A disposable Styrofoam coffee cup is attached to the exterior of a submersible o

Question

A disposable Styrofoam coffee cup is attached to the exterior of a submersible ocean research vehicle as a demonstration of the increase of water pressure with ocean depth (P = gh). At the surface the cup stands 10 cm tall. At a depth of 1000 m below the surface, it is observed through the window of the submersible to be just 5 cm tall (with its other dimensions reduced in the same proportion). Assume the average density of seawater is 1.036 g/cm3.

a. What is the additional pressure to which the cup is subject at 1000 m depth?

b. By what factor is the volume of the cup reduced?

c. What is the bulk modulus of Styrofoam?

Explanation / Answer

a) density of seawater = 1.036 g/cm3 = 1036 kg/m3

depth = 1000 m

Additional pressure = 1036*1000*9.8 = 10152800 Pa

b)the height is reduced from 10cm to 5cm . Also, other dimensions are reduced in same proportion

Therefore, thevolume reduces by 23 =8 times

Therefore, the volume becomes 1/8 th times the initial volume

c)Let the initial volume be V

Final volume = V/8

Change in volume = V - V/8 = 7V/8

Bulk modulus = Pressure / (change in volume/original volume)

= 10152800/ (7V/8V) = 11603200 Pa

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