Unformatted text preview: D" Figure 2: Pile driving 4. A load supporting cone bearing is shown below. The solid cone is designed to rotate while supporting load. The cone
has a base radius of R, density ρc , and angle φ that is immersed in a ﬂuid and adjacent to a conical seat as shown in the
ﬁgure. The cone is initially rotating at an angular velocity of ω0 . The cone and seat are separated by a ﬂuid ﬁlled gap s.
The ﬂuid has a viscosity µ. (i) Derive an analytical expression for the torque to maintain the cone at a constant angular
velocity. (ii) if the external torque driving the cone is removed, derive an equation for the cone’s angular velocity as a
function of time ω (t). ω(t)"
s" Figure 3: Rotating cone. 5. When you pour a carbonated drink (e.g. beer, soda) small bubbles of carbon dioxide form because the thermodynamic
pressure has been been reduced and the liquid is now super saturated with carbon dioxide gas.
(a) What is the pressure inside the bubble as a function of the bubble size?
(b) How many molecules are inside the bubble?
(c) If the droplet is very...
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