Acertain spring exerts a nonlinear force given by f(x) = −60x − 18x2 , where x is in meters and f is in newtons. a 0.90-kg block on a frictionless, horizontal surface is attached to the spring at x = 0. the block is pushed to x = −0.50 m and is then released. a) the work done by the spring on the block as it moves from x = −0.50 m to x = 0? b) the block’s speed when it reaches x = 0 c) what are the units of the coefficient with value –18?

An electric current in a wire will push or pull on a permanent magnet. which statement best explains how an electric current creates an electromagnetic force on another magnet?

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.)

If we relied solely on the nonrenewable resources found in the u.s., which one would we run out of first at current usage levels? a. natural gas b. oil c. uranium d. coal