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 Sunday January 17th from 2:00-3:30pm to help you. • You can also contact Aphra Rogers at email@example.com 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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