Consider a submarine on the bottom of the ocean, 1 mile below the surface. Assum
ID: 1272393 • Letter: C
Question
Consider a submarine on the bottom of the ocean, 1 mile below the surface. Assume the submarine is a cylinder with a length of 500m and a radius of 80m.
a) What is the pressure (in Pascals) that that this submarine experiences?
b)the pressure is pressing "inward" all over the body of the submarine. What is the total forcea pplied on teh submarine?
c)the cause of the pressure is molecular colisions - water molecules are striking the submarine. How many water molecules are surrounding the sub? Approzimate this by determining the surface area of the sub and dividing by the cross-sectional area of a water molecule, 10^(-15) cm^2.
d)Divide you answer from part (b) by your answer by part (c). What does this represent?
e) Repears parts a-d for a submarine near the surface of the water (assume that the submarine is completely submerged, but that it's so close to the surface that they pressure is atmospheric).
f)Notice: there are not more molecules at the bottom of the ocean! The pressure causes the same molecules to hit the boat harder (you should have found this above). But why? What's the difference, on a molecular level?
i) imagine at the surface, there is only one molecule between the surface and the top of the submarine. Draw a free body diagram for this one molecule.
ii) Imagine at the bottom of the ocean, there are only three molecuels between the surface adn the top of the submarine (obviously this is riduiculous, but it's enoug to get the idea). Draw the free body diagram for the top moleucle. Hint: the top molecule is not moving, so there must be a force canceling out its gravitational force. What is it?
iii) Now draw the free body diagram for the second molecule. Hint: Newton's 3rd Law applies. There are three forces in total. What is the magnitude of the upward force?
iv) Now draw the free body diagram for the bottom-most molecule. This molecule is allowed to accelerate and crash into the sub, so there is no upward force. What is/are the downward froce(s)? Give the total magnitude of the downward force. Hint: Newton's 3rd law applies, as before.
v) By comparing your answers to (i) and (iv), explain why, on a molecular level, the submarine feels a greater pressure at the bottom of the ocean. Are there more moleculesat the bottom of the ocean? Or are the same number of molecules pushing harder against the submarine? WHY?
Explanation / Answer
Hydrostatic pressure is given by:
P = Ps + DgH
Where:
P = Pressure at depth
Ps = Pressure at surface
D = Density of fluid
g = gravitational acceleration
H = Depth (height)
(A) For pressure.
Given:
H = 2.70km (2,700 m)
Ps = 1.01E+5 Pa
D = 1.025E+3 kg/m^3
g = 9.81 m/s^2
P = Ps + DgH
P = (1.01E+5 Pa) + [ (1.025E+3 kg/m^3) * (9.81m/s^2) * (2,700 m) ]
P = (1.01E+5 Pa) + [ 27,149,175 ]
P = 2.742E+12 Pa
(B) Now that we have pressure, we can calculate force:
P = F/A
So we need area. Diameter is 30 cm, so we need radius which is 15 cm
I hope that you know A = pi * r^2
A = pi * (15)^2
A = pi * (225)
A = 706.86 sq cm
Pressure = Force / Area (P=F/A)
P = F/A