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 weighs 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, typically water for liquids and solids. For gold, the specific gravity is approximately 20, which means it is 20 times denser than water.

Determine the Density of Water

To find the weight of the gold, we first need to understand that the density of water is about 8.34 lb/gallon. Given the 5-gallon bucket of water weighs 40 pounds, this matches the density of water as 5 gallons × 8.34 lb/gallon = 41.7 pounds (which is acceptable for rounding to 40 pounds for this problem).

Apply Specific Gravity to Gold

Since gold is 20 times denser than water, a 5-gallon bucket of gold would weigh 20 times as much as a 5-gallon bucket of water.

Calculate the Weight of Gold

To find the weight of the gold, multiply the weight of the water by the specific gravity of gold: 40 pounds × 20 = 800 pounds.

Key concepts

Understanding Density

Density is a fundamental concept in physics that describes how much mass is contained in a given volume. It is often expressed with the formula \( \text{Density} = \frac{\text{Mass}}{\text{Volume}} \). This means that density is all about how tightly packed the molecules of a substance are.

• A higher density indicates that the substance's molecules are more tightly packed.
• Conversely, a lower density means that the molecules are more spread out.

This concept is crucial when discussing specific gravity, which compares the density of a material to that of water. Understanding density helps us comprehend why certain materials, like gold, weigh more than others of the same volume.

Gold and Its High Density

Gold is famously known not just for its beauty and value but also for its high density. This means it has a lot of mass in a small volume. Gold’s specific gravity is around 20, which tells us it is 20 times denser than water.

• This density is the reason gold feels so heavy when you hold it.
• The specific gravity helps us quickly compare it to water.

For example, if you had a 5-gallon bucket of water, it would weigh about 40 pounds. However, replacing water with gold would multiply this weight by 20, giving a hefty 800 pounds.

The Weight of Water

Water is often used as a standard for measuring density because it has a density value of 1 g/cm³ in scientific terms (or roughly 8.34 lb/gallon). A common item for understanding water’s weight is the 5-gallon bucket, which weighs around 40 pounds.

• Knowing the weight of water helps to use specific gravity to compare other substances to it.
• Since a bucket of water weighs 40 pounds, this creates a baseline for other calculations.

By understanding water’s role as a reference, we can easily calculate how much more dense substances like gold weigh by using their specific gravity values.