Prove that where f is the gravitational force generated by an arbitrary mass m acting on another particle of mass m, and c is an arbitrary closed-contour in space. this integral represents the work done by the gravitational force on m ast moves around the contour c. (hint: use stokes' theorem to evaluate the closed-contour integral).

Two technicians are discussing the intake air temperature (iat) sensor. technician a says that the computer uses the iat sensor as a backup to the engine coolant temperature (ect) sensor. technician b says that the powertrain control module (pcm) will subtract the calculated amount of fuel if the air measures hot. who is correct

Aloaded platform of total mass 500 kg is supported by a dashpot and by a set of springs of effective stiffness 72 kn/m. it is observed that when the platform is depressed through a distance x = 12.5 cm below its equilibrium position and then released without any initial velocity; it reaches its equilibrium position in the shortest possible time without overshoot. find the position and velocity of the loaded platform 0.10 sec. after its release. if a further load of 400 kg is added to the platform, find, i) the frequency of damped vibrations, and i) the amplitude of vibration after 2 complete oscillations, given that the initial amplitude is 15 cm.

Ajournal bearing has a journal diameter of 3.250 in with a unilateral tolerance of 20.003 in. the bushing bore has a diameter of 3.256 in and a unilateral tolerance of 0.004 in. the bushing is 2.8 in long and supports a 700-lbf load. the journal speed is 900 rev/min. find the minimum oil film thickness and the maximum film pressure for both sae 20 and sae 20w-30 lubricants, for the tightest assembly if the operating film temperature is 160°f. a computer code is appropriate for solving this problem.