Question

for a submarine, identify when the water will be exerting a buoyant force on it. assume that neither the volume of the submarine nor the density of the water change. choose all that apply.
when it is full of cargo and fully submerged at a depth of 65 m.
when it is full of cargo, fully submerged, and resting on the bottom at a depth of 130 m.
when it is in dry dock and no part of it is submerged in water.
when it is empty and fully submerged at a depth of 65 m.
when it is empty, fully submerged, and resting on the bottom at a depth of 130 m.
when it is empty and floating on the surface.
when it is full of cargo and floating on the surface.

Explanation:

Buoyant force is exerted by a fluid (water here) on an object when the object displaces fluid, i.e., when some volume of the object is submerged in the fluid. The formula for buoyant force is \( F_b=
ho V g \), where \(
ho \) is fluid density, \( V \) is volume of displaced fluid, and \( g \) is acceleration due to gravity.

• "When it is full of cargo and fully submerged at a depth of 65 m": Submerged, so displaces water. Buoyant force exists.
• "When it is full of cargo, fully submerged, and resting on the bottom at a depth of 130 m": Fully submerged, displaces water. Buoyant force exists (even on the bottom, as long as submerged).
• "When it is in dry dock and no part of it is submerged in water": No displacement, so no buoyant force.
• "When it is empty and fully submerged at a depth of 65 m": Submerged, displaces water. Buoyant force exists.
• "When it is empty, fully submerged, and resting on the bottom at a depth of 130 m": Fully submerged, displaces water. Buoyant force exists.
• "When it is empty and floating on the surface": Floating means partially submerged (displaces water equal to its weight). Buoyant force exists.
• "When it is full of cargo and floating on the surface": Floating, so partially submerged, displaces water. Buoyant force exists.

Answer:

• When it is full of cargo and fully submerged at a depth of 65 m.
• When it is full of cargo, fully submerged, and resting on the bottom at a depth of 130 m.
• When it is empty and fully submerged at a depth of 65 m.
• When it is empty, fully submerged, and resting on the bottom at a depth of 130 m.
• When it is empty and floating on the surface.
• When it is full of cargo and floating on the surface.