Lab: Freefall - Picket Fence Introduction A Picket Fence '5 a clear plastic strip with uniformly spaced opaque bands. Each opaque band blocks the photogate beam. and the time from one blockage to the next becomes shorter as the velocity of the falling Picket Fence increases. Using the known distance between the leading edge of each band. and the time interval between photogate blocks. the student calculates the average velocity of the Picket Fence for each interval. The slope of the graph of average velocity versus time gives the acceleration of the falling object. Equipment [5151 - - Mounting Rod Mult'rClamp _ support Rod -_ The support rod is inserted into the base embedded into the lab bench. The photogate is clamped to that rod so that it is suspended over the edge of the bench. Materials are placed below to break the fall of the fence when it hits the ground. Figure 1. Dropping a Picket Fence Set-up 1. Insert the support rod into the rod holder in the bench. 2. Use the MultiClamp to fasten the Photogate to the vertical rod. The Mounting Rod (see Fig. 2) screws directly into the side of the Photogate. Position the Photogate is at a comfortable height for dropping the picket fence through. Make sure that the Photogate is aligned so the picket fence will miss the desk as it falls. 3. Power on the Photogate and connect to it using Capstone. 4. Position some material. such as a basket of waste paper, below the Photogate to protect the falling Picket Fence when it reacha the oor. 5. Practice dropping the Picket Fence through the Photogate. Hold the Picket Fence at one end between thumb and forenger, as shown in Figure 3. The Picket Fence must hang vertical, so that when it is released, it will fall straight without rotating, Make sure the bottom edge of the Picket Fence is just above the Photogate beam when you let go. Note: The procedure is easier if one person handles the Picket Fence and another operates the computer. 6. There is a built-in timer that will record the times that each opaque band blocks the photogate beam. Click on Timer Setup in the palette at left to view the setup. Picket Fence Photogate Figure 2: Picket Fence Initial Position Figure 3. Hold in Center Hold the Picket Fence at one end between thumb and forenger, as shown. The Picket Fence must hang vertical. so that when it is released. it will fall straight without rotating. Make sure the bottom edge of the Picket Fence is just above the Photogate beam when you let go. Taking Data Table 1. Calculating Average Velocities 1. Start recording data, then drop the Picket Fence through the A Block Times At Average Time V=AX/At Photogate. Stop recording data. (S) (S) (S) (m/s) 2. If the Picket Fence hits the Photogate, or if it rotates too much, you 13.47808 XXXXXXXXXXXXXXXXX XXXXXXXXXXXXXXXXXXXXXXX XXXXXXXXXXXXXXXXXX should take another run. You should have seven entries in the data N table. These are the times that each of the seven bands on the 13.52669 0.04861 13.50239 1.02859 Picket Fence broke the Photogate beam. W 13.56154 0.03485 13.54412 1.43472 13.59022 0.02868 13.57588 1.74338 Calculations 13.61516 0.02494 13.60269 2.00481 3. Starting with ti and tz, calculate the difference (At) between block 13.63751 0.02235 13.62634 2.23714 times and enter them into the column in the table. Your first value would go in the second row cell of the At column. Note that you may 13.65775 0.02024 13.64763 2.47036 have to increase the number of decimal places in each column to see 00 the difference between the numbers. You can do this using the tool at the top of the graph. a 4.Calculate the average speed of the Picket Fence during the time between the first and second block. 2.6 V = AX _ Ax 2.4 At t2 - t1 2.2 V=Ax/At 2.0 Set where t is the time each block occured. Ax is the spacing between Linear the bands on the Picket Fence, and is measured from the beginning 1.8 V=Ax/At (m/s) mx + b of one band to the beginning of the next. The value of Ax in our case 1.6 m = 9.86 + 0.083 is 0.0500m. Enter your calculated average speeds into final column of the table. You will end up with only six velocities in your table 1.4 b = -132 + 1.1 1.2 r = 1.000 6. To calculate the time that each average velocity actually occurred, calculate the average time between the Block Times. Again starting 1.0 - with ti and to, add adjacent Block Times and divide by 2. Enter these times into the table in the Average Time column. 