The deepest part of Puget Sound is just north of Seattle and reaches 930 ft (283

Question

The deepest part of Puget Sound is just north of Seattle and reaches 930 ft (283.5 m). The density of saltwater is 1030kg/m3. Part A What is the pressure at the bottom in atmospheres? Answer in ATM's. Part B If a buoy was tethered to the bottom and floated 3 meters beneath the surface of the water at high tide, what would be the tension in the rope if the buoy was a cylinder of radius 0.15 meters, a height of 0.35 meters, and has a mass of 20.5 kg. Answer in N. Part C If the buoy rope goes limp at low tide, how much of the buoy would be showing out of the water assuming it stays upright? You may assume that the mass of the rope is negligible. Express your answer in meters.

Explanation / Answer

Here,

h = 283.5 m

density of salt water , p = 1030 Kg/m^3

part A)

pressure at the bottom = Po + p * g * h/(1 atm)

pressure at the bottom = 1 + 1030 * 283.5 * 9.8/(1.01 *10^5)

pressure at the bottom = 29.33 atm

the pressure at the bottom is 29.33 atm

part B)

let the tension in the rope is T

T = p * pi * r^2 * g - m * g

T = 1030 * pi * 0.15^2 * 0.35 * 9.8 - 20.5 * 9.8

T = 48.8 N

the tension in the rope is 48.8 N

part C)

let the height above water is h1

20.5 * 9.8 = pi * 0.15^2 * 9.8 * (0.35 - h) * 1030

solving for h

h = 0.0684 m = 6.84 cm

the height of cyclinder above surface is 6.84 cm

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