Apiece of aluminum (bulk modulus 7.1 x 1010 n/m2) is placed in a vacuum chamber where the air pressure is 0.568 x 105 pa. the vacuum pump is then turned on and the pressure is further reduced to zero. determine the fractional change v/v0 in the volume of the aluminum.

Consider a small frictionless puck perched at the top of a fixed sphere of radius r. if the puck is given a tiny nudge so that it begins to slide down, through what vertical height will it descend before it leaves the surface of the sphere? [hint: use conservation of energy to find the puck's speed as a func e conservation of energy to find the puck's speed as a function of its height at what value of this normal force does the puck leave the sphere? ] here on the puck.