Prof. Matt Dobbs
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Physics 257 Asst 4
Physics 257: Assignment 4
ANSWER KEY
Due in-class before 1:05pm Thursday October 18, 2006
Remember to use the correct number of significant figures for your answers. Answers with incorrect significant figures
will get zero marks. For plots, remember to label your axes correctly and use the “graphs” checklist on page 7 of the lab
book. Graphs must be computer generated from now on. For each question, show all your steps. Assignments handed in
after 1:05pm but before the end of the day will lose 25% of the grade.
1.
The following data has been collected from an experiment:
x = [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 ]
y = [ 7.43, 13.17, 12.23, 23.54, 19.59, 23.34, 29.20, 29.17, 31.71,
32.50, 38.88, 36.99, 46.14, 51.87, 47.92 ]
x is the independent variable and y is the dependent variable. Both x and y are dimensionless. The
error for x is negligible. There measurement error for one measurement of y is
Δ
y =
σ
y
= 4.
[NOTE: so far this is the same data and question as Asst3.] You are reviewing their experiment
and trying to decide if they chose a reasonable value for the error on y.
In Asst2 you should have found:
slope = 2.9±0.2 and y-intercept = 6±2. Use these numbers
for this question even if you got the wrong answer for Asst2.
a)
How many degrees of freedom (DOF)
N
are there in the data points? How many DOF
M
are
there in the fit parameters? How many DOF are there in this straight line fit (
N-M
)? (
1 mark
)
DOF of data points: 15, as there are 15 data points.
DOF of fit parameters: 2, namely "a" and "b".
DOF of straight line fit: (15 data point – 2 fit parameters) = 13.
b)