Question

If an object has a constant density \(\delta\) and a volume \(V\), what is its mass?

Short answer

Mass is calculated by \( m = \delta \times V \).

Step-by-step solution

Understand the Given Information

We know that density, denoted here as \( \delta \), is a measure of how much mass there is per unit volume for an object. The object has a given volume \( V \). Our task is to find the mass given these two values.

Use the Formula for Density

The formula relating density \( \delta \), mass \( m \), and volume \( V \) is \( \delta = \frac{m}{V} \). This equation states that density is equal to mass divided by volume.

Rearrange the Formula to Find Mass

To find the mass \( m \), rearrange the formula to solve for \( m \). Multiply both sides of \( \delta = \frac{m}{V} \) by \( V \) to isolate \( m \): \( m = \delta \times V \).

Substitute the Values

Substitute the given values of density \( \delta \) and volume \( V \) into the formula \( m = \delta \times V \) to calculate the mass. Ensure all units are consistent before performing the calculation.

Key concepts

Density

Density is a fundamental concept in understanding how matter is packed into a given space. It's like figuring out how tightly packed a crowd is in a room. When we talk about density, we refer to the relationship between mass and volume. In more straightforward terms, density tells us how much stuff is crammed into a certain amount of space. A denser object has more mass in the same volume compared to a less dense one. For example:

• A brick and a sponge of the same size - the brick is denser because it is heavier for its size.
• Oil and water - Oil is less dense than water; that’s why it floats on top.

Understanding density is essential in various fields, from physics to engineering, as it helps in predicting how substances will behave under different conditions.

Volume

Volume refers to the amount of space an object takes up. Imagine filling a container with water and knowing how much water it holds – that's volume. It's measured in units like liters or cubic meters. The concept of volume is everywhere around us. Think about:

• The amount of liquid your bottle can contain.
• The space inside a box.
• The area your bed occupies in your room.

To calculate the volume of regular shapes, like cubes or spheres, we use simple formulas. For example: - For a cube: - Volume = side length × side length × side length, or - Volume = length³. Understanding volume helps in real-life as it contributes to planning activities like packing, construction, or even cooking.

Formula for Density

The formula that connects mass, density, and volume provides a clear pathway to solving many practical problems in physics and engineering. The core formula is written as \( \delta = \frac{m}{V} \), where:

• \( \delta \) is the density (mass per unit volume),
• \( m \) is the mass, and
• \( V \) is the volume.

If you need to find the mass, the formula can be rearranged to \( m = \delta \times V \). This rearrangement is essential when you know the density and volume but need the mass.By plugging the known values into the formula, you can easily compute the unknown variable. This process is especially useful in experiments, quality control in manufacturing, and in designing materials with specific properties.