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Unformatted text preview: PreLab Required Homework Problem Preparation for Experiment 1: Part 1 Study carefully Example 5.12 in Young and Freedman. Although the problem is simple it is a classic one because it illustrates so many of the concepts and issues that you must understand. It involves setting up and solving three equations in three unknowns. It involves a constitutive relation: that is, some mechanical constraint between the bodies that couples their motions. In this case the fact that the string has a fixed length results in the equation that the magnitude of the acceleration of m 1 is equal to the magnitude of the acceleration of m 2 . a) Explain in physical terms the form of the expression for the acceleration. It is a dimensionless fraction times g . Why that particular fraction? b) Is the tension in the string after m 1 released from rest greater than, equal to, or less than its value before m 1 is released? Explain physically why this must be so. c) Make carefully labeled sketches of the position, speed and acceleration of m 1 as a function of t . Start the sketches at t = 0 and assume m 1 is released from rest a short time afterward at t = t . d) Now imagine that m 1 is acted upon not by a constant force, as in the example, but by a time varying force that has some positive value at t = t and subsequently decreases smoothly to zero at a time t end . Again make carefully labeled sketches of the position, speed and acceleration of m 1 as a function of t . For added clarity, indicate as a dashed curve on your sketches the result you found in c) assuming the magnitude of the force at t = t is the same as the value it had in c). e) In the experiment, you will implement the situation in d) by replacing the discrete mass m 2 with a chain. The freely hanging portion of the chain decreases as m 1 moves forward, thus giving rise to a smoothly decreasing force. What additional change in the equations of motion would have to be taken into account when modeling the motion of m 1 ? [Hint: you may want to refer back to your answer to a).] Each of these changes alone is reasonably easy to handle using techniques we will learn later in the course. Together, they lead to a rather complicated analytic expression for x 1 ( t ) which we will not deal with. 1 Preparation for Experiment 1: Part 2 In 8.01 the apparatus you will use in the experiments is run by a computer application called Logger Lite. Similar but much more powerful applications (LabVIEW is an example) are used in many research laboratories to run instruments, acquire data, and perform sophisticated analyses of that data. Naturally, the applications have to be programmed to carry out each of these tasks and that takes a fair amount of (usually graduate student) labor. Initially our data acquisition software was programmed to analyze as well as take the data. However, we found that having the software do the analysis diminishes your understanding and enjoyment of the experiments. We now let you carry out most of the analysis of your data.of the experiments....
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 Fall '09
 guth
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