The question "What is the formula of GF?" is a bit ambiguous. Based on the provided context, it seems like "GF" might refer to gram-force. Therefore, this response will focus on explaining gram-force and how it relates to force and acceleration.
Understanding Gram-force
Gram-force (gf) is a unit of force defined as the force exerted on a mass of 1 gram by standard gravity on Earth. It's a convenient unit, especially in contexts where dealing with small masses is common. It’s crucial to differentiate it from the standard unit of force, the Newton (N), which uses the standard kg unit of mass.
Relationship with Dynes
The reference provided states: 1 g m = 1 g × 980 c m / s 2 = 980 dynes. This essentially means one gram-force is equal to 980 dynes. A dyne is the unit of force in the CGS (centimeter-gram-second) system.
Deriving the Gram-Force Formula
- Acceleration due to gravity (g): On Earth, g is approximately 9.8 m/s² or 980 cm/s².
- Force (F): According to Newton's second law, Force = mass × acceleration (F = ma).
Given these, we can express gram-force using the following:
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Conversion of mass: We are using 1 gram mass.
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Application of F=ma: Applying Newton’s second law:
- Gram-force (1 gf) = 1 g × 980 cm/s²
- 1 gf = 980 dynes
Key Insights
- Not a Fundamental Unit: Gram-force is not a fundamental unit of measurement like the Newton. It's derived based on the specific scenario of mass and gravity.
- Practical Application: It is mostly employed when dealing with very small forces in fields such as engineering and materials science.
- Conversion is Key: When working with other unit systems (e.g., SI system), you'll need to convert gram-force to Newton to use them.
Table Summary
| Item | Value |
|---|---|
| 1 Gram-force | 980 dynes |
| g (on Earth) | 980 cm/s² or 9.8 m/s² |
| Mass used | 1 gram |
Therefore, the formula of gram-force (GF) can be summarized as the force exerted on a 1-gram mass due to the earth's gravitational acceleration, which is equivalent to 980 dynes.
