PHYSICS-1 ACCELERATION DUE TO GRAVITY Acceleration due to Gravity REPORT FORM Table 1: Using Picket Fence Ch. 1 (Single Beam) Trial Trial Trial Trial Mear Percent 1 2 3 4 Value along row error Capstone Run Number g' from velocity versus time graph `g' from the position versus time graph "g' from acceleration versus time graph Overall mean value of 'g' = Table 2: Using Smart Gate (Single Flag) Ch 1+2 (Double Beam) Trial Trial Trial Trial Mean Percent 1 2 3 4 Value error "g' from velocity versus time graph using Ch 1+2 RESULTS Value of 'g' found by using single beam in Smart Value of 'g' found by using Gate double beam X-T Graph V-T Graph a-7 Graph V-T Graph Value of 'g' (m/s?) Percent Error in 'g - 6 -PHYSICS-1 ACCELERATION DUE TO GRAVITY REPORT SUBMISSION Upload the following in the Report for this Lab: Points in report 1 . Using your camera to show your setup online during Lab time 5 2. Sharing your screen to show at least one Capstone graph, showing 5 velocity or acceleration value in selected area. 3. The completely filled up "Report Form" and Table of Results. Make sure to 10 include units of measurements. Don't forget to write the correct units. 4. Sample Calculations 5 Avoid Calculation and Rounding Errors. 5 Graphs from Capstone (at least one for each of the four types). The graphs 4*5 = 20 should show selected data and curve fit equation. All text in graphs should be legible (make sure the size is not too small). 6 Sources of Error in this experiment. Indicate the major sources of error. 2 5 points per source of error. Do not write: Human Error, Calculation Error, and Rounding Error. These will not get you any points. 7. Discussion of Results 10 Total 60 "Sources of Error" and "Discussion of Results" are separate headings Uploading a video of your experiment being performed will get you 5 points extra credit. Video should show you performing the experiment along with the resulting capstone graphs. - 8 -PHYSICS-1 ACCELERATION DUE TO GRAVITY Determine the value of g by Speed Between Gates-Time graph: Examine the plot of Speed versus Time. This should be a straight line. The slope of the "best fit line for velocity versus time data is the value of 'g'. Record your results. (Hint: In Capstone, select 'LINEAR' from the 'FIT' menu to get the best fit line.) - 5 -PHYSICS-1 ACCELERATION DUE TO GRAVITY SAMPLE DATA Table 1: Using Picket Fence Ch.1 (Single Beam) Trial Trial Trial Trial Mean Percent error 1 2 3 4 Value along row g' from velocity versus time graph (m/s2) 9.72 0.8 g' from the position versus time graph 9.72 0.8 (m/s2) 'g' from acceleration versus time graph (m/s2) 9.71 0.8 Overall mean value of 'g' = 9.72 m/s2 Table 2: Using Smart Gate (Single Flag) Ch 1+2 (Double Beam) Percent Trial Trial Trial Trial Mean error 1 2 3 4 Value 'g' from velocity versus time graph using Ch 3 1+2 (m/sz) 9.52 SAMPLE CALCULATOIN: Percent error = 100 * 19.8 - 9.72| / 9.8 = 0.82 = 0.8%PHYSICS-1 ACCELERATION DUE TO GRAVITY GRAPHS: 3.2 3.0 2.8 2.6 24 2.2 d (m/s) 2.0 1.8- 1. 6 - Linear 14 mt + b m = 9.72 + 0.019 1.2 b = -38.5 = 0.079 1.0 r = 1.000 0.8 0.6 4.04 4.06 4.08 4.10 4.12 4.14 4.16 4.18 4.20 4.22 4.24 4.26 4.28 4.30 Time (s) SPEED VERSUS TIME FOR PICKET FENCE FALLING THROUGH SINGLE BEAM PHOTOGATE 0.40 0.35 0.30 0.25 0.20 Quadratic Atz + Bt + C 0.15 A = 4.86 + 0.0057 Position (m) B = -38.5 + 0.047 0.10 C = 76.1 + 0.097 0.05 RMSE = 2.93x10- 0.00 -0.05 -0.10 3.8 3.9 4.0 4.1 4.2 4.3 4 4 4.5 Time (s) POSITION VERSUS TIME FOR PICKET FENCE FALLING THROUGH SINGLE BEAM PHOTOGATE - 10 -PHYSICS-1 ACCELERATION DUE TO GRAVITY 10.6- 10.4 10.2 10.0 Acceleration (m/s) 9.8 Mean: 9.71 9.6 9.4 4.10 4.12 4.14 4.16 4.18 4.20 4.22 4.7 Time (s) ACCELERATION VERSUS TIME FOR PICKET FENCE FALLING THROUGH SINGLE BEAM PHOTOGATE 3.0 2.5 2.0 Linear mt + b Speed