Amass m is attached to a spring which is held stretched a distance x by a force f (fig. 7-28), and then released. the spring compresses, pulling the mass. assuming there is no friction, determine the speed of the mass m when the spring returns: (a) to its normal length (x = 0); (b) to half its origin inal extension (x/2).

Athermometer is removed from a room where the temperature is 70° f and is taken outside, where the air temperature is 10° f. after one-half minute the thermometer reads 60° f. what is the reading of the thermometer at t = 1 min? (round your answer to two decimal places.) ° f how long will it take for the thermometer to reach 30° f? (round your answer to two decimal places.)

Total solidification times of three casting geometries are to be compared: a sphere, a cylinder, in which the length-to-diameter ration - 1.0, and a cube. volume = 1000 cm^3 for all three shhapes, and the same casting alloy is used. a) determine the solidification times of each geometry b) based on the results of part (a), which geometric element would make the best riser? c) if the mold constant = 3.5 min/cm^2 in chvorinov's rule, compute the total solidification time for each casting.

When the displacement of a mass on a spring is 12a the half of the amplitude, what fraction of the mechanical energy is kinetic energy? at what displacement, as a fraction of a, is the mechanical energy half kinetic and half potential?