LAB INFORMATION TFYA76 Mekanik September 18, 2018 Lecturer: Bo Durbeej (bo.durbeej@liu.se) Lab Assistants: Tim Cornelissen (tim.cornelissen@liu.se) Indre Urbanaviciute (indre.urbanaviciute@liu.se) Contents 1 Lab rules 2 2 Preparation tasks förberedelseuppgifter 3 3 Lab reports 4 4 Annex I: Errors in measurements 6 1
1 Lab rules ˆ Sign-up for the labs. Until October 1, sign-up sheets for the labs are available in the Ampère corridor of the Physics building (ground floor). There are five different lab groups, each with a maximum of 12 students, scheduled as follows: Group A MED2 Tuesday 2018-10-09 08.15-12.00 Group B MED2 Wednesday 2018-10-10 13.15-17.00 Group C MED2 Friday 2018-10-12 13.15-17.00 Group D Yi2 Tuesday 2018-10-09 13.15-17.00 Group E Yi2 Thursday 2018-10-11 08.15-12.00 Each student will have to sign-up for only one of these slots and the experiments will be performed in groups of two students. ˆ Be on time and be prepared. Before coming to the lab you should carefully read the lab compendium and this lab information, and do all the preparation tasks. Remember that you have 3 hours and 45 minutes to perform Lab 1 (Task 1 and Task 2) and Lab 2, so you will have a bit more than an hour for each of the three experiments. It is very important that you know what you will have to do in all three experiments since you won t know beforehand in which order you will be performing them. ˆ Hand in written lab reports. In section 3 you will find more information about the written lab reports. ˆ Extra lab session. If you are not able to finish all three experiments the day that you come to the lab, there is an extra lab session on Tuesday the 16th of October between 13:15 and 21:00. If you need to use this session you should contact Tim or Indre before 12:00 on Monday (15th of October) and tell them which task you need to redo or complete so they can organize how and when each experiment will be performed. ˆ To pass the lab. To pass the lab you need to come to the lab, perform the three experiments, and hand in three reports (one for each task in Lab 1 and one for Lab 2), each of which will be graded with pass or not pass. If you have any questions about the information in this document or in the lab compendium, contact Tim, Indre or Bo. 2
2 Preparation tasks förberedelseuppgifter In order to work efficiently in the lab and to know which quantities you will have to measure and determine, you should do the following preparation tasks ( förberedelseuppgifter ). See also the lab compendium. Lab 1 Task 1: Derive an expression for the velocity of the arrow v p before the collision according to Method 2. Consider the following quantities: pendulum length L, pendulum mass M, max angle α, and arrow mass m p. Lab 1 Task 2: State the general equations that relate the traveled distance x, speed v, and acceleration a of the cart with time. Derive an equation to calculate the gravitational acceleration g (i.e., normal to the earth surface). NOTE: This task is not included in the lab compendium. Lab 2: Based on Figure 4 in the lab compendium, deduce the component equations for the total momentum before the collision, P, and after, P. To perform these tasks you can use your lecture notes and/or the recommended book for the course: University Physics with Modern Physics by Young and Freedman: 1. LAB 1: Motion ˆ Task 1: chapters 7 and 8 ˆ Task 2: chapters 2 and 4 2. LAB 2: Collisions ˆ Chapters 8 and 10 3
3 Lab reports One of the requirements to pass the lab is to hand in three written lab reports (one for each task in Lab1 and one for Lab2). The reports should be prepared together with the student that you performed the lab with. In other words, each group of two students working together should hand in three separate reports. Requirements for the lab reports: ˆ The reports should be written in English. ˆ Contents: 1. Title, authors, e-mails and date. 2. Aim/objectives of the lab. 3. Background: briefly include the basic principles and equations necessary to perform the experiment and the calculations. You can use the preparation tasks as a guideline. Number all equations included. 4. Methods: a brief description of the experimental procedure. Explain each quantity that was measured. It may help to include a figure of the experimental set-up. NOTE: In order to improve your results and reduce errors, you should repeat each experiment a number of times: Lab 1 Task 1: at least 10 times. Lab 1 Task 2: at least 3 times. Lab 2: at least 3 times. 5. Results: include all the values obtained from the experimental measurements and values calculated from the measured quantities. Consider using tables for quantities measured or calculated multiple times. Remember to use the appropriate units for all quantities! It is a requirement to include: Lab 1 Task 1: Error propagation for the determination of the speed of the arrow (v p ) using equation (3) from Annex I. Lab 1 Task 2: Plots for the traveled distance (x), the speed (v) and the acceleration (a) as a function of time (t). Error estimation for the acceleration due to gravity (g) using equations (1) and (2) from Annex I with the calculated g values. Lab 2: One of the pictures of the collision process. When you are going to calculate errors, consider which instruments you are using, whether they are digital (e.g., timer, scale) or not (e.g., ruler, angle scale). What is the resolution of these instruments? How can you estimate the standard deviations for the measurements of each physical quantity? 6. Discussion: discuss the results obtained. For example, you can compare methods, discuss sources of error, etc. Use the suggestions under Redovisning in the lab compendium as a reference for this part. 4
