The rotating loop in an AC generator is a square 12.0 cm on a side. It is rotated at 70.0 Hz in a uniform field of 0.800 T. Calculate the following quantities as functions of time t, where t is in seconds. I need help with d and e. (a) the flux through the loop
11.52cos(140πt) mT·m2
(b) the emf induced in the loop
5.067sin(140πt) V
(c) the current induced in the loop for a loop resistance of 2.50 Ω
2.03sin(140πt) A
(d) the power delivered to the loop
4.12sin2(140πt) W (wrong)
(e) the torque that must be exerted to rotate the loop
mN·m

Suppose water is leaking from a tank through a circular hole of area ah at its bottom. when water leaks through a hole, friction and contraction of the stream near the hole reduce the volume of water leaving the tank per second to cah 2gh , where c (0 < c < 1) is an empirical constant. a tank in the form of a right-circular cone standing on end, vertex down, is leaking water through a circular hole in its bottom. (assume the removed apex of the cone is of negligible height and volume.) (a) suppose the tank is 20 feet high and has radius 8 feet and the circular hole has radius 2 inches. the differential equation governing the height h in feet of water leaking from a tank after t seconds is dh dt = − 5 6h3/2 . if the height of the water is initially 8 feet, how long will it take the tank to empty? (round your answer to two decimal places.)

Carbon is allowed to diffuse through a steel plate 15 mm thick. the concentrations of carbon at the two faces are 0.65 and 0.30 kg c/m^3 fe, which are maintained constant. if the preexponential and activation energy are 6.2 x 10-7 m2 /s and 80,000 j/mol, respectively, compute the temperature at which the diffusion flux is 1.43 x 10^-9 kg/m^2 -s.

Engines for propeller-driven aircraft are limited in their maximum rotational speed by the fact that the tip speed of the propeller must not approach the speed of sound in air (mach i). taking 6 ft as a typical diameter for a propeller of a light airplane and 1100 fils as the speed of sound, find the upper limit on the rpm (revolutions per minute) of the propeller shaft.