Photogate Finish The following is adapted with permission from the University of Dallas Fall ‘01 General Physics I Laboratory Manual, Adaptation: John Boehringer Everyday experience tells us that when an object is dropped, it speeds up as it falls toward the ground. The acceleration of the object undergoing free fall is due to the force of gravity exerted by the earth on the object. The acceleration is constant provided the effect of air resistance is negligible. In this experiment the value of gravitational acceleration, g, can be measured by recording and analyzing the motion of a “picket fence” as it passes through a photogate timing system. A photogate is an instrument that emits a thin beam of infrared light that it detected by a photoreceptor. The photoreceptor produces a current when the beam is present and stops that current when the beam is blocked. When the latter occurs, a break in the electronic signal occurs that can be measured and recorded by your LabPro interface. Your PC will record each of these “signal breaks” as a data point and plot the points with respect to time. As the picket fence falls it will produce these signal breaks with decreasing time intervals between them due to the acceleration of gravity. From the intervals between the points the instantaneous velocity and the acceleration of the falling body can be extrapolated. Problem What is the acceleration of a freely falling body? How well can you measure the acceleration of a falling body? Can you achieve a precision of 0.5% in your measurements? Materials Windows PC LabPro interface Logger Pro Software Vernier Photogate Picket Fence Ringstand to mount photogate Preliminary Questions 1. Inspect your picket fence. The distance between one edge of a black band to the same edge on the next band should be exactly 5.0 cm. What additional imformation will you need 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? Its displacement vs. time graph? 3. Does the initial velocity of an object have anything to do with its acceleration? For example, does a dropped ball accelerate more slowly than one that is thrown downward with some force? Why? Procedure 1. Secure the photogate to a ring stand or equivalent so that its arms extend horizontally as shown in the figure. The entire length of the picket fence must be able to pass freely through the photogate. To avoid damaging the picket fence (it will shatter!) be certain that there is a soft surface for it to land on (carpet or several backpacks next to one another). 2. Connect the photogate to the LabPro. If you are using an older photogate you may need an adapter. Ask your teacher if one is not provided. 3. Prepare the computer for data collection by opening experiment “05” from the physics with computers folder in the vernier subdirectory of your PC. 4. Observe the reading in the status bar of Logger Pro. Block the photogate with your hand. The display should indicate that the sensor is blocked. Unblock the photogate and this should change. Confirm that your photogate is operating properly before proceeding with the experiment. 5. Click Collect to prepare the photogate. Hold the top of the picket fence and drop it completely through the sensor. You must have enough time to release it completely before it enters the sensor. Be careful when releasing the picket fence. It must not touch the sides of the sensor and needs to remain vertical. Click Stop to end data collection. 6. View the position versus time graph and sketch it on the axes below. Be sure to include increments. 7. View the velocity vs. time graph and sketch it below. Drawing Conclusions 1. What is the shape of your velocity versus time graph? Does this agree with your predictions? 2. What does this shape imply about the motion of the picket fence as it falls? 3. Determine the acceleration from your velocity graph as follows: Examine your graphs. The slope of the velocity vs. time graph is a measure of the acceleration of the falling body. If the velocity graph is approximately a straight line of constant slope, the acceleration is constant. If the acceleration of your picket fence appears constant, fit a straight line to the data. To do this, click on the velocity graph once to select that data. The click the function fit button and fit an equation of the form y=mx+b to the data. Enter the slope of the velocity vs. time graph from your data below. Repeat the experiment until you have completed six trials and have obtained the relevant data. To find the precision in this experiment, perform a percent error analysis on the average value of g from the experiment compared to a theoretical value of 9.810 m/s2. Trial Slope (m/s2) 1 2 3 Minimum 4 Maximum 5 6 Average Acceleration (m/s2) Acceleration due to gravity, g Precision %error (use g = 9.810m/s2) ±m/s2 Assessing 1. From the best fit line, what was the initial speed of the picket fence? 2. What does the vertical axis (y) intercept represent on your velocity versus time plot? 3. Is acceleration due to gravity uniform? Explain your answer using evidence from your investigation. 4. What may account for discrepancies between your data? 5. Why is it so important that the picket fence pass through the photogate while remaining vertical? 6. Inspect your velocity graph. How would the associated acceleration graph look? Sketch your prediction below. 7. Now change the upper graph to acceleration vs. time. Do this by clicking on the y-axis label. Select acceleration, then deselect distance and click OK. Comment on any differences. You may need to rescale the graph to fit your window.