Determine the immersion depth of the bathyscaphe if water presses on its 0.12 m2 porthole with a force of 1.9 MN.
July 29, 2021 | education|
Data: S (area of the bathyscaphe window) = 0.12 m ^ 2; F (the force with which the water presses on the window) = 1.9 MN = 1.9 * 10 ^ 6 N.
Constants: ρ (density of salt water) = 1030 kg / m ^ 3; g (acceleration due to gravity) = 10 m / s ^ 2.
1) Determine the pressure that water exerts on the window: P = F / S = 1.9 * 10 ^ 6 / 0.12 = 15.83 * 10 ^ 6 Pa.
2) We calculate the immersion depth of the bathyscaphe: P = ρ * g * h, whence h = P / (ρ * g) = 15.83 * 10 ^ 6 / (1030 * 10) ≈ 1537 m.
Answer: The submersion depth of the bathyscaphe is 1537 m.
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