IC-06 Acceleration due to gravity (Photo Gate)

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Aerospace Engineering

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Apr 3, 2024

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IC-06 - A CCELERATION DUE TO G RAVITY (P ICKET F ENCE AND P HOTO G ATE ) Rev 1-1-2023 6.1 OBJECTIVE The purpose of this activity is to determine the acceleration due to gravity by measuring the time of fall of a picket fence dropped through a photogate, as well as by some other method. 6.2 EQUIPMENT 1. Photogate 2. Picket Fence (ME-9377A) 3. Universal Table Clamp (ME- 9376) 4. Science Workshop 5. Capstone Software 6.3 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 i + g t , (1) and Y = V i t + (1/2)gt 2 (2) Here, V is the velocity of the object at time t and V i is the initial velocity of the object (which is usually 0). ∆Y is the distance traveled in time t and g is the acceleration due to gravity. If V i is zero, from (1) we can write V = gt (3) And from (2) we can write Y = ½ gt 2 (4) From equation (3) we see that the graph of t vs V is a straight line and its slope is g. In the same way, from (4) we observe that the graph t vs ∆Y is a parabola. The graph t 2 vs ∆Y is a straight line and its slope is ½ g. Thus knowing the values of t, ∆Y, and V we should be able to find the value of g.
6.4 EQUIPMENT DESCRIPTION: Picket Fence: This is a clear plastic strip with uniformly spaced opaque bands at fixed distances. Photo Gate: The Photo gate has one Infrared beam. At the other side is a sensor that senses the beams. When the beam is obstructed by an opaque object, a signal is sent to the Capstone software. By noting the time the obstruction occurred and was removed, Capstone can calculate the position and speed of the moving object. With several obstructions of known size (as in the Picket Fence), the instantaneous velocity and acceleration can also be calculated. You do not have to calibrate the photogate. 6.5 PROCEDURE Drop the “Picket Fence” through a Photogate. Each opaque band on the ‘Picket Fence’ blocks the Photogate beam and the time from one blockage to the next depends on the speed of the picket fence. Knowing the distance between the leading edge of each opaque band, the Capstone program calculates the average speed of the Picket Fence from one band to the next. The slope of the graph of average speed versus time gives the acceleration of the falling object. PART I: Computer Setup 1. Connect the Science Workshop interface to the computer, turn on the interface and then turn on the computer. 2. Connect the Photogate’s stereo phone plug to Digital Channel 1 on the interface. Click on Hardware Setup. A picture of the Science Workshop should appear. On the image of the Science Workshop, click at the slot where the Photogate has been attached. A dropdown list of equipment will open. Select “picket fence and photogate”. Close the Hardware setup by clicking it again. Your instructor will show you the steps to follow. PART II: Sensor Calibration and Equipment Setup 1. The program assumes a 5 centimeter (0.05 m) spacing, leading-edge-to-leading-edge, for the opaque bands on the Picket Fence. Measure this distance on the picket fence. If you need to change the default setting to another value, double-click on the Photogate & Picket Fence icon in the Experiment Setup window to open the Sensor Setup window. Enter the correct value for the spacing of the opaque bands on your Picket Fence. Click OK to return to the Experiment Setup window. 2. Set up the equipment as shown in Fig. 1. Mount the Photogate on the Pulley Mounting Rod. Turn the Photogate head sideways so that you can drop a Picket Fence vertically from above the Photogate and have the Picket Fence move through the Photogate’s opening without hitting it.
Trial Run of Data 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 stopping the program and looking at the graphs. 2. Place a piece of foam, or a backpack or other cloth on the floor directly below the Photogate, so the Picket Fence has a soft place to land. 3. When everything is ready, start recording data. Drop the Picket Fence vertically through the Photogate. Data recording begins when the Photogate beam is first blocked. Stop the recording once the Picket Fence has passed completely through the Photogate. 4. Rescale the data to fill the Graph window. 5. Erase your trial run of data. PART III: Data Recording 1. Prepare to drop the Picket Fence through the Photogate beam again. Hold the Picket Fence at one end between your thumb and forefinger so the bottom edge of the Picket Fence is above the Photogate beam. 2. Start recording data and then drop the Picket Fence through the Photogate beam. The data collection will begin automatically when the Photogate beam is first blocked. 3. After the Picket Fence passes completely through the beam, stop recording. 4. Repeat a few times, and find the mean values of ‘g’. Figure 1: Right Way to Drop Picket Fence Figure 2: Wrong Way to Drop Picket Fence
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