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I am attempting to correct a previous, unclear question. I was doing an assignment on rollercoasters and it stated that $g$-force was a major part of rollercoaster safety. It also related $g$-force to Newton's third law, which is about force pairs (equal and opposite). I was simply wondering why $g$-force correlates to Newton's third law because I thought it was simply the force of gravity on an object. More specifically, is g-force part of a force pair, and if so, how? Please try to keep the answers as simple as possible because we just got introduced to this concept of g-force very recently. Thanks!

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  • $\begingroup$ TLDR: "G-force" does not mean "force." It means "acceleration." The "g" in "g-force" tells you the scale: The acceleration that you feel when you stand still on Earth's surface (your acceleration due to gravity) equals one gee. Two gees is twice that amount of acceleration, and so on. $\endgroup$ Commented May 21 at 13:43

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"G-Force" is a colloquial term. However, it is indeed a very common one. G-forces show up most commonly in systems where one is constrained to accelerate at a certain rate (although you will hear it elsewhere). In a situation such as a roller coaster on a track or a seatbelt in a car crash, an object is compelled to accelerate. As the coaster goes around a corner, the steel pipes supporting the cart push with however much force is required to complete the turn at a given speed. In a car crash, the seat belt provides however much force is required to decelerate the passenger at the same rate as the car is decelerating.

How much force? It depends. F=ma. The constraint will apply however much force it takes to achieve the acceleration. To achieve a $5\frac{m}{s^2}$ deceleration of a $20 \text{kg}$ child requires $100 N$ of force. The same deceleration on a $60 \text{kg}$ adult requires $300 N$ of force. If you have a roller coaster full of children and adults, each one will be arrested with a different force, but they will all experience the same acceleration.

We can measure this acceleration in "gees" (usually written as "gee" rather than "g" to avoid confusion with grams). $1\text g = 9.8\frac{m}{s^2}$. It's just another unit of acceleration.

Why do we use gee's? It's because its intuitive. If I say you are experiencing 2 gees on a roller coaster, you can intuitively think of it as being the same amount of force as if you had to carry a clone of yourself.

The term "g-force" is confusing and ambiguous. Quite often g-force is an acceleration, not a force. If someone is measuring g-force in gee's, they're actually measuring an acceleration. One must multiply by a mass to get a force. Pay attention to the context to make sure you understand whether a speaker is talking of an acceleration or a force.

The connection to Newton's third law is that where there is an acceleration, there is always a force (or a pseudoforce, in a rotating frame, which you'll learn about later). And that force always comes in pairs. If the seatbelt is pushing back on you with $200 N$ to decelerate you, you must be pushing back on the belt with an equal and opposite reaction of $200N$. If that force is too much for the seatbelt, it will tear. This is why child-seats have a weight limit to them. Above a certain weight, the seat is no longer designed to withstand the forces that will occur when decelerating in a car accident.

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