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MatRiv

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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!