In the world of physics and engineering, precise conversions between units of measurement are crucial for accurate calculations and design. One such conversion involves converting forces expressed in dyne per square centimeter (dyne/cm²) to newton per square millimeter (N/mm²). While both dyne and newton are units used to measure force, their magnitudes differ significantly, necessitating a conversion when switching between these units in scientific calculations.
This article will explore the conversion formula for converting 85.8 dyne/cm² to newton/mm², step by step, providing a detailed explanation of the relationship between the units, the conversion factors, and how to calculate this conversion.
Units Involved
To begin, it’s essential to understand the two units involved in this conversion:
- Dyne (dy): The dyne is a unit of force in the centimeter-gram-second (CGS) system of units. It is defined as the force required to accelerate a mass of one gram by one centimeter per second squared. One dyne is equivalent to 10−510^{-5}10−5 newtons (N).
- Newton (N): The newton is the SI (International System of Units) unit of force. It is defined as the force required to accelerate a mass of one kilogram by one meter per second squared. One newton is equal to 10510^{5}105 dynes.
- Square Centimeter (cm²): A unit of area in the metric system, equal to the area of a square with sides of one centimeter in length.
- Square Millimeter (mm²): Similarly, this is a unit of area in the metric system, representing the area of a square with sides of one millimeter in length. One millimeter is 10−110^{-1}10−1 centimeters, so 1 mm2=10−2 cm21 \, \text{mm}^2 = 10^{-2} \, \text{cm}^21mm2=10−2cm2.
Given these units, the problem at hand requires us to convert the force density of 85.8 dyne/cm² into newton/mm².
Step-by-Step Conversion Process
To carry out this conversion, we need to account for both the force and the area units involved. Here’s the step-by-step process:
1. Convert Dyne to Newton
We know that:1 dyne=10−5 newtons1 \, \text{dyne} = 10^{-5} \, \text{newtons}1dyne=10−5newtons
Thus, to convert the force from dynes to newtons, we multiply the number of dynes by 10−510^{-5}10−5.
2. Convert Square Centimeter to Square Millimeter
We also know the relationship between the units of area:1 cm2=102 mm2=100 mm21 \, \text{cm}^2 = 10^2 \, \text{mm}^2 = 100 \, \text{mm}^21cm2=102mm2=100mm2
Therefore, to convert from dyne/cm² to dyne/mm², we divide the value in dyne/cm² by 100.
3. Apply the Conversion to the Given Value
We are tasked with converting 85.8 dyne/cm² to newton/mm². Using the conversion factors above:Conversion formula=85.8 dyne/cm2×10−5 newtondyne×1 cm2100 mm2\text{Conversion formula} = 85.8 \, \text{dyne/cm}^2 \times \frac{10^{-5} \, \text{newton}}{\text{dyne}} \times \frac{1 \, \text{cm}^2}{100 \, \text{mm}^2}Conversion formula=85.8dyne/cm2×dyne10−5newton×100mm21cm2
This formula simplifies to:Value in newton/mm2=85.8×10−5×1100\text{Value in newton/mm}^2 = 85.8 \times 10^{-5} \times \frac{1}{100}Value in newton/mm2=85.8×10−5×1001
Simplifying further:Value in newton/mm2=85.8×10−7\text{Value in newton/mm}^2 = 85.8 \times 10^{-7}Value in newton/mm2=85.8×10−7
4. Final Answer
The result is:85.8 dyne/cm2=8.58×10−6 newton/mm285.8 \, \text{dyne/cm}^2 = 8.58 \times 10^{-6} \, \text{newton/mm}^285.8dyne/cm2=8.58×10−6newton/mm2
Conclusion
The conversion of 85.8 dyne/cm² to newton/mm² yields a result of 8.58×10−6 newton/mm28.58 \times 10^{-6} \, \text{newton/mm}^28.58×10−6newton/mm2. Understanding the relationship between the CGS and SI units, as well as the importance of both force and area in such conversions, is essential for accurate scientific calculations.
This detailed breakdown ensures that anyone can confidently convert between dyne/cm² and newton/mm², a crucial step in many fields of physics and engineering where accurate measurements are vital for success.