The following diagrams show pictures of blocks of different densities that resti

Question

The following diagrams show pictures of blocks of different densities that resting at the bottom of a container filled with water. The mass and total volume of each of the blocks is given below each of the diagrams Rank each of the scenarios from least to greatest on the basis of the the magnitude of the buoyant force (F_B) on each of the blocks. (If two are exactly equal then list them alphabetically.) Rank each of the scenarios from least to greatest on the basis of the the magnitude of the NET force on each of the blocks. (If two are exactly equal then list them alphabetically.) Imagine that prior to the block being on the bottom of the container that the block is placed at the surface of the liquid and then released. By inspection, and knowing that the density of water is 1 g/cm^3, in which of the scenarios above will the block have the greatest acceleration? (If two have the highest acceleration then select both.)) What is the value of the block with the greatest acceleration in part c? (Pick up to be positive and down to be negative.)

Explanation / Answer

a) buoyant force is equal to the weight of the fluid displaced, hence the one which displaces maximum fluid would experiance greatest buoyant force.

D < E < A < C < B < F

b) net force = weght - buoyant force

F = mg - dVg = (m-V) g

as density of water is one unit

FA = (60-20)g = 40g

FB = (65-15) = 50 g

FC = (40-30)g = 10g

FD = (12-10)g = 2g

FE = (20-15)g = 5g

FF = (70 -60) =10g

so the rankings are

D < E < F=C <A <B

c) the one with greatest net force would have greatest acceleration.

so B would have greatest acceleratiion.

d) a = FB/m = 50 g/65 =7.54 m/s2

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