# Error Analysis Worksheet by hsw90420

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```									           APSC100 Module 2                             Error Analysis Worksheet *
Due by 3:00pm Monday January 18th, Outside Room 405 Stirling in LOCKED box

•   Use Appendix 4 in the lab manual to complete this worksheet. In Appendix 4 you will find a
brief description of error analysis and examples for all of the problem types given below.
•   Show all of your work.
•   In each case give the answer as result +/- uncertainty.
•   Use Appendix 3.3 to make sure your result and uncertainty have the correct number of
significant figures. (Uncertainty should have 1 sig. fig., result should be matched to the
uncertainty. i.e. if uncertainty is ±0.01, then the result has 2 dec. places eg. 3.89±0.01)
•   Note that a plot of “a vs. b” has a on the “y” axis and b on the “x” axis.
•   Make sure you indicate your name, student number and Section on your work.
δy       δx1       δx 2
1. Show that if y = Ax1 x 2 the error equation shown in Table 1,                    =         +          , can be derived
y       x1        x2
from equation (1). (This question is designed to show that ALL of Table 1 can be derived from Equation
(1))

2. The initial position of the free end of a horizontal beam is 56.7 ± 0.1cm above the ground.
After a load has been added to the free end the position is remeasured and found to be
42.8 ± 0.1cm above the ground. By how much has the beam deflected?
3. A force T = 4.28 ± 0.09 N acts on an Xbox at an angle θ = 52  ± 6  to the horizontal. What
is the x component of the force Tx?

4. A force F acting on a beam of length l at an angle θ to the beam exerts a torque about the
end of the beam given by τ = Fl sin θ . If F = 3.01 ± 0.02 N , θ = 32° ± 4° and
l = 1.340 ± 0.005m what is the torque?

5. A nitrite solution is made by diluting 6.33 ± 0.02 ml of a 5.00 ± 0.05mg/L stock nitrite
solution to 50.0 ± 0.3ml. What is the concentration of nitrites in the final solution (in mg/L)?
4πω 2
6. An experiment was done to measure β where y =             x . The experiment manipulated x
β
and recorded the resulting values of y. A graph of y versus x is plotted which results in a
straight line. The slope of the line is measured to be equal to the last 2 non-zero digits of
your student number and the uncertainty is calculated to be δm = 2 . (i.e. if your student
number ends in 31 the slope would be 31±2).. If ω has been measured to be 1.33 ± 0.04 ,
what is the value of β ?

7. A graph of pressure vs. 1/volume is made to see if a gas obeyed Boyle’s law (pV = constant).
For a point where V = 0.803 ± 0.007 L what would the horizontal error bars be?

8. An experiment was done to complete a model of the form y = Qz n were Q and n must be
determined (it is assumed that n is an integer). A plot of lny vs. lnz is made and a linear
regression produces a best estimate of the slope of 5.02 ± 0.01 and the intercept of
3.25 ± 0.08 . What are n and Q?

•      Note - if you are having problems with this worksheet TAs will be available in Stirling room 405 on
•      You can also contact Aphra Rogers at leacha@physics.queensu.ca
Scheduled labs for APSC100 Module 2 start NEXT WEEK. The
schedule for weeks 2 and 3 is below.
All classes in Stirling room 405.

Monday       Tuesday     Wednesday      Thursday         Friday

8:30-9:00                  Section I   Section M,3 Section N,4      Section Q
9:00-9:30                     ↓             ↓           ↓               ↓
9:30-10:00                     ↓             ↓           ↓               ↓
10:00-10:30                     ↓             ↓           ↓               ↓
10:30-11:00                     ↓             ↓           ↓               ↓
11:00-11:30                     ↓             ↓           ↓               ↓
11:30-12:00                                Section K                  Section O
12:00-12:30                                    ↓                          ↓
12:30-1:00                  Section L         ↓                          ↓
1:00-1:30                      ↓             ↓                          ↓
1:30-2:00                      ↓
2:00-2:30                      ↓
2:30-3:00                  Section P
3:00-3:30                      ↓
3:30-4:00                      ↓
4:00-4:30                      ↓
4:30-5:00
5:00-5:30

Only attend at the scheduled time for YOUR section.

SCHEDULE FOR WEEKS 2 AND 3:
Section I - Tuesday 8:30-11:30am
Section K – Wednesday 11:30am-1:30pm
Section L – Tuesday 12:30-2:30pm
Section M and 3 – Wednesday 8:30-11:30am
Section N and 4 – Thursday 8:30-11:30am
Section O – Friday 11:30am-1:30pm
Section P – Tuesday 2:30-4:30pm
Section Q - Friday 8:30-11:30am

Note: The tutorial labs that run in Weeks 2 and 3 should only take about 2 hours to perform. 3
hours are allocated for the larger sections as there are more students for the TAs to assist and
sign out at the end.

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