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

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

Step-by-step solution

Understanding Specific Gravity

Specific gravity is the ratio of the density of a substance to the density of a reference substance; typically, water is used as the reference. Given that gold has a specific gravity of 20, it essentially means that gold is 20 times denser than water. Hence, for any given volume, gold will weigh 20 times more than the same volume of water.

Calculating Water Weight

A 5-gallon bucket of water weighs 40 pounds, as provided in the problem statement. This weight will remain our reference for calculating the weight of the bucket full of gold.

Applying Specific Gravity to Gold

If gold has a specific gravity of 20, then a 5-gallon bucket of gold would weigh 20 times the weight of the same volume of water. Thus, we multiply the weight of the bucket of water by the specific gravity of gold: \[\text{Weight of gold} = 40 \text{ pounds} \times 20 = 800 \text{ pounds}.\]

Key concepts

Density

Density is a fundamental concept in science that describes how much mass is contained within a certain volume. Imagine placing a small piece of steel and a larger piece of sponge in your palm. Even though the sponge is larger, the steel will feel heavier. This is because steel is denser than the sponge. The formula for density is expressed as: \[ \text{Density} = \frac{\text{Mass}}{\text{Volume}} \]In this context, density helps us understand how compact the mass of a substance is. Substances with higher density will have more mass packed into the same volume compared to those with lower density. Understanding density allows us to predict how substances will behave in different situations, like sinking or floating, or how different materials will compare in terms of weight when subjected to the same volume.

Weight Calculation

Weight calculation is essential for determining how heavy an object is based on its mass and the gravitational force acting on it. In everyday terms, weight is what we feel when we lift an object. To calculate weight, we use the formula:\[ \text{Weight} = \text{Mass} \times \text{Gravity} \]However, when talking about specific gravity, which involves a ratio, we compare weights of different substances relative to water. This simplifies our tasks when handling materials like gold. For example, if we calculate the weight of gold using specific gravity, we rely on understanding the weight of the same volume of water first, as seen in our problem where we compare a 5-gallon bucket of water to the same volume of gold.

Gold Density

Gold, known for its rarity and luster, is highly valued not only for its beauty but also for its density. The density of gold is quite high, approximately 19.32 grams per cubic centimeter, surpassing many other metals and substances. This high density contributes to gold's weightiness, even in small quantities. When specific gravity is used, it conveys this density relative to water. Gold's specific gravity being around 20 implies that for the same volume, gold is 20 times denser than water. Thus, in practical terms, a gold object will weigh significantly more than a water object of the same size, as evidenced by the example calculation involving the 5-gallon bucket.

Water Weight Comparison

Comparing the weight of different substances to a known reference is a common practice in science. Water is typically used as this benchmark due to its widespread availability and consistent properties at various conditions. In our example, a 5-gallon bucket of water weighs 40 pounds. This weight serves as the baseline for comparing other substances, such as gold. By knowing the specific gravity of gold, we can easily estimate how much more it will weigh compared to water. Since gold's specific gravity is 20, it will be 20 times heavier than the same volume of water, making the 5-gallon bucket of gold weigh 800 pounds. This comparative approach simplifies calculations and is widely used in material sciences and industries dealing with different liquids and solids.