Question

use the densities shown in the table to answer the question. corks are used on fishing lines because they float. develop an explanation supported by the data about the density of cork.
substance density (g/ml)
water (at 4.0°c) 1.000
hydrogen 0.00090
carbon dioxide xxx
gasoline 0.68
copper 8.89
silver 10.5
mercury 13.595
tungsten 19.3
corks are used on fishing lines because they float. what can you say about the density of cork?
250 words remaining

Explanation:

To determine the density of cork, we use the principle of flotation: an object floats in a fluid if its density is less than the fluid’s density. The table shows water (at \(4.0^\circ\text{C}\)) has a density of \(1.000\ \text{g/mL}\). Cork is used on fishing lines because it floats in water, so its density must be less than \(1.000\ \text{g/mL}\). Comparing to other substances: gasoline has a density of \(0.68\ \text{g/mL}\), and cork floats in gasoline too (if we assume, though not directly stated, but the key is water). Since floating in water implies \(\text{density}_{\text{cork}} < \text{density}_{\text{water}}\), cork’s density is less than \(1.000\ \text{g/mL}\). This explains why it floats—its density is lower than water’s, so the buoyant force (equal to the weight of displaced water) exceeds cork’s weight, causing it to float.

Answer:

The density of cork must be less than \(1.000\ \text{g/mL}\) (the density of water at \(4.0^\circ\text{C}\)). An object floats in a fluid when its density is less than the fluid’s density. Since cork floats in water (used on fishing lines to float), its density is lower than water’s density (\(1.000\ \text{g/mL}\)). For example, gasoline has a density of \(0.68\ \text{g/mL}\), and if cork floats in gasoline too (consistent with flotation principles), its density is also less than \(0.68\ \text{g/mL}\) or at least less than water’s. This lower density means the buoyant force from displaced water (or other fluids) is greater than cork’s weight, enabling it to float, which is why it’s useful on fishing lines.