Between Gates (m/s) m = 9.52 + 0.088 1.5 b = -33.6 + 0.33 O = 1.000 1.0 0.5 0.0 3.5 3.6 3.7 3.8 3.9 4.0 4.1 4.2 Time (s) [Graph title here] - 11 -PHYSICS-1 ACCELERATION DUE TO GRAVITY LK-DE Acceleration due to Gravity Smart Gate and Picket Fence Rev 3-23-2021 OBJECTIVE The purpose of this activity Is to deten'nlne the acceleration due to gravity by measuring the time of fall of a picket fence dropped through a smart gate. MA ERIALS . ME-sssii PASTrack or Small A-Base Psazzs Wireless Smart Gate ME-ssrra Picket Fence Mounting Rod ME-ssati Track Rod Clamp MEQED? Mum-Clamp ME-B'i'SB 45 cm Steel Rod THEORY A freely falling object has a vertically downward acceleration. This Is known as acceleration due to gravity and Its values Is almost the same all over the world. We start with the equations of motion for constant acceleration: V= V.- + 31. i1} and Y= Vii + (mgr? {2} Here, Vis the velocity of the object at time I and V,- is the initial velocity of the object [which is usually n). AYis the distance caveled in time i' and g is the acceleration due to gravity. If V.- Is zero. from (1} we can write V= g! (31 And from (2] we can write 1' = (ng (4} From equation [3} we see that the graph of V vs 1 is a straight line and Its slope is g. In the same way, from {4} we observe that the graph 1" vs t Is a parabola. The graph of Y vs I? is a straight line and its slope Is wig. Thus knowing the values of 1. Y, and Vwe should be able to nd the value of g. PHYSICS-1 ACCELERATION DUE TO GRAVITY Pad m: Tg' [Eln gfg 1. Before recording data for later analysis. experiment with the Photogate and Picket Fence by dropping the picket fence a few times and starting and stepping the program and looking at the graphs. 2. When everything is ready. start recording data by clicking RECORD near the bottom of the screen. Held the Picket Fence at one end behveen your thumb and forenger so the bottom edge of the Picket Fence Is Just above the Photcgate beam. Drop the Picket Fence vertically through the Photogete. Date recording begins when the Photogate beam is first blocked. Stop the recording once the Picket Fence has passed completely through the Photogate. You do NOT have to hurry to step the recording1 and you DO NOT have to start the recording JUST before dropping. Time legs on both sides are OK. Rascals the date to fill the Graph virihdovii. Erase the trial we oi data. WW 1. Select Picket Fence Ch.1 in the Smart Gate. Select Position on Yaxls and Time on X-axls. 2. New drop the picket fence and record the data. Repeat four times. 3. Obtain the value of 'g' and enter data In Table 1, from the: a) Quadratic t to the Position-Time graphr b] Slope of the Velocity-Time graph, and c} The Average value in the acceleration-Time Graph. Calculate the mean values. Now select Smart Gate {Single Flag} Cl'i 1+2 in the Smart Gate. Select "Speed Between Gates\" on the Y-aitls and Time on X-axls. Drop the picket fence four times. The slope of the straight line that you get for each run is the value of 'g'. Get Ila average. Enter data In Table 2. 5. Turn off the Smart Gate (or its battery will be consumed). int; instead orstertrng and stopping RECORD for each run, you can open Record, and drop the picket fence four times in a row. Then you will have sit {our cases on the some graph. Remember to get the stops for each drop serialstory. Willis When using the Picket Fence ch.1 setting in the Smart Gate: WWW: Examine the plot oi Velocity versus Time. This should be a straight line at an angle. The slope oi the \"best flt' line for velocity versus time date is the value of '3'. Record your results. (Hint: lh Capstone. select 'LINEAR' from the 'FlT' menu to get the bestflt line.) WWW: Examine the plot of Position versus Time. This should be a curved line and the quadratic equation: 