Date of completing experiment:______________________ Physics with Vernier © Vernier Software & Technology 1 Picket Fence Free Fall Group Members:_____________________________ ______________ 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 essentially constant. As a result, an object in free fall accelerates downward at a constant rate. This acceleration is usually represented with the symbol, g (acceleration due to gravity). 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 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 photogate measures 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 software calculates and plots the velocities and accelerations for this motion. Figure 1 OBJECTIVE To measure the acceleration due to gravity, g, to better than 0.5% precision using a Picket Fence and a Photogate. 2 Physics with Vernier Picket Fence Free Fall MATERIALS computer Vernier computer interface Logger Pro Photogate Picket Fence clamp and ring stand to secure Photogate PRELIMINARY QUESTIONS (PRE-LAB)…FORMATIVE ASSESSMENT 1. Inspect your Picket Fence. You will be dropping it through a Photogate to measure g. The distance, measured from one edge of a black band to the same edge of the next band, is 5.0 cm. What additional information is needed to determine the average speed of the Picket Fence as it moves through the Photogate? 2. If an object is moving with constant acceleration, what is the shape of its velocity vs. time graph? 3. Does the initial velocity of an object have anything to do with its acceleration? For example, compared to dropping an object (from rest), if you throw it downward would the acceleration be different after you released it? PROCEDURE 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, provide a soft landing surface (such as carpet). 2. Connect the Photogate to the digital (DIG 1) port of the Vernier computer interface. Make sure all connections are complete (photogate to LabQuest or LabPro via BT Photogate cable and USB to computer before going to step 3). 3. Open the file “05 Picket Fence Free Fall” in the Physics with Vernier folder. Physics with Vernier 3 Picket Fence Free Fall 4. Observe the reading in the status bar of Logger Pro at the top of the screen. Block the Photogate with your hand; note that the GateState is shown as Blocked. Remove your hand and the display will change to Unblocked. 5. Click to prepare the Photogate for data collection. Hold the top of the Picket Fence between two fingers, allowing the Picket Fence to hang freely just above the center of the Photogate (see diagram above), without blocking the gate. Release the Picket Fence so it leaves your grasp completely before it enters the Photogate. The Picket Fence must remain vertical and should not touch the Photogate as it falls. 6. Examine your graphs. The slope of a Velocity vs. Time graph is a measure of acceleration. If the Velocity vs. Time graph is approximately a slanted (oblique) line of constant slope, the acceleration is constant. If the acceleration of your Picket Fence appears constant, fit a straight line to your data. To do this, click the Velocity vs. Time graph once to select it, then click Linear Fit, , to fit the line, y = mt + b, to the data. Record the slope in the data table. Remember to always title your graphs and then save it. Call it…”g Expt Trial 1”. 7. To establish the reliability of your slope measurement, repeat Steps 5 and 6 five more times. Do not use drops in which the Picket Fence hits or misses the Photogate. Record the slope values in the data table. Remember to always title your graphs and then save them. Call them…”g Expt Trial 2, 3, 4, 5, & 6”. DATA TABLES (DATA COLLECTION) TABLE 1 Trial Slope (m/s2) 1 2 3 4 9.844 9.750 9.431 9.722 5 6 9.585 TABLE 2 Acceleration (m/s2) Minimum slope value from Table1 Maximum slope value from Table1 Average slope value from Table1 9.431 9.844 9.6664 TABLE 3 Acceleration due to gravity, g 4 = 5.1 ± m/s2 Physics with Vernier Picket Fence Free Fall Precision = 4.8% % (DATA) ANALYSIS 1. From your six trials, determine the minimum, maximum, and average values for the acceleration of the Picket Fence. Record them in the Data Table 1 above. Insert screenshots printouts of all 6 Velocity vs. Time graphs with their respective Linear Fits included. [ WILL ATTACH FILE IN SUBMISSION ] Physics with Vernier 5 Picket Fence Free Fall 6 Physics with Vernier Picket Fence Free Fall 2. Describe in words the shape of the Position vs. Time graph for the free fall. You may want to look at the Distance vs. Time graph to help you answer the question. The graph is starting from rest, it is non constant motion its ganing speed by going down and its negative, it is also curved. 3. a. Describe in words the shape of the Velocity vs. Time graph. - The graph is starting from rest, it is constant motion, it is also a straight line, and its also ganning speed cause its positve and going up Physics with Vernier 7 Picket Fence Free Fall b. How is the velocity determined from the Position vs. Time graph? 