Question

A buoy is a floating device that can have many purposes, but often as a locator for ships. Collin constructs a hollow metal buoy by welding together two identical cones of height h and diameter d. The resulting double-cone buoy has average density equal to half the density of seawater meaning that its total mass divided by total volume is half the density of seawater. Throughout this problem, you can ignore the air above the sea’s surface.

1.1. When the buoy is at rest in a calm ocean, with its axis of symmetry perpendicular to the water’s surface, what fraction of it will be submerged?

1.2. If the buoy is at rest at time t = 0 and is then pushed down slightly into the water and let go, what will be its angular frequency ω of small oscillations in terms of the given variables? Note: the volume of a cone of height h and base area A is hA/3.

1.3. What should be the height h of each cone in the buoy so that the buoy will execute one oscillation period every second and therefore be usable as a clock with one-second accuracy?

Answer 1

let 'B. be the density of sea-water density of busy will be 3/2. then radius = d 2 total height = an tofal volume = a (988hx1x2 = 7d²h For inmessed part eet v' be the volume immersed in water and v be total volume of buoy FB = Fg [force of buoyancy = force of growity] 3.vigo Livig » V = Half of the balloy will be emmersed in water.

let us say that the baby is displaced by a neight it in the water. Net upward force = F - Fg Finang let im' be the total mass of the busy ma = (alg ma = 43 Angular frequency, w = 1 39 1.3 T = 20 = 1 » W=24 4A² = 3g h= 4x² -) h=1.34m YE