1" - A T3 + 3]" + C fits the date. Comparing with equation {2] we see that A - if} 3. Record your results. (Hint: In Capstone, select 'QUADRATIC' from the 'FlT' menu to get the best fit line.) ' WW: Examine the plot of Acceleration versus Time. This should be a straight. horizontal line. The average value for acceleration versus time data is the value of 'g'. Record your results. (Hint: In Capstone, select the Z icon). lit'v'hen using the Smart Gate (Single Flag]: Ch 1+2 setting in the Smart Gate: .4. PHYSICS-1 ACCELERATION DUE TO GRAVITY 5w Me; This is a clear plastic strip with uniformly spaced opaque bands at fixed distances. mm; The Smart gate has two laser beams at known distance from each other {1.50 cm]. At the other side are two sensors that sense these beams. When any of them beams is obetmcted by a moving opaque object, a signal is sent to the Capstone software. By noting the time the obetructlon occurred. or was removed. Capstone can calculate the position, speed and acceleration of the moving object. The Smart Gate can be used with both or only one of the two beams being active. EBQQEDHBE W Depending on the availability of apace at your home, you can uee either of the following two methods to attach the Smart Gate: Method A: Using a Table. See gure 1. 1. Place the PASka on a tabla. Attach the Track Rod Clamp to the Track near its and. 2. Attach one and of the black Mounting Rod to the Smart Gate, and the other and to the Track Rod Clamp. Make sure the Mounting Rod to horizontal. Method 2: Keeping the Track on the Floor. See Figure 2. 1. Place the PASTrack on the oor. Attach the Track Rod Clamp to the Track near its end. 2. Face the 45 cm Steel Rod through the Track Rod Clamp, so that It is vertical. The purpose of the track is only to hold the clamp which will hold the steel rod. If desired, you can use the Small ABaee to hold the rod eteel instead of the PASTrack. 3. Attach the Mum-Clamp it) the Steel Rod. 4. Attach one and of the black Mounting Rod to the Smart |Sate. and the other end to the Multt Clamp. Make sure the Mounting Rod is horizontal. it we 45 cm Steel Ho ' .' Figure 1: Setup on a Table. m Figure 2: Setup on the Floor Track Rod Clamp PHYSICS-1 ACCELERATION DUE TO GRAVITY Continue Turn the Smart Gate head sideways so that you can drop a Picket Fence vertically from above the Smart Gate and have the Picket Fence move through its opening without hitting the Smart Gate (see Figure 3 and 4 for correct way of holding the picket fence, and the correct orientation while dropping it). 2. Place an old article of clothing, foam, or piece of cardboard on the floor or table directly below the Photogate, so the Picket Fence has a soft place to land. 3, If you are using a brand new picket fence, there may be a plastic protective film on it that should be removed. Figure 3: Right Way to Drop Picket Fence Figure 4: Wrong Way to Drop Picket Fence Part II: Computer Setup 1. Press and hold the power button on the Smart Gate, until the red LED starts to blink. Bluetooth is now on. 2. Turn on Capstone Software on your Laptop or Tablet. 3. In the Tools Palette (on left side of screen), click Hardware Setup to open Hardware Panel. 4. Click on the Bluetooth icon. It will sense the Bluetooth devices near it. Select the Smart Gate This will open a picture of the smart gate. Confirm the Smart Gate ID. 5. You will have a few different options on how to use the Smart Gate. We will first use: Picket Fence Ch.1, and then Smart Gate (Single Flag) Ch 1+2. 6. Click Hardware Setup once again. This will close the Hardware panel. 7. You will now see in the Display Panel, a number of options. Select Sensor Data. This will open a graph. Click on the label for the Y-axis, and select "Position" or "Speed". The X-axis should have time. - 3