MASSACHUSETTS INSTITUTE OF TECHNOLOGY Physics Department. Physics 8.01 Fall Term Experiment 01: Force and Motion

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1 MASSACHUSETTS INSTITUTE OF TECHNOLOGY Physics Department Physics 8.01 Fall Term 2010 Experiment 01: Force and Motion Purpose of the Experiment: In this experiment you will study the motion of a cart on a track in response to an applied force. The experiment is intended to help you investigate the following ideas, many of which you may already know. Velocity is the rate of change of an object s position with respect to time, and acceleration is the rate of change of an object s velocity with respect to time. Compute the instantaneous velocity from (i) a position vs. time graph of an object s motion and (ii) from a mathematical function describing the position of an object as a function of time. Understand that an object s acceleration may be either constant or may change with time or position. Determine experimentally whether an object moving in one dimension has constant or variable acceleration. Describe mathematically the motion of objects with either constant or variable acceleration; in particular see if you can verify F = ma. Learn how to represent the motion of an object using words, graphs, numerical tables, and equations. Learn to move comfortably among the different ways to represent motion. Experimental Materials: Logger Lite Software 50 gm weight/hanger 80 cm string adjustable end stop pulley/clamp PASCO track 250 gm PASCO cart Vernier Motion Detector Vernier LabPro Interface Setting Up the Apparatus: You will use a PASCO cart rolling on a track. A motion detector will let you measure its position as a function of time. The motion detector works by sending ultrasonic pulses to the cart and detecting the return echoes. Experiment 01 1 September 23/24, 2010

2 First attach an adjustable end stop and a pulley to the end of the track as shown in the photo to the left. (The adjustable stop is to keep the cart from crashing into the pulley.) Adjust the leveling screw at the other end of the track to get the track as level as you can; test by checking that the car does not have a greater tendency to roll in one direction than another. One end of a string will attach to the cart and the other end will pass over the pulley and attach to a weight that provides the force to accelerate the cart. Use a wire hook to attach one end of the string to the plastic tab at the Velcro padded end of the cart. To obtain a constant force to accelerate the cart, a 50 gm brass weight should be attached to the other end of the string. For future reference, note that the mass of the empty cart is 250 gm. Adjust the string length so that the falling weight hits the floor when the the cart is about two inches from hitting the the stop on the track. To obtain a variable force to accelerate the cart, replace the brass weight with a length of sash chain, as shown in the photo above. The motion detector should be placed at the other end of the track, against the stop that is permanently fastened to the track, as in the photo at the right. Make sure the slide switch on the top of the motion detector is set to the narrow beam position. Connect the motion detector to input DIG/SONIC 1 of the Vernier LogPro interface to the computer. The apparatus is now ready to use. The position of the cart will be measured using the motion detector, and the data will be taken by the Logger Lite program ForceMotion.gmbl, found in 8.01 labs. The motion detector measures the times for the echoes of ultrasonic pulses sent to the cart to return. The program calculates the distance to the cart (using a sound speed of 344 m/s). The program can plot the position, velocity, and acceleration of the cart and display them. The motion detector works best if it is aimed slightly above the center of the cart rather than pointing directly at it. (That reduces the effect of sound waves that bounce off the track before hitting the cart; you may be having this problem if the position seems to jump as the cart rolls along the track.) Experiment 01 2 September 23/24, 2010

3 Using the Logger Lite Program: Run Logger Launcher from the Desktop and select ForceMotion.gmbl from the resulting dialogue. When the program is running, you should get a window that looks like the one below. When you open the program, graphs of position, velocity, and acceleration vs. time are already displayed. You may change the data collection settings by navigating to the Experiment menu at the top left of the screen and selecting Data Collection. Set an appropriate length of data acquisition and sampling rate (default settings are 2 sec at 20 samples/sec). The maximum suggested sample rate is 31 samples/sec, and the absolute maximum is 50 samples/sec. Experiment 01 3 September 23/24, 2010

4 Making a measurement: The first thing you will probably want to do is to make a measurement. To do that, hold the cart on the track about 15 cm from the motion detector (the motion detector may give silly results for objects closer than 15 cm), then select the green play button labeled Collect. As soon as you click the button (or press the space bar) the program will start to measure the cart position, and will continue to do so for the amount of time chosen in the Data Collection settings. (If it does not stop automatically at this point, press the space bar to stop it.) The best way to make a measurement is to click space bar and then release the cart. You should see several graphs of the raw data like the one below. On this graph, the y axis is position of the cart with respect to the motion detector and the x axis is the time elapsed since you clicked the Collect button. If an obvious glitch appears in the plot, redo the measurement until you have a plot similar to the one shown below. Experiment 01 4 September 23/24, 2010

5 Plotting data: Plots are automatically generated and displayed in the 3 windows. To change settings for individual graphs (i.e. truncate axes, add title, etc.) simply double click on a graph. A Graph Options window will appear, from which you may augment your graph settings. Additionally, you may scroll over parts of your graphs and manually adjust settings or navigate to the Analyze menu and select Zoom In/Out or Autoscale. All 3 graphs should have their horizontal axes aligned. If this is not the case, they can be realigned by navigating to the Page menu and selecting Group Graphs. You may drag or enlarge graphs individually and then restore them to their original configuration by selecting Auto Arrange (ctrl+r). Storing Your Measurements: Every time you make a measurement, the new data replace the results of the previous measurement in the Logger Lite memory. Once you have obtained a measurement you are pleased with and want to analyze, you should export the data from Logger Lite to your data folder. To do this select Save from the File Menu to save as a Logger Lite file or Export to save as a.csv file (.csv files are comma delimited files that may be opened in Excel). You will do this at least twice once for the fixed 50 gm mass and once for the chain so choose appropriate names. The result will be a textfile on your computer that you will later open in Excel. What You Should Do: Carry out the experiment with a fixed 50 gm mass. Save the data from your best run. Carry out the experiment with the chain. Save the data from your best run. Analyze the data from the fixed mass experiment following the instructions in the Pre-Lab Homework problem. Compare your measured acceleration with the value expected theoretically. Analyze the data from the chain experiment following the instructions in the Pre-Lab Homework problem. What is the best indication that the acceleration in this case is not constant? Fill out the information on the following page and hand it in at the end of class, together with the graphs from your Pre-Lab Homework Problem. 5

6 8.01 Experiment 1: Force and Motion Name Section Table Fixed Mass Experiment Acceleration from theoretical model Acceleration from fit to x(t) Acceleration from fit to v(t) Acceleration from fit to a(t) Falling Chain Experiment a) Write the expression you obtained from a 3rd order polynomial fit to x(t). b) Write the expression you obtained from a 2nd order polynomial fit to v(t). c) Write the expression you get for v(t) by taking the derivative of your result in a) 6