Question

i am very confused with these questions. can someone help me solve? and can you explain neatly and clearly? will rate, thank you.

1. In this experiment, you will be generating time measurements that have both random uncertainty (Stran) and systematic uncertainty (dtsys). Using Eq. 4 as a starting point, write down an equation that will allow you to calculate &t from Stran and otsys 2. The acceleration due to gravity is related to the time, t, it takes the ball to fall a distance, y, by Eq. 3. With this equation and Eq. 5, show that the fractional error &g/g is:

Answer 1

System errors are that are not determined by chance but are introduced by an inaccuracy inherent to the system like our linear may been running consistently fast or slow. These error will not show up by comparing multiple readings. As a result total uncertainty delta t delta t = squareroot (delta t_rans)^2 + (delat t_system)^2 system can be identified and reduced until they are much less than the required precision In a leaching laboratory however the is often not so muter should be considered to have some definite systematic uncertainty like all stop watch have up to 0.5 % systematic uncertainty 2 y = 1/2 gt^2 g = 2y/t^2 delta g/g = squareroot (delta y/y)^2 + (2 delta t/t)^2 dg = partial differential g/partial differential y dy + partial differential g/partial differential t dt dg = (2/t^2) delta y + (- 2/t^3) delta t dg = (2y/t^2) delta y/y + - 2/t delta t/t dg/g = delta y/y + - 2 delta t/t dg/g = squareroot (delta y/y)^2 + (2 delta t/t) since delta y and delta t are independent so they should be combined in quadrature