To convert a density value from kilograms per cubic decimeter (kg/dm³) to kilonewtons per cubic meter (kN/m³), we can use the relationship between these units.

1. **Understand the Units**:
   - \(1 \ \text{kg} = 9.81 \ \text{N}\) (using the standard acceleration due to gravity, \(g = 9.81 \ \text{m/s}^2\)).
   - \(1 \ \text{dm}^3 = 0.001 \ \text{m}^3\).

2. **Conversion from kg/dm³ to kg/m³**:
   - Since \(1 \ \text{dm}^3 = 0.001 \ \text{m}^3\), we multiply by \(1000\) to convert:
   \[
   1950 \ \text{kg/dm}^3 \times 1000 = 1,950,000 \ \text{kg/m}^3
   \]

3. **Convert kg/m³ to kN/m³**:
   - Knowing \(1 \ \text{kg} = 9.81 \ \text{N}\), we can convert from kg/m³ to N/m³:
   \[
   1950 \ \text{kg/m}^3 \times 9.81 \ \text{N/kg} = 1950 \times 9.81 \ \text{N/m}^3
   \]
   - Now, convert N/m³ to kN/m³ by dividing by \(1000\):
   \[
   1950 \times 9.81 \ \text{N/m}^3 = 1950 \times 9.81 \ \times 0.001 \ \text{kN/m}^3
   \]
   \[
   = 19.12 \times 9.81 \ \text{kN/m}^3
   \]
   \[
   = 19111.1 \ \text{kN/m}^3 \approx 19.1 \ \text{kN/m}^3
   \]

The value of \( 1950 \ \text{kg/dm}^3 \) is approximately \( 19111.1 \ \text{kN/m}^3 \).

### Would you like more details or have any questions?

Here are 5 related questions to expand on this information:
1. How do you convert units of force from N to kN?
2. What is the relationship between density and gravity in unit conversions?
3. How would you convert units if gravity was different from \(9.81 \ \text{m/s}^2\)?
4. How do you convert other volume-related units, such as cm³ to m³?
5. What are some practical applications of knowing density in kN/m³?

**Tip:** Always ensure the correct units for each physical quantity when performing conversions to maintain consistency and accuracy.

Learn how to convert 1950 kilograms per cubic decimeter (kg/dm³) to kilonewtons per cubic meter (kN/m³) using detailed step-by-step instructions. This problem involves unit conversions, density calculations, and force conversions.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation