is now the answer to (a) and what is the critical angle for propagation?
1. Air enters a horizontal, well-insulated nozzle operating at steady state at 12 bar, 500K, with a velocity of 50 m/s and exits at 7 bar, 440 K. The mass flow rate is 1 kg/s. Determine the net force, in N, exerted by the air on the duct in the..
Methane is completely burned with 20% excess air, with 30% of the carbon going to CO. What is the partial pressure of the CO in the stack gas if the barometer reads 740 mm Hg, the temperature of the stack gas is 300°F
A common approach to system testing is to test the system until the testing budget is exhausted and then deliver the system to customers. Discuss the ethics of this approach for systems that are delivered to external customers.
100 kmol/h of biogas (75 mol% CH4 and 25 mol% CO2) is produced in a digester and is drawn off from the headspace under a slight vacuum and piped to a natural gas burning boiler. A slight leak develops in the pipe allowing air (79 mol% N2 and 21 mol% ..
a system receives 10 kj of energy to do something. the system is adiabatic and its super efficient. how much work
Explain the difference between applying the Method of Sections to trusses and applying it to beams.
A particle slides freely on a flat surface, attached to a mass less string that passes through a hole in the surface. At a given moment, the particle is moving in a circle of radius r0 with angular velocity w0. Assume that the string is pulled throug..
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