Archimedes, one of the great mathematicians of all time, is famous for the story of how...

 

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Archimedes, one of the great mathematicians of all time, is famous for the story of how he man- aged to determine whether the king's crown was really made of gold. The mathematical law that he derived which enabled him to accomplish this challenge, states that any fluid applies a buoyant force to an object which is partially or completely immersed in it, the magnitude of which is equal to the weight of fluid the object displaces. Equation I Fb = Wfluid where F₁ = magnitude of the buoyant force and Wuid = weight of fluid displaced, Once the maxi- mum buoyant force possible is greater than or equal to the weight of the object, the object will float. Consider the situation where a square block of pine wood is being immersed in water. Density of water = 1.00 x 103 kg m-³ Density of pine = 500 kg m-³ Gravitational acceleration = 9.8 m s-² Length of one side of the block = 4.0 m 4) What is the maximum possible buoyant force that can be obtained when the block is held underwater? A. 6.27 x 105 N B. 1.57 x 105 N C. 8.62 x 104 N D. 2.16 x 104 N 64m³ d = m V (1 Archimedes, one of the great mathematicians of all time, is famous for the story of how he man- aged to determine whether the king's crown was really made of gold. The mathematical law that he derived which enabled him to accomplish this challenge, states that any fluid applies a buoyant force to an object which is partially or completely immersed in it, the magnitude of which is equal to the weight of fluid the object displaces. Equation I Fb = Wfluid where F₁ = magnitude of the buoyant force and Wuid = weight of fluid displaced, Once the maxi- mum buoyant force possible is greater than or equal to the weight of the object, the object will float. Consider the situation where a square block of pine wood is being immersed in water. Density of water = 1.00 x 103 kg m-³ Density of pine = 500 kg m-³ Gravitational acceleration = 9.8 m s-² Length of one side of the block = 4.0 m 4) What is the maximum possible buoyant force that can be obtained when the block is held underwater? A. 6.27 x 105 N B. 1.57 x 105 N C. 8.62 x 104 N D. 2.16 x 104 N 64m³ d = m V (1

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