13.50 13.52 13.54 13.56 13.58 13.60 13.62 13.64 Average Time (s) Avg Velocity vs. Time6. Select a Linear Curve Fit from the graph toolbar. 2.5 7. What is the physical meaning of the slope? Does it 2.4 have units? What is the uncertainty in your value? V=Ax/At 2.3 Set 8. Compare to the accepted value using the % error calculation. 2.2 2.1 % error = Measured-Accepted x 100 Accepted 2.0 9. Was your value too high or too low? What might 1.9 account for that? 1.8 Answers: V=Ax/ At (m/s) 1.7 1.6 Linear mx + b 1.5 m = 9.86 + 0.083 1.4 b = -132 + 1.1 r = 1.000 1.3 1.2 1.1 1.0 13.50 13.52 13.54 13.56 13.58 13.60 13.62 13.64 Average Time (s) Average Velocity vs. TimeAnalysis In the previous sections, you used the Photogate only to V measure the time of block, and then calculated the speeds 2.4 by hand. The computer can also be configured to calculate Run #1 14 these speeds automatically, allowing you to take multiple runs in a short period of time. This is in the Timer Setup, which you can open at left. 2.2 1. Start recording data, then drop the Picket Fence through the Photogate as before. Stop recording data 2.0 2. The speed vs. time data for this run will be graphed at right. Select a Linear Curve Fit to find the acceleration as 1.8 before. Speed (m/s) 3. Repeat several times to get an average value. Also C record your highest value. 1.6 4. In the set-up procedure, you were instructed to start the Picket Fence as low as possible. This decreases the speed 1.4 and lowers the amount of air drag. Try letting go of the Picket Fence higher up to see if you can affect the measured acceleration. Do you get a lower value? Linear 1.2 mt + b m = 9.86 + 0.080 b = -132 + 1.1 1.0 r = 1.000 13.50 13.52 13.54 13.56 13.58 13.60 13.62 13.64 Time (s) Speed vs. timeAnalysis In the previous sections, you used the Photogate only to V measure the time of block, and then calculated the speeds 2.4 Run #2 Linear by hand. The computer can also be configured to calculate these speeds automatically, allowing you to take multiple mt + b runs in a short period of time. This is in the Timer Setup, m = 9.84 + 0.053 2.2 which you can open at left. b = -150 + 0.82 r = 1.000 1. Start recording data, then drop the Picket Fence through the Photogate as before. Stop recording data. 2.0 2. The speed vs. time data for this run will be graphed at right. Select a Linear Curve Fit to find the acceleration as 1.8 before. Speed (m/s) 3. Repeat several times to get an average value. Also record your highest value. 1.6 4. In the set-up procedure, you were instructed to start the Picket Fence as low as possible. This decreases the speed 1.4 and lowers the amount of air drag. Try letting go of the Picket Fence higher up to see if you can affect the measured acceleration. Do you get a lower value? 1.2 1.0 15.30 15.32 15.34 15.36 15.38 15.40 15.42 15.44 Time (s) Speed vs. timeAnalysis 2.6 In the previous sections, you used the Photogate only to V measure the time of block, and then calculated the speeds 2.5 by hand. The computer can also be configured to calculate Run # 3 these speeds automatically, allowing you to take multiple 2.4 runs in a short period of time. This is in the Timer Setup, 2.3 which you can open at left. 2.2 1. Start recording data, then drop the Picket Fence through the Photogate as before. Stop recording data 2.1 Linear mt + b 2. The speed vs. time data for this run will be graphed at 2.0 m = 9.74 + 0.014 right. Select a Linear Curve Fit to find the acceleration as b =-249 + 0.36 before. 1.9 1 Speed (m/s) r = 1.000 3. Repeat several times to get an average value. Also O 1.8 record your highest value. 1.7 4. In the set-up procedure, you were instructed to start the Picket Fence as low as possible. This decreases the speed 1.6 and lowers the amount of air drag. Try letting go of the Picket Fence higher up to see if you can affect the measured 1.5 acceleration. Do you get a lower value? 