and we have measured both x and y and determined their mean values and standard deviations, then we can find the standard deviation in z using the formula below. Note that the derivatives with respect to x and y are evaluated using the mean values of x and y.
Here is a problem for you to try. In lab #7
you will measure the charge over mass ratio (e/m) of the electron. You will do
so by shooting electrons from an electron gun through a uniform magnetic field,
which is perpendicular to their velocity. The electrons will move in a circle.
You will measure the magnetic field B, the accelerating voltage of the electron
gun V (this will determine the velocity of the electrons) and the radius of the
electron orbit r. You will find e/m from the formula:
a)
( 20 points) Write an expression for the standard deviation in the
quantity e/m in terms of the measured quantities and their standard deviations.
b) (
20 points) If you can measure each V, B and r with an accuracy of 1%, what would
be the relative (%) error in your measurement of e/m ?
2.
You have a pendulum and have done several measurements to determine the length
of the string and the period of the pendulum. You tabulated your data ( Table1)
and your goal is to determine the acceleration due to gravity. The accepted
value of g in Nashville is g = 9.79822 m/s^2 .
| Period [s] | Length[cm] |
| 2.026 | 102.8 |
| 2.021 | 102.7 |
| 2.024 | 102.7 |
| 2.020 | 102.6 |
| 2.025 | 102.8 |
| 2.024 | 102.6 |
| 2.022 | 102.9 |
| 2.022 | 102.8 |
| 2.024 | 102.5 |
| 2.019 | 102.8 |
| 2.023 | 102.7 |
| 2.024 | 103.0 |