PHYSICS LAB FREE FALL Printed Names: Signatures: Date: Lab Section: Instructor: GRADE: PHYSICS DEPARTMENT JAMES MADISON UNIVERSITY Revision August 2003
Free Fall FREE FALL Part A Error Analysis of Reaction Time An important facet of experimentation is error analysis (finding uncertainty). In this section of this lab, you will be introduced to this concept in relation to measurements of your reaction time. This lab will also provide instructions and experience using the program Logger Pro in entering and manipulating data. OBJECTIVES To measure and compare the reaction times of your left and right hands. To develop skills in use of Logger Pro for data entry and analysis. To become familiar with basic techniques in error analysis and propagation. MATERIALS Dell computer Meter stick Logger Pro PROCEDURE 1. Have your partner hold the meter stick vertically in front of you. Place your thumb and forefinger of your dominant hand on either side of the stick at the 50 cm mark. Make this measurement as accurately as you can. 2. Your partner will release the meter stick. Try to grab the stick as it falls as quickly as possible. Try not to anticipate the drop and do not move your hand down with the motion of the stick. 3. Measure the distance the stick has fallen. Make this measurement at least to the nearest millimeter. Record your data with pencil and paper. Complete 10 trials. 4. Enter your data into an Excel spread sheet. You will need a column for the distance (reaction distance). Add a column for the uncertainty in the measured distance and a comment or text box comment justifying these numbers. Make an educated guess. Do not use a mathematical formula. Consider the measurement and decide how well you can make a measurement of the reaction distance. (Note you may decide to use a single value as an estimate for all your measured distances. You may decide to use a different value for each measurement. There is no correct answer. Your justification is important. Be sure that you have made a good argument to justify your educated guess.) Your data sheet will be your report for this lab so label columns and include comments with text boxes whenever necessary. 5. Calculate your reaction time. a. d = ½ g (? t) 2 is the equation relating the distance an object will fall from rest as a function of time. Rearrange the equation to solve for? t.? t is reaction time. b. Add a column deltat and use Excel formulas to calculate. ANALYSIS 1. Use Excel to find the Mean, Standard Deviation, Standard Deviation of the Mean and Number of Points for the distance dropped and for the reaction time. Free Fall 54
Picket Fence Free Fall 2. Build a table with these results for your dominant hand (see example below.) Include a row that shows your reaction distance and one for the reaction time. Express results with correct significant figures, and units. Dominant Hand Distance Dropped Reaction Time Number of Points Mean Standard Deviation Std. Dev. of Mean 3. Repeat the experiment on the same person using the other hand. Answer these questions in text boxes on the spread sheet. QUESTIONS 1. Compare the SD in table with your uncertainty for a single measurement (procedure step 4). Should the values agree? If so, why don't they agree? DO NOT CHANGE YOUR GUESS. For the following questions assume that the mean is the best guess for your result. Assume that the SDM is the best estimate for the uncertainty in your result. 2. Is there a statistically significant difference in the reaction time between the two hands? (Justify your answer.) 3. How many points would be required to reduce the SDM to a value ten times smaller? 4. How does the uncertainty in the reaction time compare with the uncertainty in the distance? a. First calculate the percent uncertainty in the distance d, (uncertainty in d)/d x 100. ( Use the SDM and mean calculated on the previous page.) b. Now calculate the percentage uncertainty in the time t. c. Construct the following table in Excel. Dominant Hand Non-Dominant Hand A: percent uncertainty in B: percent uncertainty d. (EXTRA CREDIT answer this question after you have finished the entire lab.) Look through the "Error Analysis Cookbook" at the front of the lab and write a brief explanation of this result. Free Fall 55
Free Fall Part B - Picket Fence Free Fall We say an object is in free fall when the only force acting on it is the earth s gravitational force. No other forces can be acting; in particular, air resistance must be either absent or so small as to be ignored. When the object in free fall is near the surface of the earth, the gravitational force on it is nearly constant. As a result, an object in free fall accelerates downward at a constant rate. The magnitude of this acceleration is usually represented with the symbol g and has been found to be equal to 9.8 m/s 2. Physics students measure the acceleration due to gravity using a wide variety of timing methods. In this experiment, you will have the advantage of using a very precise timer connected to the computer and a Photogate. The Photogate has a beam of infrared light that travels from one side to the other. It can detect whenever this beam is blocked. You will drop a piece of clear plastic with evenly spaced black bars on it, called a Picket Fence. As the Picket Fence passes through the Photogate, the computer will measure the time from the leading edge of one bar blocking the beam until the leading edge of the next bar blocks the beam. This timing continues as all eight bars pass through the Photogate. From these measured times, the program will calculate the velocities and accelerations for this motion and graphs will be plotted. Picket fence OBJECTIVE Figure 1 To determine the acceleration of gravity (g) by measuring the acceleration of a freely falling body. To become more familiar with the concept of velocity and acceleration. To gain experience in using graphical methods in the analysis of experimental data. Free Fall 56
