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Physics Online Acceleration due to Gravity Introduction A freely falling object near the surface of the Earth is predicted by theory to undergo constant acceleration. The magnitude of this acceleration is given the symbol g. This value varies a bit from place to place; geology, latitude, and altitude all cause subtle changes. An equation1 that takes into account altitude and latitude is the following: [1] g = 9.780327(1 + 0.0053024(sin(θ))2 – 0.0000058(sin(2θ))2) – 0.000003086h θ = latitude h = altitude in meters Since the acceleration is assumed constant, we can use kinematics to find an experimental value of g. If we drop an object from rest, measure the distance to the ground, and measure the time to impact, we can calculate the acceleration using the following kinematics equation: [2] Δy = viyt + ½ayt2 Since viy is assumed to be zero, the equation simplifies and can be solved for a in terms of Δy and t. This is left as an exercise for the student. Exercise is fun! Equipment You Procure tape measure ladder or large building digital camera timekeeping device anvil, refrigerator, or other object for dropping Equipment from Kits digital calipers (optional) scale solid metal spheres (2) Experimental Procedures Calculations of Theoretical g 1) Research your altitude, latitude, and longitude. You might try Wikipedia for your town or Google Earth. 2) Use equation [1] to calculate the free fall acceleration for your location. Be sure to set your calculator to degree mode. Note that Excel will default to radian mode, so you will need to convert latitude to radians if you use it. You need not propagate error for this calculation. 3) Use the following webpage to calculate another theoretical value for g which takes into account local geology: http://www.ngs.noaa.gov/cgi-bin/grav_pdx.prl Calculations of Experimental g 4) Measure the mass and diameter of a solid metal sphere (or other dense object). You may skip the mass measurements if you don’t yet have a scale or the mass is too large (simply assert the relative mass). 5) Drop the sphere from a measured height. Larger heights generally give better results. 6) Measure the time to impact. 7) Solve equation [2] symbolically for acceleration. Use your formula and your data to calculate the acceleration. 8) Repeat steps 4 through 7 with two other objects. 9) Graph theoretical and experimental values with the mass on the x axis and the acceleration on the y axis. Be sure to obey the required graph format as specified in the general lab instructions. 10) Repeat steps 4 through 9 with a significantly different height. This will give you a total of 6 calculations of experimental g and 2 graphs. If you do not have 6 calculations of experimental g and 2 graphs, you will not receive full credit on your report. 11) Theory predicts that the free fall acceleration due to gravity will be fixed for all objects at a given location. Do your calculations of acceleration overlap with one another? Do they overlap with the accepted value? Directly address these questions in your conclusion. 1 http://en.wikipedia.org/wiki/Gravity_(Earth) accessed 7 October, 2008.