3. Use the relationships you just described to compute the values needed to fill

Question

3. Use the relationships you just described to compute the values needed to fill in the blanks in the table in Fig. A1.4.1. 4. Imagine a rectangular prism of pure water whose density (p) is 1,0 g/cm'. The base of this imaginary prism is 1 cm on a side, and the remaining side of the prison is the water depth (a) measured in cm. The mass (m) of that prism of water, expressed in grams, is related to the water depth (a) in the following way: the value of ais.. the value of m. One way of restating Archimedes' Principle is that the mass of a block that is floating in a fluid is equal to the mass of the fluid displaced by the block. Imagine that we have a solid block in which all of the sides are 1 cm longa cube with a volume of 1 cm (Fig. A1.4.2A). We set it in a beaker of pure water and find that, when the block and water come to rem, 70% of the block is submerged under water, so a = 0.7 cm and b = 1.0 cm (Fig. A1.4.2B). block (a cube) V= 1 cm3 water density (p) = 1.0 g/cm3 Figure A1.4.2 1. What is the volume of water displaced by the block? _cm 2. The density of the water (water) is 1,0 g/cm, so what is the mass of water displaced by the block? Multiply the volume of water by the density of the water. The mass of water displaced by the block isg. 3. Using the previous answer, apply Archimedes' Principle to find the mass of the block. The mass of the entire block (m) 4. The block is a cube with a volume of 1 cm'. Now that you know the mass and the volume of the block, what is the density. of the block (Pblock)? Pblock = - g/cm 5. The submerged part of the block is 70% of the total volume of the block. What is the ratio of the density of the block to the density of the water; that is, what is Plock divided by Pwater? Express your answer as a percentage (e.g., 0.7 - 70%) Pblock/pwater 6. Using words rather than numbers, compare the ratio of the volume of the submerged part of the block (Vubmerged) to the total volume of the block (Voul) with the ratio of the density of the block (Polock) to the density of the water (water). The ratio Vaubmerged/Votal is the ratio Palack/pwater.

Explanation / Answer

Ans:

1. Volume of water displaced = 0.7 cm * 1 cm * 1 cm = 0.7 cm3

2. Mass of displaced water = 0.7 cm3 * 1 g/cm3 = 0.7 gm

3. 1 cm3 of block displaced 0.7 cm3 of water which had 0.7 gm weight

so

0.7 gm of water is displaced by block so weight of block is 0.7 gm.

4. Density of block = 0.7 gm/cm3
5. p(block)/p(water) = 0.7/1 = 0.7

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