Ahypothetical metal alloy has a grain diameter of 2.4 × 10−2 mm. after a heat treatment at 575°c for 500 min, the grain diameter has increased to 4.1 × 10−2 mm. compute the time required for a specimen of this same material (i. e., d0 = 2.4 × 10−2 mm) to achieve a grain diameter of 5.5 × 10−2 mm while being heated at 575°c. assume the n grain diameter exponent has a value of 2.2.

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.)

Photoelectrons with a maximum speed of 6.50 x 107 m/s are ejected from a surface in the presence of light with a frequency of 6.75 x 1014hz. if the mass of an electron is 9.10 x 10-31 kg, calculate in joules the maximum kinetic energy of a single electron. 3.84 x 10-15 j 1.92 x 10-15 j 5.92 x 10-23 j 3.07 x 10-16 j

In an old-fashioned amusement park ride, passengers stand inside a 3.0-m-tall, 5.0-m-diameter hollow steel cylinder with their backs against the wall. the cylinder begins to rotate about a vertical axis. then the floor on which the passengers are standing suddenly drops away! if all goes well, the passengers will “stick” to the wall and not slide. clothing has a static coefficient of friction against steel in the range 0.60 to 1.0 and a kinetic coefficient in the range 0.40 to 0.70. part a what is the minimum rotational frequency, in rpm, for which the ride is safe? express your answer using two significant figures. f f = rpm