A research submarine has a 10-cm-diameter window that is 8.4 cm thick. The manufacturer says the window can withstand forces up to 1.2×106 N . What is the submarine's maximum safe depth in salt water? The pressure inside the submarine is maintained at 1.0 atm .
Express your answer using two significant figures.
2 answers:
Pnet = Po + dgh <span>Density of saltwater = 1030 kg/m^3. </span> <span>Disregard the thickness. Assuming it's a circular window, then the area is pi(r^2). </span> <span>d = 20 cm = 0.2 m </span> <span>r = d/2 = 0.1 m </span> <span>A = pi(r^2) </span> <span>A = 3.14159265(.1^2) </span> <span>A = 0.0314159265 m^2 </span> <span>p = F/A </span> <span>p = (1.1 x 10^6) / (0.0314159265) </span> <span>p = 35,014,087.5 Pa </span> <span>1 atm = 101,325 Pa </span> <span>P = Po + dgh </span> <span>h = (P - Po) / dg </span> <span>h = (35,014,087.5 - 101,325) / (1030 x 9.81) </span> <span>h = 3 455.23812 m </span> <span>h = 3.5 km</span>
Answer: 15 km
Explanation:
The maximum pressure that the submarine can withheld would be equal to the maximum pressure that the window can withstand.
The maximum pressure that window can sustain is given by:
Force = 1.2×10⁶ N
Area of the window =
∵radius = (0.1 m)/2 = 0.05 m
⇒P = 1.2×10⁶ N ÷ 7.85 ×10⁻³ m² = 1.52 ×10⁸ N/m²
The pressure of the salt water at depth h is given by
P = ρ g h
where, ρ = 1027 kg/m³ is the density of the salt water, g is the acceleration due to gravity and h is the depth.
⇒1.52×10⁸ Pa = (1027 kg/m³)(9.8 m/s²)(h)
⇒ h ≈ 15 km
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