1.4 1.3 1.2 25.68 25.70 25.72 25.74 25.76 25.78 25.80 Time (s) Speed vs. timeAnalysis In the previous sections, you used the Photogate only to 2.4 V measure the time of block, and then calculated the speeds by hand. The computer can also be configured to calculate Run # 4 these speeds automatically, allowing you to take multiple 2.2 runs in a short period of time. This is in the Timer Setup, which you can open at left. 1. Start recording data, then drop the Picket Fence through 2.0 the Photogate as before. Stop recording data. Linear mt + b 2. The speed vs. time data for this run will be graphed at 1.8 m = 9.84 + 0.039 right. Select a Linear Curve Fit to find the acceleration as b = -13.0 # 0.058 before. Speed (m/s) r = 1.000 1.6 3. Repeat several times to get an average value. Also O record your highest value. 4. In the set-up procedure, you were instructed to start the 1.4 Picket Fence as low as possible. This decreases the speed and lowers the amount of air drag. Try letting go of the Picket Fence higher up to see if you can affect the measured 1.2 acceleration. Do you get a lower value? 1.0 0.8 1.40 1.42 1.44 1.46 1.48 1.50 1.52 1.54 1.56 Time (s) Speed vs. time D OAnalysis In the previous sections, you used the Photogate only to V measure the time of block, and then calculated the speeds 2.4 by hand. The computer can also be configured to calculate Run #5 these speeds automatically, allowing you to take multiple runs in a short period of time. This is in the Timer Setup, 2.2 which you can open at left. 1. Start recording data, then drop the Picket Fence through 2.0 the Photogate as before. Stop recording data. Linear mt + b 2. The speed vs. time data for this run will be graphed at m = 9.84 + 0.080 right. Select a Linear Curve Fit to find the acceleration as b = -20.1 + 0.18 before. Speed (m/s) r = 1.000 3. Repeat several times to get an average value. Also 1.6 record your highest value. 4. In the set-up procedure, you were instructed to start the Picket Fence as low as possible. This decreases the speed 1.4 and lowers the amount of air drag. Try letting go of the Picket Fence higher up to see if you can affect the measured acceleration. Do you get a lower value? 1.2 1.0 2.14 2.16 2.18 2.20 2.22 2.24 2.26 2.28 Time (s) Speed vs. timeAnalysis In the previous sections, you used the Photogate only to 2.4 V measure the time of block, and then calculated the speeds by hand. The computer can also be configured to calculate Run # 6 these speeds automatically, allowing you to take multiple runs in a short period of time. This is in the Timer Setup, 2.2 which you can open at left 1. Start recording data, then drop the Picket Fence through 2.0 the Photogate as before. Stop recording data Linear mt + b 2. The speed vs. time data for this run will be graphed at 1.8 m = 9.74 + 0.025 right. Select a Linear Curve Fit to find the acceleration as b = -34.3 + 0.091 before. Speed (m/s) r = 1.000 3. Repeat several times to get an average value. Also 1.6 record your highest value. 4. In the set-up procedure, you were instructed to start the 1.4 Picket Fence as low as possible. This decreases the speed and lowers the amount of air drag. Try letting go of the Picket Fence higher up to see if you can affect the measured acceleration. Do you get a lower value? 1.2 1.0 3.62 3.64 3.66 3.68 3.70 3.72 3.74 3.76 Time (s) Speed vs. timeAnalysis In the previous sections, you used the Photogate only to 2.4 V measure the time of block, and then calculated the speeds by hand. The computer can also be configured to calculate Run #7 these speeds automatically, allowing you to take multiple runs in a short period of time. This is in the Timer Setup, 2.2 which you can open at left. 1. Start recording data, then drop the Picket Fence through 2.0 the Photogate as before. Stop recording data. Linear mt + b 2. The speed vs. time data for this run will be graphed at 1.8 m = 9.75 + 0.10 right. Select a Linear Curve Fit to find the acceleration as b = -55.7 + 0.60 before. Speed (m/s) r = 1.000 3. Repeat several times to get an average value. Also 1.6 record your highest value. 4. In the set-up procedure, you were instructed to start the 1.4 Picket Fence as low as possible. This decreases the speed and lowers the amount of air drag. Try letting go of the Picket Fence higher up to see if you can affect the measured 1.2 acceleration. Do you get a lower value? 1.0 5.80 5.82 5.84 5.86 5.88 5.90 5.92 5.94 5.96 Time (s) Speed vs. time