Create a bucket by rotating around the y axis the curve y = 2 ln ( x − 1 ) y=2ln(x-1) from y = 0 to y = 10. If this bucket contains a liquid with density 780 kg/m3 filled to a height of 6 meters, find the work required to pump the liquid out of this bucket (over the top edge). Use 9.8 m/s2 for gravity.

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?