Use the pressure-depth relationship, p = Ïgh ,to showmathematically that the buoyant force on a wooden cube being heldin a liquid is equal to the weight of the volume of liquid itdisplaces.

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Sixta KovacekLv2

27 May 2019

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As shown in the figure below, a wooden cube measuring 20.0 cm oneach side floats in water with 80.0% of its volume submerged.Suspended by a string below the wooden cube is a metal cube. Themetal cube measures 10.0 cm on each side and has a specific gravityof 6.00. This means that the density of the cube is 6.00 timeslarger than that of water, which we take to be 1000 kg/m3.

(a) Which cube has a larger buoyant force acting on it?

i. the wooden cube

ii. the metal cube

iii. the buoyant forces are equal for both

(b) Taking the density of water to be 1000 kg/m³,what is the density of the wooden cube? (kg/m3)

(c) What is the tension in the string between the cubes? Assumethe string itself has negligible mass and volume. Use g =9.8 m/s². (N)

(d) The pair of blocks is now placed in a different liquid. Whenthe blocks are at equilibrium in this new liquid, the buoyant forceacting on the wooden cube is exactly the same as the buoyant forceacting on the metal cube. What is the density of this new liquid?(kg/m3)

A wooden block floats in water, and a steel object is attached to the bottom of the block by a string as in Figure OQ14.3. If the block remains floating, which of the following statements are valid? (Chose all correct statements.)

(a) The buoyant force on the steel object is equal to its weight.

(b) The buoyant force on the block is equal to its weight.

(d) The tension in the string is less than the weight of the steel object.

(e) The buoyant force on the block is equal to the volume of water it displaces.

salmonhare193

In the figure, a cube of edge length L = 0.344 m and mass 1140 kg is suspended by a rope in an open tank of liquid of density 1.03E+3 kg/m3. Find (a) the magnitude of the total downward force on the top of the cube from the liquid and the atmosphere, assuming atmospheric pressure is 1.00 atm, (b) the magnitude of the total upward force on the bottom of the cube, and (c) the tension in the rope. (d) Calculate the magnitude of the buoyant force on the cube using Archimede's principle.