Question

One of the moons of Jupiter, Europa, is reported to have its surface covered by an ocean
of water which is 100 km deep. The outermost 8 km are frozen as ice. The radius of
Europa is approximately 1/4 the radius of the earth. Estimate the pressure at the bottom of
Europa’s ocean.

I don't understand the solution for this at all - http://ocw.mit.edu/courses/physics/8-01sc-physics-i-classical-mechanics-fall-2010/introduction-to-mechanics/problem-solving-and-estimation/MIT8_01SC_problems02_soln.pdf.

Any help would be much appreciated!

Thanks

Answer 1

I think you should type the full problem or repost the link. I'm getting a 'page not found' error.

Answer 2

SohamK's question is topic 2. Problem Solving and Estimation, Challenge Problem, problem 1.
It involve "FLUID MECHANICS" and "Gravitation" .

The problem is want to find "Pressure in a Fluid",
which is equals to (density of fluid) x (gravity) x (depth under the fluid)
( for estimation, assumption Gravitation force in the fluid is same from depth 0 to 100km )

( step 1.1 to 1.7 are derive formula).

(ref: University Physics with Modern Physics (13th Edition) , 12.2 Pressure in a Fluid )

1) density of fluid
For estimate, we can use the density of water ( 1000 kg / m^3)
because ice's density is very closed to water.
( ref: http://en.wikipedia.org/wiki/Ice )

2) gravity

equation 1.9 states the ratio of Gravitational Force at the land in Earth and Europa.
In the solution pdf, in right most sides of equation 1.9, it should be upper case M (Me , Meur) rather then lower case ( m e , m eur ).

Between 1.9 and 1.10,
there is a hidden steps.

Mass of a sphere = (4/3 ) ( pi ) ( radius ^3)
Assume Earth, Europa are sphere, then Me / Meur = 4^3 = 64 ........ (equ 1)

Put qua1 to equation 1.9,
F grav,eath / F grav, eur = 4 ..... (equ 2)

Since F=mg ( Netwon 2nd law of motion ),

F grav,eath / F grav, eur
= ( ( m) ( g earth ) ) / (( m) ( g eur ) )
= ( g earth ) / ( g eur ) ....... ( equ 3)

combine equ2 and qu 3,
( g earth ) / ( g eur ) = 4 ( that is equation 1.10 and 1.11 )

remark:
Equation 1.13 has typing mistake while the answer 2.5 x 10E8 Pa is correct.
g ear should be 10m/s^2 rather than 90m/s^2.

( http://en.wikipedia.org/wiki/Pascal_(unit) )

Answer 3

I forgot to put density to the equation of mass:
Mass of a sphere = (4/3 ) ( pi ) ( radius ^3) (density of sphere ).

Foe estimation, assume density of earth and Europa are same, the density of earth will cancel the density of Europa.

Me / Meur still equal to 4 ................ (equ 1)