0.1 – 0.2 divided by 0.06 – 0.11 = -3.343 c. How is the acceleration determined from the Velocity vs. Time graph? O.6 - 0.1 = -0.5 0.05-0.10=0.05 divided =10 4. The average acceleration you determined represents a single best value, derived from all your measurements. The minimum and maximum values give an indication of how much the measurements can vary from trial to trial; that is, they indicate the precision of your measurement. One way of stating the precision is to take half of the difference between the minimum and maximum values and use the result as the uncertainty of the measurement. Express your final experimental result in Table 3 as the average value ± the uncertainty. Round the uncertainty and the average value to one decimal place. For example, if your minimum, average, and maximum values are 9.12, 9.93, and 10.84 m/s2 respectively, express your result as g = 9.9 ± 0.9 m/s2. Next is the precision. This is done by expressing the uncertainty as a percentage of the acceleration i.e the precision of your experiment. To calculate the precision, divide the uncertainty by the average. Enter the value of the precision rounded to the nearest whole number in Data Table 3. Using the example numbers of 9.12, 9.93, and 10.84 m/s2 as minimum value, average value, and maximum value respectively, the precision would be Acceleration: 9.8-9.4 divided 2 = 5.1 Precision: 48 X 100% =48% divided 9.81 = 4.8% 8 Physics with Vernier Picket Fence Free Fall 5. Make sure to record all values in their respective Data Tables above. We did the Acceleration and Precision above !!! 6. Compare your measurement of g to the generally accepted value of g (from a Physics textbook or classroom Physics lecture). Does the accepted value fall within the range of your values i.e is 9.8 m/s2 between your minimum and maximum values of g in your table above? If so, your experiment agrees with the accepted value of g. Answer: The measured value of g does fall within the accepted value of g or…The measured value of g does not fall within the accepted value of g. 9.6664 X 5.1 = 49.2 divided by 9.81= 5.02 b. Find the relative error, ER in your measurement of g using the formula: ER = | 𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑 (𝑜𝑏𝑠𝑒𝑟𝑣𝑒𝑑) 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝑔 − 𝑇𝑟𝑢𝑒 (𝑎𝑐𝑐𝑒𝑝𝑡𝑒𝑑)𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝑔 | Physics with Vernier 𝑇𝑟𝑢𝑒 (𝑎𝑐𝑐𝑒𝑝𝑡𝑒𝑑)𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝑔 𝑋 100% 9 Picket Fence Free Fall Note: You’re taking absolute value in the numerator above…Hence, it must be a positive number. 7. Inspect your Velocity vs. Time graph. How would the associated Acceleration vs. Time graph look? Now, change the upper graph to Acceleration vs. Time. To do this, click the yaxis label and select Acceleration. You may want to rescale the graph so that the acceleration axis begins at zero. Insert your Acceleration vs. Time graph in the space below. Remember to always title your graph. 10 Physics with Vernier Picket Fence Free Fall 8. Use the Statistics tool on the Acceleration vs. Time graph to find the average acceleration. How does this compare with the acceleration value for the same drop, determined from the slope of the Velocity vs. Time graph? In the space below, record the value for the acceleration from the slope of the Velocity vs. Time graph and record the average acceleration from the Statistics tool on the Acceleration vs. Time graph. Use anyone of your 6 Trials that is the closest in value to 9.8 m/s2. Begin with the phrase… ”For trial # 4 , the value for the acceleration due to gravity, g from the slope of the Velocity vs. Time graph is 9.722 m/s2 while the average acceleration for the same drop from the Acceleration vs. Time graph is 9.555 m/s2. RESULTS: Write complete sentence(s). For example, “The results gathered from this experiment showed that the acceleration due to gravity near the surface of the earth is 9.31 m/s2 with a relative error of 5 % and a precision of 0.3%. - Thee results for the slope in the Velocity vs. Time graph is 9.722 m/s2 While the acceleration for the Acceleration vs. Time graph is 9.555 m/s2. Physics with Vernier 11 Picket Fence Free Fall Conclusion: Write at least 3 paragraphs with a minimum of 10 complete sentences summarizing your experiment. Your final sentence should include a careful explanation of improvements/extensions to the methods used in this experiment that would produce a more accurate result. You should begin by restating the objective (verbatim), summarize the procedure used to collect data in your own words, and state your results including precision and the relative (percentage) error, and then cite your CER. 12 Physics with Vernier
Purchase answer to see full attachment