Question

Gold has a specific gravity of almost 20. A 5-gallon bucket of water weighs 40 pounds. How much would a 5 -gallon bucket of gold weigh?

Short answer

The 5-gallon bucket of gold would weigh 800 pounds.

Step-by-step solution

Understand Specific Gravity

Specific gravity is the ratio of the density of a substance to the density of a reference substance, usually water for liquids. In this problem, gold has a specific gravity of 20, meaning it is 20 times denser than water.

Determine Weight of Water

We know a 5-gallon bucket of water weighs 40 pounds. This gives us a reference for comparing the weight with gold.

Calculate Weight of Gold

Multiply the weight of the water by the specific gravity of gold to find the weight of the gold: \[\text{Weight of gold} = 40 \text{ pounds} \times 20 = 800 \text{ pounds}\]

Verify Calculation

Reassess the relationship between specific gravity and weight; if gold is 20 times denser than water, then multiplying the weight of the water by 20 should indeed give us the correct weight for the gold.

Key concepts

Density: The Base Concept

In our exercise, density plays a pivotal role when considering specific gravity and weight. Density is a property of matter, representing how much mass is contained within a unit volume of a substance. For instance, gold is a dense metal, meaning a small amount of it weighs quite a bit compared to other substances. One important formula expresses density as \[ \text{Density} = \frac{\text{Mass}}{\text{Volume}} \].

• Density depends on both mass and volume. A larger mass in a given volume means higher density.
• In our example, the density of water is the reference for calculating how dense gold is compared to it.

When we talk about specific gravity, we often refer to the density of substances. Gold, with its specific gravity of 20 from the exercise, is 20 times denser than the reference substance, which is water in this scenario.

Weight Calculation: The Process Simplified

Let's delve into how we calculate weight using specific gravity. The specific gravity tells us how many times denser gold is compared to water. Given that water fills the 5-gallon bucket and weighs 40 pounds, we have a baseline for calculations. To find how heavy gold would be in the same volume, we use its specific gravity:

• Specific gravity of gold = 20.
• Weight of 5-gallon water bucket = 40 pounds.
• Weight of 5-gallon gold bucket = 40 pounds × 20.

The total weight calculation is straightforward. Simply multiply the known weight of water by the specific gravity to understand how much the same volume of gold weighs: \[ 40 \text{ pounds} \times 20 = 800 \text{ pounds} \]. This shows us how the weight calculation reflects density differences between substances.

Reference Substance: The Importance in Comparison

Using a reference substance like water aids in understanding specific gravity. Specific gravity compares the density of a material with that of the reference substance.

• Water is commonly used as the standard reference due to its prevalence and well-known properties.
• It helps simplify calculations by providing a direct comparison for other substances' densities.

In practical terms, knowing that water has a specific gravity of 1 allows us to see relative density quickly. For instance, a specific gravity of 20 means gold has a density 20 times higher than that of water. This approach is particularly useful in various fields, such as geology and engineering, where the density properties of materials are crucial. By comparing to a standardized substance, it's easier to communicate and calculate the properties of different materials.