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Chapter 1: Problem 41

Define one gram force.

Short Answer

Expert verified
Answer: One gram force (gf) is an older unit of force defined as the force exerted by the Earth's gravity on a mass of one gram. In modern terms, force is usually measured in Newtons (N), which is the SI unit of force. One gram force is approximately equal to 0.00981 Newtons.

Step by step solution

01

Definition of one gram force

One gram force (gf) is an older unit of force that was used before the widespread use of the modern metric system (SI units). Gram force is based on the weight of a mass due to gravity. Specifically, one gram force is defined as the force exerted by the Earth's gravity on a mass of one gram.
02

Relation of gram force to Newtons

In modern terms, force is usually measured in Newtons (N), which is the SI unit of force. One Newton is defined as the force needed to accelerate a mass of one kilogram by one meter per second squared (1 N = 1 kg * m/s²). To understand the relation between gram force and Newton, it's important to recall that 1 gram is equal to 0.001 kilogram (1 g = 0.001 kg).
03

Conversion between gram force to Newtons

In order to convert gram force to Newtons, we first need to find the acceleration due to gravity, which is approximately 9.81 m/s². The conversion formula is: 1 gf = 1 g * 9.81 m/s² Since 1 g = 0.001 kg, we can write: 1 gf = 0.001 kg * 9.81 m/s² Upon calculation, we have: 1 gf ≈ 0.00981 kg * m/s² = 0.00981 N In summary, one gram force is defined as the force exerted by the Earth's gravity on a mass of one gram, and it is approximately equal to 0.00981 Newtons.

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