7. Conclusions 8. References ˆ Hand in.pdf versions of your reports by e-mail to Tim (tim.cornelissen@liu.se) or Indre (indre.urbanaviciute@liu.se). Preferably state the course code TFYA76 in the mail subject and include your names in the filename. ˆ Deadline: There are two important deadlines that you should consider to hand in the lab reports: The first deadline is on Tuesday the 30th of October: if you hand in your lab reports before this deadline, you will get a chance to correct anything that is necessary to pass. The second and FINAL deadline is on Sunday the 11th of November: you should hand in the final version of your reports not later than this deadline. 5
4 Annex I: Errors in measurements The measurement of physical quantity usually involves a comparison with some internationally accepted standard value. Unfortunately, these standard values are not necessarily 100% accurate and the comparison process can also be accompanied by different types of errors that result in a deviation of the measured value from the true value of the quantity in question. Types of errors During a measurement process the errors in the measured value can be separated into two categories: quantifiable errors and non-quantifiable errors. The non-quantifiable errors are related to mistakes during the measurement process, e.g., if the instruments for measurements are wrongly used, if the operator doesn t know how to read the values or doesn t properly record the values, etc. In these labs, we won t care about these errors since we will assume that all the operators (i.e., you!) are using the instruments properly and make no mistakes in the acquisition of data. The quantifiable errors or measurement errors are the result of the deviation of a measurement from the true value. random errors 1. They can be separated into systematic errors and Systematic errors occur due to faults in the measuring device and can be classified as follows: ˆ Instrumental errors: are due to the construction of the measuring device. For example, the minimum or maximum values that the instrument can measure, the truncation in the values given by a digital display, the low resolution of the instrument, etc. These errors can be estimated or deduced from the calibration of the device. ˆ Environmental errors: are due to the external conditions in which the device is operated, e.g., temperature, humidity, etc. ˆ Observational errors: are due to incorrect observations or reading of the device. ˆ Theoretical errors: are due to simplifications in the model system or to errors in the physical constants used in theoretical calculations. For example, we may apply conservation laws even in instances when friction forces are not negligible. Random errors are caused by sudden changes in the experimental conditions, noise and tiredness in the operator. These errors may be reduced by taking the average of a large number of readings and the deviations can be calculated by statistical methods. 1 There are other ways to classify measurement errors. For example, based on whether the calculation of the associated uncertainty is based on a statistical analysis of data (Type A errors) or not (Type B errors). 6
The best way to estimate random errors is to make a series of measurements of a given quantity x and calculate the corresponding mean value x and the standard deviation σ x according to: and x = 1 N N x i (1) i=1 σ x = ( 1 N ) 1/2 N (x i x) 2 i=1 where x i is the result of measurement i and N is the total number of measurements. Assuming a Gaussian distribution of the measured values x i around the mean value x, then it is expected that 95% of the measured values fall in the range x ± 2σ x. Therefore, the result of the experiment may be expressed in those terms. (2) Error propagation Sometimes the quantity that we are interested in cannot be extracted directly from an instrument, but is calculated using theoretical equations and measured values. In these cases, one has to consider how the uncertainties associated with the measured values affect the calculated value of the desired quantity. To this end, one uses error propagation. If you are interested in a derivation of the theory and equations you can look in the references given below. Here we will just state the equations needed for a simple error propagation in which we ignore the possible covariance between different measured quantities. Say that we are interested in determining the value of a quantity Q which can be calculated based on the measured quantities x 1, x 2,..., x n as Q = f(x 1, x 2,..., x n ). Then, the propagation of error approach is to determine the standard deviation σ i from the measurements x 1, x 2,..., x n and combine them into a standard deviation σ Q for Q. The formula for the propagation of error is: σ Q = n ( ) 2 Q σi 2 (3) x i i=1 where Q x i are the partial derivatives of Q with respect to the measured quantities x i. References http://www.itl.nist.gov/div898/handbook/mpc/section5/mpc55.htm https://www.edgefx.in/different-types-of-measurement-errors-and-their-error-calculations/ 7