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...
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 buoyancy: 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 floats on water (used in fishing lines, so 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 on water (denser than gasoline? No, wait—if cork floats on water, its density is \(< 1.000\). For example, if an object floats in a fluid, \(\text{density of object} < \text{density of fluid}\). Since cork floats in water, \(
ho_{\text{cork}} <
ho_{\text{water}} = 1.000\ \text{g/mL}\). Also, substances like copper (\(8.89\)), silver (\(10.5\)), etc., sink in water (denser than water), confirming that floating objects (like cork) have lower density than the fluid. So cork’s density is less than \(1.000\ \text{g/mL}\), likely similar to or less than gasoline’s \(0.68\ \text{g/mL}\) (though we infer from buoyancy in water).

Answer:

The density of cork must be less than the density of water (1.000 g/mL) because objects float in a fluid when their density is less than the fluid’s density. Since cork is used on fishing lines (implying it floats in water), its density (\(
ho_{\text{cork}}\)) satisfies \(\boldsymbol{
ho_{\text{cork}} < 1.000\ \text{g/mL}}\). This is consistent with the buoyancy principle: if an object’s density is less than the surrounding fluid’s density, it displaces a weight of fluid equal to its own weight (Archimedes’ principle) and floats. For example, substances like copper (\(8.89\ \text{g/mL}\)) or silver (\(10.5\ \text{g/mL}\)) sink in water (denser than water), while cork (and gasoline, \(0.68\ \text{g/mL}\)) floats (less dense than water). Thus, cork’s density is lower than water’s, enabling it to float and function in fishing lines.