An elastomer is a polymer that can stretch and contract. in a perfect elastomer the force opposing extension is proportional to the displacement x from the resting state of the elastomer, so |f|=k_f x, where k_f is a constant. but suppose the restoring force weakens as the elastomer is stretched, and k_(f(x))=a-bx^(1/2) . evaluate the work done on extending the polymer from x = 0 to the final displacement of x = 1.

Awave is produced in a rope. the wave has a speed of 33 m/s and a frequency of 22 hz. what wavelength is produced?

Boxing gloves are padded to lessen the force of a blow. (a) calculate the force exerted by a boxing glove on an opponent’s face, if the glove and face compress 7.50 cm during a blow in which the 7.00-kg arm and glove are brought to rest from an initial speed of 10.0 m/s. (b) calculate the force exerted by an identical blow in the gory old days when no gloves were used and the knuckles and face would compress only 2.00 cm. (c) discuss the magnitude of the force with glove on. does it seem high enough to cause damage even though it is lower than the force with no glove?

The rocket is fired vertically and tracked by the radar station shown. when θ reaches 66°, other corresponding measurements give the values r = 32700 ft, r¨ = 85 ft/sec2, and θ˙ = 0.019 rad/sec. calculate the magnitudes of the velocity and acceleration of the rocket at this position.