I got these results in gravitational accereration experiment I dropped the picke

Question

I got these results in gravitational accereration experiment

I dropped the picket fence through the photogate making sure it undergoes

free fall. and recorded the value of g for 50 trials. please calculate/ answer the following :

1) +and - standared deviation

2) % error

3) Compute the percent error from the theoretical value of 9.79149901 m/s^2 for the gravitational acceleration g. Why are you using the percent error rather than the percent difference?

4) Why is your value for g not 9.79149901 m/s^2?

AVG=9.852

These are the values of g in 50 trials.

please have the answer typed

9.771 9.667 9.359 9.454 9.861 9.473 10.27 9.102 9.813 9.787 9.813 9.842 9.97 10.52 9.598 9.793 9.856 9.861 9.703 9.605 9.564 9.972 9.814 9.817 9.797 9.602 9.931 9.869 10.47 9.888 10.01 9.532 9.859 9.826 9.811 9.812 10.33 9.469 9.945 9.929 9.825 9.798 9.804 9.79 10.45 9.861 9.737 10.48 10.11 10.38

AVG=9.852

These are the values of g in 50 trials.

please have the answer typed

Explanation / Answer

Here are the easy steps to find standard deviation.

Step 1 - You have 50 trials. Add them up and find their mean or average.

Step 2 - Now subtract the mean from each individual trial and square it. For example - you found average as 9.852. For first trial, It should be (9.771-9.852)2. Do this with all the 50 trials.

Step 3 - Now add up all the values you got in step 2 and find the average again. You will get a number which is called as variance.

Step 4 - Finally, take the square root of variance and you have your standard deviation.

% error = (|experimental value - Theoretical value| / Theoretical value) * 100

Now if we consider the average you found as an experimental value then percentage error will be

(|9.852 - 9.79149901| / 9.79149901) * 100 = 0.617%

Why do we use percentage error, not percentage difference ?

Percentage difference is used where we are comparing two experimental values. On the other hand, percentage error is used where we are comparing experimental value with theoretical value.

Why we don't get g as 9.79149901 because value of g depends on location. This can be due to varying geological densities at different locations. Also, our planet is not completely spherical. It has a bulge at the equator and flatness at the poles. It would result in higher g values at the poles.

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