Measuring The Velocity Of Various Objects In Freefall

1490 words - 6 pages

Purpose:The purpose of this experiment was to measure the velocity of various objects in freefall. Upon completion of this lab one will be able to calculate the values for acceleration and the effect of air resistance.Apparatus:2m clear plastic tubeAcculab sonic ranger (speed of sound = 343 m/s period = 0.03 seconds)SensorNet softwareMacintosh computer with system 6.07 or laterBlank 3.5 HD Macintosh formatted diskElectronic mass scale, calipersVarious objects to dropProcedureFor the first part of Experiment 1 we dropped three objects of the same shape, but of varying mass. To promote accuracy, we performed three trials for each object. The first object we dropped was a 301 gram ball of radius 1.85 cm, followed by a 225 gram ball with radius 1.82 cm, and finally a 20 gram ball of radius 1.81 cm. From this information we were able to derive the mass densities of the objects.mass density = mass/((4/3)pR3 )We recorded the relevant data and evaluated the average acceleration by means of the slope of the velocity graph. From the following equation we determined the magnitude of the net force acting on the object:Force net = mass x acceleration = Force gravity + Force air resistanceNext, we calculated the errors and uncertainties:mean = 1/N [t1 + t2 + ... + tN] º 1/N S tis = [1/N S (mean - ti )2]1/2For the next part of Experiment 1, we simply conducted three trials for a ping pong ball of mass 20 grams and radius 1.81 cm. We followed the same basic procedure as above. Upon completion of three trials, we compared the data collected for the light object with that of a heavy object.The method used in Experiment 2 is a lot like that used in the previous experiment. Only now we are concerned with the velocity and acceleration during a jump. It took us several attempts to finally achieve three data samples in which the ball did not hit the wall of the tube. We evaluated the acceleration at several different key points and recorded our data. Then we calculated the errors using the equations stated above.Relevant DataOn the following page are three representative samples of raw data from one trial for each of the experiments we conducted. The slope of the velocity graph, which can be calculated by the computer, is equivalent to the average acceleration. The mass density was calculated using the equation stated in the Procedure. The mean values of the slope for the three combined trials is calculated using the mean formula. The standard deviation is found using the standard deviation formula.Sample Calculations (using Mass = 301 g; Radius = .0185 m)Mass Densitymass density = mass/((4/3)pR3 )mass density = 301 g/((4/3)p(.0185)3 )mass density =1.13 ´ 107Mean Average Accelerationmean = 1/N [t1 + t2 + ... + tN] º 1/N S timean = 1/3 [14.605 + 6.394 + 5.634] º 8.877Standard Deviation of the Means = [1/3 S (8.877 - {14.605, 6.394, 5.634})2]1/2s = 2.344Average Accelerationaverage acceleration = mean average acceleration ± standard...

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