Physics 161 Pendulum/Spring Lab 'Practical' Objective You will be using your experimental skills and scientific thinking. In this set of experiments, you are not going to be asked to follow specific steps. For this experiment you will collect data and determine what measurements are important and which are not. Then once you have determined what is important, you will analyze data to investigate a mathematical relationship between parameters. As things happen in scientific research, there can be several ways of performing experiments to answer a specific question. You need to think all the options you have and provide reasoning for your choices. It is usual that the first trial of measurements in an experiment does not lead to a conclusive answer, but it should point into the direction of improved measurements. You need to apply those improvements until you are convinced if the equation is correct or not. When doing an experiment, scientists do not always have the most ideal equipment. Sometimes that equipment does not exist and the scientists must do their best with the available items in the lab. You are going to do an exercise of coming up with the best way to get decent scientific results with a simple setup. You will not be graded based upon how sophisticated the experiment is or the precision your results are with theory. This experiment can be done with material as simple as a string and a mass and a stopwatch from your watch or cell phone. Keep in mind that this experiment is designed so that you develop your critical scientific thinking. You are given freedom to decide what works best. But you need to justify your steps and decisions. Turn In This two-week experiment will consist of investigating experimental parameters by collecting data which will be turned in at the end of the second week. Week one will focus on creating and devising a plan and lab report to set up for success in week two. Details for lab report format are at the end of this handout. Background A simple pendulum is a physical system defined by a small mass attached to a string on one end and the string attached to a pivot point on the other. When the bob is moved from its equilibrium position (the string vertical) and released it starts to oscillate with a simple harmonic motion. It undergoes a periodic motion with a well defined period. A period is the time it takes for the pendulum to complete one complete swing (starting on one side, swinging the opposite direction then returning to the point where the swing started). The drawing to the right shows a pendulum setup. A mass is connected to the end of a string and when the pendulum is at rest the mass and string are aligned with the equilibrium position (dashed vertical line). When the mass is pulled away from the equilibrium position by some angular displacement, 0, with the with the string tight and released the mass will swing back and forth between +0 and -0. This type of motion is called simple harmonic motion. 3-1A spring will apply a force equal and opposite the force pulling or pushing that spring from its rest equilibrium. That force is related to the spring constant of that particular spring. Measuring the spring constant requires knowing mass and displacement, the displacement can be measured according to the diagram shown. The value is distance from center, or rest. Spring should not be moving for this measurement. (a) shows spring at rest, and (b) shows spring displaced by added mass, and therefore weight. (a) Task for week 1 Don't worry if you are not an expert on simple harmonic motion. For this lab you will be able to determine how the physical parameters of a simple pendulum relate to each other without knowing the theoretical framework, more specifically, the time it takes a pendulum to complete one full swing (period) vs some important parameter or parameters. Data collected from a series of experiments will provide information to determine how the following pendulum physical parameters relate to each other. "L' the length of the pendulum is the maximum deflection from equilibrium "m' the mass as the end of the string "T' the time it takes to complete one full swing. This is also called the "period." The last parameter is gravitational acceleration 'g'. However, this is one parameter that you cannot adjust, but it will be something that is part of the pendulum period equation. This two-week lab has two goals: 1. Create a set of experiments to determine if the period depends on L, m or 0. As you test the other 2 variables, use an angle of around 10 degrees. Also consider that you want to identify and prove the following equation: T = 2n [1] 2. As well as creating an experiment for another simple system, that of a spring: mg = -kx [2] A Where 'k' is the spring constant and 'x' is the displacement from center/rest. For the spring, you are simply determining the spring constant of at least 2 springs and looking at how consistent the data is. The idea here is to prove good lab practice. (Hint: take two sets of data each for two different springs, See that for each spring, the associated two sets of data are within a small percentage of each other. This will tell you that you have taken consistent lab data.) 3-2Del iverables: .' Week 1: By end of day Friday (5pm), please email your prelab I'CpOlt, which will include the following: ' Title. name, section on cover page. ' Abstract: Brief summary of what you are doing, why you are doing it, and what you expect to nd. (This can be one paragraph for each goal) ' Introduction: Explain the physics and math that your readers need to know to understand your work. (This can be one paragraph for each goal) ' Methods and Materials: This is a brief section where you include what you need, and your procedure. (This can be bullet points for each goal) ' Results: Present your numerical results using several graphs and tables (Graphs of Period versus length, period versus mass, period versus angle.) This section for your PRELAB will include tables and labelled graphs where you EXPECT to enter data. Include a short (one sentence) detail about each graph/result you expect to nd. What does it mean? What should it look like? A straight line? Curved? This is the most important part of the prelab. Doing this well will allow you to head out quickly and easily next week. ' Conclusions: Present your conclusion, supported by your data. For the PRELAB, state what you expect to nd. Do you expect to prove these equations? How much error do you expect to nd between spring trials? Should T change with mass? Angle? Or only with '1'? Will 'k' be exactly the same for multiple trials of the same spring? Do you expect it to be perfect? Why? Human error? Lab limitations? What did you look for to prove the equations right or wrong? Try to go in depth here. ' Be Brief if you can state your nding with less words, do so. Week 2: Either print your week 1 prelab to ll in, or just use paper to write down all data, graphs (results), and conclusions you have found now that you have done your experiments. These might agree with what you expected to nd, and they might not. Be sure to say why or why not. Be sure to also include both experiments (pendulum with the goal of proving SHM equation and what variable inuences T, and springs with the goal of proving consistent lab practices). You will also turn in the following lab questionnaire. Some of the answers will cross apply to your report conclusions. One questionnaire per person. MYou must follow your prelab procedure or be sure to note where you differ in the actual lab portion. I will cross reference submissions with prelab. Note that if your prelab is well done and thorough, you can breeze through lab week. That's the idea! It's wonderful if that happens