The bathyscaphe Trieste consists of a thin-walled but very strong cylindrical hull, 15.2 m long and 3.66 m in diameter, filled with gasoline with a density of $880 \mathrm {~kg} / \mathrm { m } ^ { 3 }$ to make it buoyant. If it is totally submerged in seawater with a density of $1025 \mathrm {~kg} / \mathrm { m } ^ { 3 }$ and neither rising nor sinking, what is the weight of the Trieste craft?
A) 227 kN
B) 527 kN
C) 127 kN
D) 327 kN
E) 427 kN

Question

The bathyscaphe Trieste consists of a thin-walled but very strong cylindrical hull,  15.2 m long and  3.66 m in diameter, filled with gasoline with a density of $880 \mathrm {~kg} / \mathrm { m } ^ { 3 }$ to make it buoyant. If it is totally submerged in seawater with a density of $1025 \mathrm {~kg} / \mathrm { m } ^ { 3 }$ and neither rising nor sinking, what is the weight of the Trieste craft?
A)  227 kN
B)  527 kN
C)  127 kN
D)  327 kN
E)  427 kN

Quizplus · Accepted Answer

The weight of the Trieste craft is equal to the buoyant force acting on it. The buoyant force is equal to the weight of the water displaced by the craft. The volume of the water displaced is equal to the volume of the craft. The weight of the water displaced is equal to the density of the water multiplied by the volume of the water displaced. Therefore, the weight of the Trieste craft is equal to the density of the water multiplied by the volume of the craft.$$F_b=ho g V$$$$W=ho g V$$$$W=(1025	ext{ kg/m}^3)(9.8	ext{ m/s}^2)(15.2	ext{ m})(3.66	ext{ m})$$$$W=527	ext{ kN}$$

The Bathyscaphe Trieste Consists of a Thin-Walled but Very Strong 880 kg/m3880 \mathrm {~kg} / \mathrm { m } ^ { 3 }880 kg/m3

The Bathyscaphe Trieste Consists of a Thin-Walled but Very Strong $880 \mathrm {~kg} / \mathrm { m } ^ { 3 }$