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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.
if 10m3 of hydrogen at 0.4 mpa and room temperature is adiabatically mixed with 20m3 of nitrogen at 0.1 mpa and room
a gas within a piston-cylinder assembly undergoes a thrmodynamics cycle consisting of three processesprocess from state
the wear out of a machine is normally distributed with 90 percent of the failures occurring between 200 and 270 hr of
a flatbed truck is traveling with a velocity v 51i mph and is brought to a stop with a constant deceleration over a
Calculate the maximum eccentricity e for zero tension at the base of the pedestal. Include the weight of the pedestal using a concrete unit weight of 150 pcf.
The radius of gyration about an axis passing through the axis of symmetry of the 1.6-Mg space capsule is kz = 1.2 m and about any transverse axis passing through the center of mass G, kt = 1.8 m.
A steel plate of 950 kg accelerates from rest with 3 m/s^2 for a period of 10 s. What force (N) is needed and what is the final velocity ( in m/s and ft/s) ?
when the discharge upstream is suddenly increased to 70 cfs/ft. What is the speed and height of the surge wave
if an automobiles braking distance from 60 mph is 150 ft on level pavement determine the automobiles braking distance
A one dimensional wall of material (Kw=10w/mk) is 50 mm thick with uniform heat generation q‘‘‘=5*10^6w/m^3. The left side is exposed to a fluid hl=500w/m^2k at 20 degree Celsius. The right side has a 10mm thick plate attached that has no heat genera..
A closed system undergoes a process in which there is a heat transfer of 110 btu into the system. The work done on the system is 70 btu. Initial internal energy of the system is 1300 btu, what is the final energy of the system in btu.
100-kg of R-134a at 180kPa are contained in a piston-cylinder device whose volume is 14.715 cubic meter. The piston is now moved until the volume is one half its original sizes. This is done such that the pressure does not change. Determine the final..
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