Question

A truck loaded with \(2 \mathrm{~m}^{3}\) dry sand appears to weigh " 3 tons" more than the weight of the empty truck. What is the meaning of the term " 3 tons", and what is the volumetric weight of the sand?

Short answer

Answer: The term "3 tons" in this context refers to the weight of the dry sand loaded on the truck, which is 3000 kg. The volumetric weight (density) of the sand is 1500 kg/m³.

Step-by-step solution

Understand "3 tons" in context

In this context, "3 tons" represents the difference in weight between the loaded truck and the empty truck, which means it is the weight of the dry sand that the truck is carrying.

Calculate the Weight of the Sand in Metric Units

Since "3 tons" refers to the weight of the dry sand, we need to convert it into kilograms (the usual metric unit for weight) for further calculation. 1 ton = 1000 kilograms, so 3 tons = 3000 kilograms. The dry sand weighs 3000 kg.

Calculate the Volumetric Weight of the Sand

The volumetric weight of the sand, also known as density, is found by dividing the weight of the sand by its volume. We are given that the volume of the sand is 2 cubic meters (m³). Using the formula for density, 𝜌 = m/V, where 𝜌 is the density, m is the mass (weight) of the sand, and V is the volume of the sand, we get: 𝜌 = \frac{3000 \mathrm{kg}}{2 \mathrm{m^3}} = 1500 \frac{\mathrm{kg}}{\mathrm{m^3}}

Interpret the Results

So the term "3 tons" refers to the weight of the dry sand loaded on the truck, which is 3000 kg. The volumetric weight (density) of the sand is 1500 kg/m³.

Key concepts

Soil Mechanics

Soil mechanics is a branch of civil engineering that focuses on the behavior of soil and its applications in construction and design. It considers how soils respond to various forces and changes in the environment, such as load-bearing, compaction, and water content.

A crucial aspect of soil mechanics is understanding the characteristics and properties of soil, including density, shear strength, and consolidation. Properties like the volumetric weight of soil are fundamental for engineers to calculate the load soil can carry, how it will settle over time, or how it will behave during an earthquake.

Density Calculation

Density calculation is fundamental to understanding the properties of materials. In soil mechanics, it provides insight into the compaction of soil and how much weight it can support.

The density of a substance is its mass per unit volume, typically expressed in kilograms per cubic meter (kg/m³) or pounds per cubic foot (lb/ft³) in the Imperial system. In the case of our truck and sand problem, knowing the density allows us to understand the mass of sand that can be transported without overloading the vehicle. The step-by-step solution efficiently converts tons to kilograms and then uses this to find the sand density.

Mass-Volume Relationship

The mass-volume relationship is crucial for determining the density of a material. It's directly applicable in scenarios where knowing the available volume and required mass allows the calculation of the material's density.

This relationship is particularly important when dealing with materials like sand in construction, as it helps in estimating the material amounts needed and the transport means required. The exercise demonstrates a practical application of the mass-volume relationship by dividing the mass of sand (3000 kg) by its volume (2 m³) to arrive at its density (1500 kg/m³). The exercise improvement advice emphasizes the importance of understanding such relationships to solve real-world problems in soil mechanics and construction.