Many fish maintain buoyancy with a gas-filled swim bladder. The pressure inside the swim bladder is the same as the outside water pressure, so when a fish descends to a greater depth, the gas compresses. Adding gas to restore the original volume requires energy. A fish at a depth where the absolute pressure is 3.0 atm has a swim bladder with the desired volume of 5.0×10−4m3. The fish now descends to a depth where the absolute pressure is 5.0 atm.

a) The gas in the swim bladder is always the same temperature as the fish's body. What is the volume of the swim bladder at the greater depth?

b) The fish remains at the greater depth, slowly adding gas to the swim bladder to return it to its desired volume. How much work is required?

Three different objects, all with different masses, are initially at rest at the bottom of a set of steps. each step is of uniform height . the mass of each object is a multiple of the base mass : object 1 has mass 4..00m , object 2 has mass 1..96m , and object 3 has mass . when the objects are at the bottom of the steps, define the total gravitational potential energy of the three-object system to be zero. if the objects are then relocated as shown, what is the new total potential energy of the system? each answer requires the numerical coefficient to an algebraic expression. each algebraic expression is given using some combination of the variables , , and , where is the acceleration due to gravity. enter only the numerical coefficient. (example: if the answer is 1..23mgd , just enter 1.23)

Unpolarized light of intensity so passes through two sheets of polarizing material whose transmission axes make an angle of 60∘ with each other as shown in the figure. what is the intensity of the transmitted beam, st?

Apulley with mass mp and a radius rp is attached to the ceiling, in a gravity field of 9.81 m/s2 and rotates with no friction about its pivot.