Physics 290 Lab 2 Motion and Force

Transcription

1 Physics 290 Lab 2 Motion and Force "Why," said the Dodo, "the best way to explain it is to do it." Lewis Carrol in Alice in Wonderland. Imagination is more important than knowledge. Albert Einstein Its hard to imagine what knowledge would be like without some imagination. Instructor Introduction Physics Lab Some of the earliest work in physics involved developing theories that govern how things move. Aristotle s divided motion into two classes: natural motion and violent motion. Things moving with natural motion on Earth followed a line straight up and down. Violent motion resulted from pushing or pulling forces (see Conceptual Physics, Ninth Edition by Hewitt). To explain why an object kept moving after an obvious force was exerted on it, Aristotle resorted to forces that continued to act, but decayed over time. For example, an arrow after it leaves the bow would be acted on by a force imparted by it splitting air and having the air squeeze the arrow forward as it rejoined behind it. This force would act on the arrow, decaying until the arrow fell to the Earth. To test Aristotelian theories about motion, one must first define measurable characteristics of motion. We commonly use terms such as position, velocity and acceleration in describing the motion of an object, what exactly do they mean, and how are they related? Without a formal basis with which to describe motion it is useless to try to relate motion to force. To test Aristotle s theories it is also useful to be able to characterize and measure different types of forces. Finally, it is helpful to visually represent the temporal evolution of an object in motion using graphs of these characteristics, rather than tables of numbers. This lab, then, provides the opportunity to use a motion detector to create graphs representing the motion of objects and a force probe to measure forces acting upon them while in motion. First you will gain some experience relating graphs to the motion of a familiar object yourself! Next you will use a hanging mass and pulley system to apply a constant force to a low-friction cart on a track. By experimenting with this setup one can see how objects move under various forces and relate that to position, velocity and acceleration. Also, it is possible to test hypotheses predicted by Newton s model for motion. Finally, careful consideration of Newton s model can explain an initially strange observation. 1

2 Laboratory 2 Goals Familiarization with sensors such as motion detectors and force probes, interfacing them to a computer, and using LoggerPro to produce useful graphs. Moving yourself to match graphs of position, velocity and acceleration vs. time. Making predictions of the motion of an object under various, constant forces, and testing those predictions. Newton s second law: predictions, verification, and a subtlety. IMPORTANT NOTE: Be sure to address bold questions/directions (below) in your lab notebook. What is expected of you: This lab will probably require two sessions to complete. Keep a detailed lab notebook recording your responses to each assigned task. Not much analysis is required beyond answering the questions posed in this lab sheet. You may want to write up a short conclusion discussing your test of Newton s 2 nd law in Goal 4. Goal 1: Familiarize yourself with equipment Experiment setup: The experiment setup is (crudely) depicted below: A motion detector is connected to a LabPro interface which, in turn, is connected via USB to a computer running LoggerPro software. The first thing you should do is play with the sensor, setup and software. Think of answers for the following questions (write questions 1, 2, 5 & 6 and their answers in your lab notebook): 2

3 1. How does the motion detector work? 2. What are the limits of detection for the motion detector (short and long range)? 3. How can I modify the graphs made with LoggerPro to my liking? 4. What do the settings accessible under menu item Experiment:Data Collection in LoggerPro control? How do they affect my experiment? 5. Which direction is positive and which negative? Can that be changed? 6. How accurate and repeatable are the measurements? Are there circumstances under which the measurements might be unreliable? What variables like air temperature, pressure, density, etc. might be important? Useful tidbits about LoggerPro: Graph axes: One can adjust the axes of graphs in LoggerPro by clicking on the axis minimum or maximum and typing in a positive or negative number. One can also autoscale the individual axes (see the button with the A inside a dotted-line box). Data Analysis: Under the Analyze:Examine menu one can bring up a crosshair allowing one to read individual graph values and associated times. Try making some graphs of various motions of members of your lab group. Your graphs will most likely be displayed as lines. Do the lines constitute the actual data? Can you change the graph style to display the real data? Goal 2: Move yourself to match graphs of position, velocity and acceleration It is instructive to try to match given graphs of position, velocity and acceleration vs. time. Open the experiment file PHYS 290 Position Match. Clear any data remaining you re your previous experiments. Look at the graph and determine how one would move to match it. Be sure to record this in your lab notebook. Try it a few times. Record in your notebook how you moved to match each segment of the graph. How would you move to make a curved position vs. time graph? Try it. Record your predicted graph and your results, commenting on the graphs. 3

4 What aspects of your position-time graphs indicate the direction of your motion? What aspects indicate your speed? Does the Position Match graph tell you where to start relative to the motion detector? Predict what the velocity graph for your Position Match curve would look like. Play with LoggerPro until you get a velocity graph as well as the original position graph. Move as you did for Position Match and see what the velocity graph looks like. Did it match your prediction? Try making other velocity graphs. Open the experiment file PHYS 290 Velocity Match. Clear any data remaining from previous experiments. Again, look at the graph and determine how you would move to match it. Record your predictions, then try it. In the Velocity Match graph you were given, there are vertical lines between the various segments of the graph. How must you move to match those vertical lines? What can you say about this? Does the Velocity Graph (alone) tell you where to start relative to the motion detector? Open the experiment file PHYS 290 Acceleration Match. Can you move to match this graph? How must you move? Goal 3: Make predictions of the motion of an object under various constant forces and test those predictions. During the last task you may have found it difficult to match an acceleration graph by moving yourself. Perhaps there is an easier way. For these experiments we will be using a low-friction cart on a smooth aluminum track, using the force of gravity on a hanging mass (transmitted via a string) to act on the cart. I would make another fine drawing of the setup below, but that s now your job! (and put it in your lab book, with everything properly labeled.) What is force related to position, velocity or acceleration? Make a prediction and record it. Draw position-time, velocity-time and acceleration-time graphs describing your predictions. Explain your reasoning. Now use the hanging mass/string/pulley system to apply a (mostly) constant force to the cart. Will the position, velocity or acceleration of the cart be constant when you let go of it? Try it, with the force applied to move the cart away from the motion detector. Explain your results. Organize your experiment such that the hanging mass pulls the cart pulls away from the motion detector. What would happen were you to give the cart a shove towards the motion detector with this setup? Make predictions (graphs, 4

5 in words, etc.) in you lab book. Now try it using LoggerPro/etc. to make graphs, and summarize your results in your lab book. What can you say about the cart s acceleration just when it is closest to the motion detector? Is it zero or something else? Goal 4: Newton s second law: predictions, verification, and a subtlety. You probably know Newton s laws by now. Newton s first law codified the findings of Galileo an object at rest or in motion remains in that same state unless acted upon by a (non-zero) net force. Here we will focus on Newton s second law. Your setup will allow you to experimentally verify this law, which relates an object s motion to its mass and applied force(s). Design simple experiments using your cart/track/mass-on-string/pulley setup to verify Newton s second law. Do this by making a prediction using the law as to what happens when you change variables. Think carefully about what you want to verify is varying one parameter (say, mass?) sufficient? Should you vary two parameters at the same time? Can you verify Newton s second law with just one type of experiment? After you have made your predictions confirm experimentally that they are correct. (Hint: you may want to make plots of one variable vs. the other {with the third held constant} that verify or refute your predictions). You can use the force probe attached to the cart to measure the force applied to the cart during your experiments. Rather, you should use the force probe to do this. Don t forget to zero the probe before each run. It useful, of course, to plot force vs. time during your experiment(s). 5