Gram force

Unit system
Unit of	Force
Symbol	gf
Named after

Introduction

The gram force (symbol: gf) is a unit of force in the centimetre–gram–second (CGS) system of units. It is defined as the force exerted by one gram of mass in a standard gravitational field. The gram force is a non-SI unit that is still used in some contexts, particularly in engineering and materials science.

Definition

The gram force is defined as the force exerted by a mass of one gram under the influence of standard gravity, which is defined as exactly 9.80665 m/s². Therefore, one gram force is equal to:

1 gf = 1 g × 9.80665 m/s² = 9.80665 mN

Relation to Other Units

The gram force is related to other units of force, such as the newton and the dyne.

Newton

The newton (symbol: N) is the SI unit of force. One newton is defined as the force required to accelerate a one-kilogram mass by one metre per second squared. The relationship between the gram force and the newton is given by:

1 gf = 9.80665 mN = 0.00980665 N

Dyne

The dyne (symbol: dyn) is another unit of force in the CGS system. One dyne is defined as the force required to accelerate a one-gram mass by one centimetre per second squared. The relationship between the gram force and the dyne is given by:

1 gf = 980.665 dyn

Applications

The gram force is used in various applications where small forces are measured or where the CGS system is preferred. Some common applications include:

• Material testing: In material testing, gram force is often used to measure the force required to deform or break a material.
• Calibration: Gram force is used in the calibration of small force measurement devices, such as load cells and force gauges.
• Engineering: In some engineering fields, particularly those dealing with small components, gram force is used to specify the force exerted by or on a component.

Historical Context

The gram force, like other CGS units, was more commonly used before the widespread adoption of the SI system. The CGS system was developed in the 19th century and was widely used in scientific research and engineering. However, with the adoption of the SI system in the mid-20th century, the use of CGS units, including the gram force, has declined.

Conversion to SI Units

To convert gram force to newtons, the following conversion factor is used:

1 gf = 0.00980665 N

To convert newtons to gram force, the inverse conversion factor is used:

1 N = 101.971621 gf

Conclusion

The gram force is a unit of force in the CGS system that is defined as the force exerted by one gram of mass in a standard gravitational field. Although it is not an SI unit, it is still used in certain applications where small forces are measured or where the CGS system is preferred. Understanding the relationship between gram force and other units of force, such as the newton and the dyne, is important for converting measurements and ensuring accuracy in scientific and engineering contexts.

See Also

• Force
• Newton (unit)
• Dyne
• Centimetre–gram–second system of units
• Standard gravity