The Gravitational Field on 4th Bryan
Introduction and Goal: We generally use 9.80 N/kg (or m/s2) as the value of the gravitational field, termed g. This is also the value of the acceleration of a free-falling object at the surface of the Earth. The actual value, however, depends on your location. The purpose of this lab is determine--as precisely and accurately as possible, but within 0.1% should be a goal--the value of the gravitational field on the NCSSM Physics floor. A worthy goal is to achieve 4 significant figures in the value of g. For instructional purposes, you're required to use a simple pendulum, but you may use any timing device that is available on the physics floor. You must design your method to achieve maximum accuracy and precision using the measuring devices that you choose, and you must provide a quantitative assessment of these errors.
This lab provides an excellent opportunity to see the interplay between theory and experiment. We know that the period, T, of a simple pendulum in the small-angle approximation is T = 2p(L/g)1/2, where L is the length of the pendulum. One can use this formula to calculate g, given measurements of T and L. The precision of the calculation, of course, depends on the smallness of the angle as well as the measurements of T and L. In order to achieve 4-significant figure precision, the angle must be smaller than it would be if you only had to achieve 3-significant figure precision. Thus, your method must include a way to determine whether the amplitude that you use is small enough.
In order to achieve the goal of the experiment, you must understand--among other things--the meanings of the terms precision, accuracy, and significant figure. You must also know how to assess quantitatively and to minimize the sources of error in your experimental design. The latter will be taught. The former should be something that you already have in your repertoire of physics knowledge. We will, however, review it.
4. Do all work for this lab with your lab partner with this exception: Do calculations, analysis, and error analysis independently. However, partners may compare results after both have completed these tasks.
Design Document for HLab1
Meet with your lab group and prepare an initial design document for your experiment in which you answer the following questions. In answering the questions, keep in mind the goal of the experiment. All members of the group must participate fully in preparing the document. Submit one response from the group using Moodle by 5 pm Thursday. You should also be prepared to give a 5 minute presentation on your design in class on Friday.
1. How long should the pendulum be? Explain your answer. (Since length affects period, consider whether you can choose the length in such a way as to improve the accuracy of your measurement of period.)
2. How will the string be anchored at the top?
3. What characteristics will the bob have and why?
4. What things will be kept constant? How will the constants be measured?
5. How will angular displacement be measured?
6. What equipment will you use for time measurements? Be as specific as you can in describing it.
7. How will you ensure that the angular displacement does not have a significant effect on the period measurement (to the number of significant figures that you need)?
You may find it useful to do some experimental testing in advance of the actual lab period. One purpose of this, which you may find essential, is to determine how much timing error you should expect in synchronizing the start (stop) of timing with the beginning (end) of a cycle. If you carry out such preliminary measurements, be sure to record the data in your lab journal. Provide appropriate heading and labels. Describe your timing technique as well as recording your data.