VDU_Physics_2_010  
Solved UniversityPhysics ProblemsPhysics 2. Archimedes Principle (Buoyant force)
Javier Montenegro Joo 

Archimedes Principle  
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(1) A 0.50 kg object weighs 1.50 N in water and 0.70 N in petroleum. Determine the density of the petroleum. Solution. The upthrust or buoyancy “E” is the real weight minus the apparent weight of the object in the fluid:


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(2) From an unidentified flying object flying at 500 m altitude drops a mechanical piece made of an extraterrestrial metal. The terrestrials find that the weight of the piece is 25 N. When the piece is hung from a spring scale, also known as Roman scale, and immersed completely in water, the scale shows that the piece apparently weights 15 N. Determine the density of the metallic piece
Solution. · The buoyancy B is the force the liquid exerts on the immersed body and, it is given by the difference between the real weight of the body and its apparent weight. · According to Archimedes, the buoyancy is given by the weight of the displaced fluid.


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(3) A hollowed ball is floating right beneath the surface of a liquid of known density D. The volume of the ball is Vb and its density is 4D. Determine: (a) The force applied by the liquid on the ball, (b) The mass of the ball (c) The volume of the cavity inside the ball. Solution. · The force applied by the liquid on the ball is the pushup force, also known as buoyancy B and, it is equal to the weight of the displaced fluid. · Since the hollowed ball is a shell and it is completely immersed in the liquid, the buoyancy equals the weight of this shell. · The total volume of the ball Vb includes the volume of the shell and that of the cavity. 

(4) Consider a compact cylindrical block of radius R and height H, made of a material of density D. In order to study the block, it is placed in a liquid, where the block floats with 25% of its volume above the surface. Determine: (a) The density of the liquid (b) The density of the liquid if the block were a cube of side L and its density were two times higher. Solucion. Since the block is floating on the liquid, the weight of the block is equilibrated by the buoyancy (upthrust), and the buoyancy B is equal to the weight of the displaced fluid.


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[5] A compact ball having a radius of 30 cm and a density of 600 kg/m3 is released at 10m depth in a tank full of water. Taking into consideration the weight of the ball but disregarding the friction between the ball and the water, determine: (a) velocity of the ball when reaching the surface of the water (b) time for the ball to reach the surface (c) Acceleration of the ball. (d) Height the ball jumps out of the surface (e) Time the ball is in the air. Solution. While the ball is in the water it experiments a push up or buoyancy, this implies an upward acceleration. When the ball reaches the surface of the water it has a certain velocity v and the ball jumps out of the water with that velocity, thus the ball reaches some height H in the air and this takes some time t. The total time the ball spends in the air is the time spent to go upwards and the time spent to fall back to the water, both times are equal.


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[6] The sketch shows a body of irregular shape floating at the interface between two liquids identified as 1 and 2. The body has 65% of its total volume immersed in liquid 1, while the rest is immersed in liquid 2. Only the density of liquid 2 is known and, it is also known that the density of liquid 1 is 9/10 of that of liquid 2. Determine: (a) The numerical value of B_{1} / B_{2 } between the buoyancy forces experimented by the body (b) The density of the body.
Solution. The buoyancy B or push up is the upward force experimented by the body immersed in a liquid, and it is equal to the weight of the displaced fluid.


