# Finding the 'g-force' of a decelerating falling mass.

• MatRiv
In summary, the conversation is about determining the g-force experienced by a mass during deceleration after free falling for a set distance. Three methods are discussed, with the first method using the formula v=√(2gd) and the second method using F=ma. The third method, based on the Wikipedia page for g-force, calculates g-force as the ratio of free fall height to deceleration distance. The speaker is looking for confirmation and discussion on the accuracy and appropriateness of these methods.

#### MatRiv

Hey all,

I need a reality check and verification on some work I have been doing. I feel as though I might be too close to the problem now and am missing something about this. It's also been a few years since I studied physics at University, so I'm a little rusty.

Problem:

An initially stationary mass (m) free falls for a set distance (d) before decelerating (a) until stationary. The peak Force (F) of the event is measured and the time (Δt) of the deceleration period can be obtained through external measurement analysis. Determine the g-force that the mass experiences during deceleration.

Method 1. Knowing free fall distance and time of deceleration period.

Using v=√(2gd) to find the velocity of the mass when the free fall period ends and the deceleration begins.

then using a= (vf-vi)/Δt to find the deceleration in m/s^2 where vf = final velocity = 0m/s as the mass has stopped and vi is the initial velocity at the start of the deceleration period, as determined above.

So a= -√(2gd)/Δt

This gives the deceleration in m/s^2 and so dividing by gravity (9.81m/s^2) would give the 'g-force'.

I feel fairly confident about this method, but would appreciate some conformation. Also, I think this would produce an average deceleration during the time period? If the deceleration was not at a constant rate, this method would be less accurate? Method 2. Knowing peak force experienced during deceleration

Using F=ma, a=F/m so imputing those values into the formula would provide the acceleration experienced at the force during the deceleration period? So if 'F' was the peak force during the period, 'a' would be the peak acceleration experienced? (obviously F would be -ve, making acceleration into deceleration).

Then again, dividing by gravity (9.81 m/s^2) would give the 'g-force'.

This feels sort of right, but also just feels like an oversimplification of the scenario. If it's correct, this would have the advantage of finding the deceleration at any point in the deceleration period, provided the force at that point is known as opposed to the average produced in the above method?Method 3. Other possible methods.

Looking at the Wikipedia page for g-force there is a section towards the bottom on short duration shock, impact and jerk.

They give g-forces as free fall height (h) divided by deceleration distance (d). ie h/d (g's)

As the deceleration time period for my above scenario is only about 0.2 to 0.5 seconds, would this method be appropriate?I would appreciate any and all help/comments. It'd be great to hear your thoughts and get a discussion going as like I said, it's been a while since I did any formal physics study and I am definitely out of practise but have thoroughly enjoyed throwing myself into this topic. I can put out some actual numbers too if needed.

Thanks!

g-force is really just the force per unit mass. If you assume constant acceleration you can calculate it as you have above. The "short duration shock" is about what happens if you hit the ground!

## 1. What is the definition of "g-force" in relation to deceleration?

"G-force" is a measurement of the force exerted on an object due to acceleration or deceleration. It is often expressed in units of gravity, with 1 g being equivalent to the force of Earth's gravity on an object.

## 2. How is the g-force of a decelerating falling mass calculated?

The g-force of a decelerating falling mass can be calculated by dividing the deceleration (in meters per second squared) by the acceleration due to gravity (9.8 m/s²). For example, if an object is experiencing a deceleration of 19.6 m/s², it would have a g-force of 2 g (19.6 m/s² ÷ 9.8 m/s² = 2 g).

## 3. How does the mass of an object affect its g-force during deceleration?

The mass of an object does not directly affect its g-force during deceleration. However, a larger mass will require a greater force to decelerate at the same rate as a smaller mass, resulting in a higher g-force.

## 4. What factors can influence the g-force experienced by a decelerating falling mass?

The g-force experienced by a decelerating falling mass can be influenced by the rate of deceleration, the mass of the object, and external forces such as air resistance or friction. The angle of the surface the object is decelerating on can also affect the g-force.

## 5. How is the g-force of a decelerating falling mass measured?

The g-force of a decelerating falling mass can be measured using a variety of instruments, such as an accelerometer or a force sensor. These devices can measure the acceleration of the object and calculate the g-force using the formula mentioned in question 2.

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