Help with accelration due to gravity experiment

[keil]

Hey, I'm doing a science project thing, and I'm measuring g. One method was freefall, I got times of

0.53
0.55
0.57
0.60
0.63
0.65
0.66
0.67
0.68
0.70

For distances of 0.1m intervals, starting at 1.5m, and ending at 2.4m However, uncertainties are confusing me, reaction time I'm taking as 0.5s, so there's uncertainty of between 94% and 71%, depending of course on the time, anyhoo, to calculate g you use 2s/t squared, so you double uncertainty, and combine them, and it's really confusing, so can anyone help?

(i'm aware this post sort of lacks clarity, so if you need me to explain anyu bit again please ask)

oh, and I need to find overall uncertainty in g, sorry, forgot that bit

Thanks in advance for help. I swear I have tried my best, and the rest of the project is done, it's just the uncertainty in this.

 

[turin]

Determining the uncertainty of the time measurements is the trickiest part, for sure, assuming you used the human operated stop-watch method. I doubt, though, that it is 0.5s. Just look at your data. They are reasonably consistent with what you would expect, in a relative sense, at least to a certainty of 0.1 s, don't you think? Is there any way you can get more sophisticated equipment? Human reaction time is just asking for trouble at this timescale. Oh, one more thing, reaction time won't give you a σ style uncertainty, as it would actually introduce a systematic error and give you more of a μ style uncertainty.

The biggest question is:
Are you experimentally demonstrating a known value of g, or are you trying to start from scratch with the assumption that there is an acceleration, but you should have no idea what value it is? The former would allow you a legitimate easy method to determine the uncertainty in the time measurements. The latter would require more sophisticated analysis (which I can't think of off the top of my head and would have to look up).

 

[Soilwork]

If you're using a stopwatch, then maybe a slightly better way of determining the acceleration of gravity would be to analyse a simple pendulum.
Maybe conduct 5 trials where you measure the time it takes to complete 10 periods.
Still many uncertainties associated with this technique (using stopwatch), but it's another method I guess.
But in calculating the uncertainties it's probably easiest to do partial derivatives.
Never done a free fall experiment, but using your equation I will give an example (assuming you weren't using partial derivative method).
g=2s/t^2
I will use D to be the absolute uncertainty and d is partial derivative sign.
Dg= (dg/ds)Ds + (dg/dt)Dt
anyway with partial derivatives you just keep one of the variables constant while differentiating with regards to the other. (say Ds=0.01m and Dt=0.1s)
So the equation becomes:
Dg=(2/t^2)(0.01) + (4s/t^3)(0.1)
By the way you take the absolute values of the partial derivatives so that is why 4s/t^3 is positive.
I'm not sure if this has helped at all, and I'm sorry if it hasn't.