# Calculating G-force | Top Marks QA #2

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Today’s topic is G-Force, which is a hard topic in HSC Physics.

Its definition is that it’s the apparent weight felt due to acceleration. So if anyone is standing on a surface vertically, he will experience two forces. The first one, the weight force, due to the earth’s gravitational field and has given by the formula: w=mg, as we’ve studied in an earlier dot point. The second one, is the normal force, which is supplied by the surface with the intention to prevent breaking down through the surface. So the normal force on earth is generated upwards because our surface is usually below us.

G-force is the ratio between the magnitude (which means the size) of the normal force and the weight force. We’re not considering directions here. We only considering a size or the magnitude of the normal force or the weight force.

So to work out a formula or more full formula for G-Force we have to have separate formula for weight and normal force.

So directly, the normal force and weight force will act together to give a resultant force which we call Fnet or net force. Because normal force and weight force on earth are usually on opposite directions to each other, where the normal force is upwards and weight force is downwards, we can put the absolute value sign around them and minus sign in between them to show the opposite directions.

The net force of an object is given by Newton’s Second Law to be ma, and then weight force is given by the formula to be mg.

So if I substitute the ma and g into an equation here I will get ma = | N – mg |.

Noticed that this g here is always positive 9.8 in Physics so we don’t have to put an absolute value sign around it.

Now if we make normal force a subject then normal force is now equal to ma + mg.

Now we can insert the formula for normal force back into the G-Force formula so normal force goes on a top size of the normal force magnitude of normal force is equal to ma + mg and size of the weigh force is equal to mg.

And if we simplify that formula, it give us 1 + a/g.

Now in your school exams or the HSC, questions on G-Force will be focused on calculating or estimating G-Force at a particular position using this formula. Now if we use this formula, we’ll always assumes that upwards is the positive direction – you always assume that upwards is always a positive. So if a here is positive then the object is accelerating upwards. If a is zero then the object is not accelerating upwards or downwards, it’s just staying there vertically. If a is negative then the object is accelerating downwards.

Now, usually when the object is accelerating upwards, because acceleration a would be positive, if you substitute into this formula, G-Force will be greater than 1. If you look back at this formula when you’re accelerating upwards your normal force needs to be greater than the weight force. So it satisfies this formula as well. The size of the normal force is greater than the size of the weight force giving a G-Force of greater than 1.

If you’re not accelerating, if you’re stationary in your lift then your acceleration will be zero and if you sub equals 0 back to the G-Force formula you’ll get G-Force equals to 1. So if you’re stationary like standing in the lift the G-Force that you experienced is 1. If we look back at this original formula then we can see that the ratio between the normal force and weight force when standing stationary at the lift is 1:1 ratio. The normal force acting on you by the ground of the lift and the weight force by the earth is cancelled out, it’s equal so you have no acceleration.

And if your acceleration is negative it means that you’re accelerating downward. It means your acceleration using a downwards direction as we assume positive to the upwards. If that happens, if you saw the negative number for a you’ll get G-Force of a value smaller than 1.

However, you can never get a negative G-Force because as G-Force is the ratio between the magnitude of these two and we talk about magnitude it’s a size of something, size of something can’t be negative so G-Force can never be smaller than zero. Under what scenario is it zero exactly? The scenario is when the acceleration downwards is exactly 9.8 m/s^2 which means you’re free falling in space. It happens when you’re in an orbit or if you’re free falling from a high point to a low point without air resistance. If that’s the case there’s a 9.8 – 9.8 as a and G-Force turns out to be zero. We call that scenario micro gravity or weightlessness.

What happens if the acceleration is – 20 or – 30 instead of that? Your G-Force is still a positive ratio because now we’re just thinking about taking the normal force in the opposite direction. How do we calculate the G-Force then? The trick here which you don’t really need in the HSC is you put an absolute value sign around the formula so if is – 30 you apply the formula and then you absolute value it to get the G-Force. It still a positive ratio because it’s a ratio between of these 2 things.

So in the HSC these type of questions will most likely be in a multiple choice question or a one or two marker calculation question. When you apply the formula always remember that a is positive if acceleration is upwards and a is negative if acceleration is downwards, is zero if you have no acceleration.

Before you attempt the questions I think the best idea is to draw a diagram of what’s going on so that you can analyse your forces and apply the formula correctly. I hope this video was useful for you, guys. If you have any more concerns with this topic, please comment below. If you think that there’s any other topic in space that you want me to do please just comment below and I’ll do them. Thank you very much.