MATERIALS Power Macintosh or Windows PC Universal Lab Interface Logger Pro Picket Fence Free Fall Vernier Photogate Picket Fence clamp or ring stand to secure Photogate PROCEDURE BE SURE YOU COLLECT THE DATA BEFORE YOU LEAVE THE LAB. IF THE ANALYSIS IS INCOMPLETE YOUR INSTRUCTOR MAY REQUIRE YOU TO COMPETE THE ANALYSIS AT HOME. 1. Fasten the Photogate rigidly to a ring stand so the arms extend horizontally, as shown in Figure 1. The entire length of the Picket Fence must be able to fall freely through the Photogate. To avoid damaging the Picket Fence, make sure it has a soft surface (such as a carpet) to land on. 2. Connect the Photogate to the DG 1 input on the LabPro. 3. Prepare the computer for data collection by opening Exp 05 from the Physics with Computers experiment files of Logger Pro. Two graphs will appear on the screen. The top graph displays distance vs. time, and the lower graph velocity vs. time. 4. Observe the reading in the status bar of Logger Pro at the bottom of the screen. Block the Photogate with your hand; note that the Photogate is shown as blocked. Remove your hand and the display should change to unblocked. If this is not so, consult your instructor. 5. Click to prepare the Photogate. Hold the top of the Picket Fence and drop it through the Photogate, releasing it from your grasp completely before it enters the Photogate. Be careful when releasing the Picket Fence. It must not touch the sides of the Photogate as it falls and it needs to remain vertical. Click to end data collection if necessary. 6. Move the data to your Excel spread sheet (new worksheet). Enter values for the uncertainties in position, velocity, and time as unknown (You may just include a comment). Plot the data. The slope of a velocity vs. time graph is a measure of acceleration. If the velocity graph has a constant slope, the acceleration is constant. If the acceleration of your Picket Fence appears constant, fit a straight line to your data (see FITTING DATA appendix.). Be sure that you have an uncertainty for each parameter. Cut and paste the parameters from the fit to excel. Be sure to organize and label these values. 7. To establish the reliability of your measurement, repeat Steps 5 and 6 at least three more times. Do not use drops in which the Picket Fence hits or misses the Photogate. Record the slopes and initial velocities in the spread sheet as shown. Trial 1 2 3 4 5 6 Acceleration (m/s 2 ) uncertainty based on fit Initial Velocity (m/s) uncertainty based on fit ANALYSIS Use text boxes to include text answers in the spreadsheet. Free Fall 57
Free Fall 1. From your trials calculate mean value, standard deviation, and the standard deviation of the mean for the acceleration of the Picket Fence. Record them in an excel data table. Acceleration (m/s-s) Mean St. Dev. (SD) Std. Dev.of Mean (SDM) 2. Plot and describe in words the shape of the velocity vs. time graph of your final successful trial. How is this related to the shape of the distance vs. time graph? 3. Compare your measurement to the generally accepted value of g (from a textbook or other source). Do this by determining how well the accepted value lies within your value ± your Accepted Value - Your Value? Your Uncertainty uncertainty (i.e., your Standard Deviation of the Mean) through the following formula: If this number is less than 3, then you have an experimental value that does not exclude the accepted value to at least 95% certainty, meaning your experiment did not go against the accepted value. 4. Did you have a systematic error in your data compared with the theoretical value of g? How do you know? How do you account for this systematic error? Item Measured distance dropped and made an educated guess at uncertainty. Calculated values for? t and correctly calculated the uncertainty. Mean, Standard Deviation and Standard Deviation of Mean for d and? t Reaction time with uncertainty and significant figures Question 1 (Difference in right and left hand) Question 2 (Improve accuracy x10) Question 3 (Relationship uncertainties in? t and d) Photogate data -> spreadsheet, plotted, fit Placed fit on plot and evaluated Tabulated several trials Mean, Standard Deviation and Standard Deviation of Mean for g Examine 1 of the distance vs time graphs Comparison of distance vs time and velocity vs time Comparison g measured to accepted value with understanding of uncertainty. Analysis of distance vs time using trendline Instuctor's Evaluation Free Fall 58
Picket Fence Free Fall Free Fall 59