Question

Does a 2-kilogram solid-iron brick have twice as much mass as a 1-kilogram solid-iron brick? Twice as much weight? Twice as much volume?

Short answer

Yes, the 2-kg brick has twice the mass, weight, and volume of the 1-kg brick.

Step-by-step solution

Determine Mass

Mass is a measure of the amount of matter in an object. Since mass is directly proportional to the amount of matter, a 2-kilogram brick does indeed have twice as much mass as a 1-kilogram brick because 2 is twice 1.

Evaluate Weight

Weight is the force exerted by gravity on an object. It is calculated using the equation \( F = mg \), where \( m \) is mass and \( g \) is the gravitational acceleration (approximately \( 9.8 \, m/s^2 \) on Earth). Since the 2-kilogram brick has twice the mass compared to the 1-kilogram brick, and gravity is constant, the 2-kilogram brick also has twice the weight.

Compare Volume

Volume is the amount of space occupied by an object. For solids of the same material, like iron, density is constant. Density is defined as mass divided by volume: \( \text{density} = \frac{\text{mass}}{\text{volume}} \). Since both bricks are made of iron, they have the same density. Therefore, the volume of the 2-kilogram brick will be twice that of the 1-kilogram brick because the mass is doubled, maintaining the constant density.

Key concepts

Density

Density is a fundamental concept in physics that refers to how much mass is contained within a given volume. Imagine density as the compactness of matter in an object. It is calculated using the formula:\[ \text{Density} = \frac{\text{Mass}}{\text{Volume}} \]In this formula, the mass is measured in kilograms and the volume in cubic meters. The resulting density is expressed in kilograms per cubic meter (kg/m³).
It's important to understand that density is a characteristic property of materials. This means that the density of iron, for example, is constant, regardless of the size of the iron piece being measured. Therefore, whether you have a 1-kilogram or a 2-kilogram block of iron, the density remains the same. This property is what allows us to easily compare the volume based on mass when we know the density is constant.
If you double the mass of an object while maintaining its material density unchanged, as in the case of the two iron bricks, you will also double its volume.

Gravitational Force

Gravitational force is the force of attraction between any two masses. On Earth, this force is what gives objects weight. This force can be calculated with the equation:\[ F = mg \]where:

• \( F \) is the gravitational force or weight,
• \( m \) is the mass in kilograms,
• \( g \) is the acceleration due to gravity, approximately \( 9.8 \text{ m/s}^2 \) on Earth's surface.

In the case of the iron bricks, when mass increases, the gravitational force or weight also increases proportionally, because gravitational acceleration \( g \) remains constant. Hence, the 2-kilogram brick has twice the weight of the 1-kilogram brick. This is why heavier objects exert more weight than lighter ones under the same gravitational conditions.

Volume and Mass Relationship

The relationship between volume and mass is a key concept in understanding how objects occupy space. When considering objects made of the same material, such as the solid iron bricks described in the exercise, the characteristics of the material dictate how mass and volume relate to each other. This relationship can be explained by the formula for density:\[ \text{Density} = \frac{\text{Mass}}{\text{Volume}} \]Since density is constant for a given material, any change in mass directly affects volume. In simpler terms, if the mass of an object doubles, as seen with the comparison of the 2-kilogram iron brick to a 1-kilogram brick, the volume also doubles. This is because each kilogram of the material occupies the same amount of space, meaning more mass means more volume. Thus, maintaining constant density allows us to predict volume changes simply based on changes in mass.