Vectors and Statistical Error

Report sections:

You required minimum of two pages plus all tables and graphs. If the lab requires graphs then make 1 graph on the computer and attach the remaining graphs to be drawn by hand on graph paper. Type one page of text describing the experiment and one page of math (see below). A separate cover page is not required; on the first page in upper left corner write: your name, PHY lab course number and section number. Include the official lab title centered 1 inch down from the top in size 14 font bold face, and number your labs as “1st required lab,” “2nd required lab,” “3rd required lab,” … etc. etc.

Type report in size 12 font, Calibri or Times Roman, use 1.5 line spacing; set 1 inch margins on all 4 sides of page. Do not use pronouns such as “I, we, us, our” Purpose and scientific goals: in one paragraph explain the scientific goals of the experiment. Experimental procedure, results and discussion (this is the largest section) In a narrative explain experimental setup, steps used to perform lab and results. Do not copy text out of the lab book, don’t itemize the sequence of procedural steps as 1, 2, and 3 nor A, B, C …. Discuss key results such as slope calculations and comparisons to theoretical values.

Math equations and calculations: Write them on the computer in MS Word under Insert-> Equation->Insert New Equation: Derivations of the physics law and/or key formulae which is the main idea of the lab and that being tested; example calculations of how your data is used to calculate the key variables. Error analysis When instructed to do so an error analysis will be performed to calculate the percent error that exists between the measured result and the known, accepted or theoretical value;

1) Resolution of measuring devices: due to limitations of ruler, timer, scale, etc.

2) Systematic errors: due to accepted errors introduced by experimental equipment

3) Human errors: due to limitations of eyesight, reaction time, etc.

4) Statistical error: is the standard deviation on the average value obtained from the distribution of repeated measurements. Total uncertainty: combine the above 4 uncertainties by adding them in quadrature to obtain a total uncertainty. Express this total uncertainty in scientific units and also in percentile of the final result.

Results of measurements and conclusion In one paragraph state the main numerical results obtained, the final error calculated, compare results to theoretical values and explain scientific conclusions drawn. Please, do not use any other sources aside the use of the physics textbook if possible.

Purpose and scientific goals

Vectors are quantities that are fully described by both magnitude and direction. Vectors are represented by lines with arrow heads. The length of an arrow is made proportional to the magnitude of the vector, and it is drawn in the correct direction. Examples of vectors are forces, velocities, and accelerations. Adding vectors means more than just adding magnitudes. The direction must be considered also. There are various approaches to add vectors. In this lab we will explore the following methods of vector addition: (i) parallelogram rule, (ii) triangle rule, and (iii) components method

Purpose: To use the parallelogram method to find the resultant of two vectors. Here are the vectors in question: Force A (magnitude 3 N direction, 60^o), Force B (magnitude, 4N, direction 100^o). The angles are measured with respect to the x axis.

Theory: The parallelogram rule is employed when vectors are starting at the same origin (Figure 1). You draw the vectors to scale, starting from the same origin and complete the parallelogram. The diagonal of the parallelogram which starts from the same origin represents the resultant of the two vectors, R.

1. Draw force Ato scale on a white plain paper (e.g., 1cm represents 1N)

2. Draw vector Busing the same scale as above (starting from same origin as A)

3. Complete the parallelogram and draw the diagonal

4. Measure the diagonal and determine R.

5. Measure the angle with which Rmakes with respect to the x axis counterclockwise.

Purpose: To use the triangle rule to find the resultant of two vectors: Force A (magnitude 3 N direction, 60^o), Force B (magnitude, 4N, direction 100^o). The angles are measured with respect to the x axis.

Theory: The triangle rule is employed when vectors are joined head to tail. The sum of A and B is then R, which is directed from the tail of the first vector to the head of the second vector. You draw the vectors to scale, head-to-tail and create the triangle, then measure R.