Question

I have a question on experimental uncertainties. Eugenia wants to find out how fast she walked along the hiking trail that took her 1.5 h to complete. she counted the number of steps with a pedometer and got 10000 steps. in order to calculate the distance she walked she estimated the length of her stride. she walked 10 steps three times at her usual rate and measured the distance with a measuring tape (the smallest division is 1cm) and got 745cm, 748 cm, 739 cm. Find the length of her stride. What is the length of the hiking trail? What are absolute and relative uncertainties in that length? C

Answer 1

The reason nobody has answered your question is because it is very long and involved. You have all sorts of decisions to make. First of all we have an uncertainty in the measurement - because we can only measure to the nearest centimetre. Then we have to process the thirty trial steps she has taken to cover whatever total distance those three numbers add up to. You will have to do some statistics to get a number for an average stride length and the uncertainty in that - and I am not sure that you want to do that.

Anyway the absolute uncertainty is the actual amount of length. So if you found that her stride length was 75cm +/- 3cm, the absolute U is this 3cm. The relative U is just this as a percentage of the measurement found = 3/75 = 4%. I hope that this helps.

Answer 2

Never been great at error propogation but as far as I can tell, the only source of error comes from the metre stick that she uses to measure her 10 paces. As the smallest division on her metre stick is 1cm then it is common to assume the error is half the smallest division, i.e. 0.5cm. Averaging the length of 10 strides gives:
(745 + 748 + 739)/3 = 744 ± 0.5 cm. Seeing as she walks 10000 steps, that is 1000 x (744 ± 0.5 cm) = 744000 ±500 cm. The absolute error is the magnittude of the error in this form, i.e. 500cm. The relative error is the absolute error divided by the actual value, i.e. 500 cm/744000 cm = 6.72 x 10^4. This is commonly converted to a %, which would be 0.07%.

This is all assuming you're not using the statistical methods for error analysis.