Physics 211 Experiment 1 Free Fall Determining the acceleration of gravity Prior to Lab Derive the numbered equations Equations 1 2 and 3 in the lab instructions using the definitions of velocity and acceleration a dv dt and v dy dt Object The object of this experiment is to determine the value of the acceleration of gravity by measuring the rate of acceleration of a freely falling object In addition one will be able to compare theory with experiment for constantly accelerated motion Discussion An object dropped near the earth s surface will accelerate uniformly with the acceleration due to gravity g toward the earth The magnitude of g at the Berks Campus is 9 801 m s2 Thus according to the equation describing motion for a uniformly accelerated object its position y as a function of time t is 1 y v ot gt 2 2 1 where down is assumed to be the positive direction and its initial position is at the origin of the coordinate system used A graph of this equation would yield a parabolic curve as shown in the example below y Distance m t Time s The speed can be determined from the equation 1 by differentiating the displacement equation with respect to time yielding v v o gt 2 which when graphed is the straight line as shown v Speed m s t Time s where the y intercept is the initial speed v o and the slope of the line is the acceleration g Apparatus The experiment makes use of the Behr Free Fall apparatus shown at the right a dc source to power the electromagnet needed to hold up the falling object plummet and a high voltage spark generator to mark the spark tape every 1 60 second see figure below To measure the record spark tape a 2meter stick is also needed Procedure 1 For safety purposes follow the instructions of your lab instructor carefully The high voltage is dangerous DO NOT TOUCH THE LARGE WHITE CERAMIC HIGH VOLTAGE CONNECTOR OR ANY PART OF THE WIRE LEADING FROM IT TO THE APPARATUS 2 Start the spark generator and immediately thereafter open the switch controlling the magnet to release the plummet Turn off the spark generator as soon as the plummet hits the ground 3 With the lab instructor s help examine the spark tape to see if the record dots are useable 4 Remove the spark tape from the apparatus and lay it flat on the table Anchor its ends with some masking tape 5 Mark every third dot starting at the bottom of the tape and working toward the top There can be no unusually large gaps or missing dots in this marked set 6 Starting at the top where the dots are closest together set the 10 cm mark of the 2 m stick on the first dot on the tape t is set equal to zero here Measure the position of the marked dots of the tape Record these measurements on a table in the column marked scale reading See the sample table below Mark Number Time t s Scale Reading cm 1 2 3 0 0 05 0 10 10 0 14 3 23 4 Distance Below First Dot y cm Distance Below First Dot y m Average Speed y t 4 3 13 4 0 043 0 134 0 86 1 34 The first three columns are to be recorded at the time of reading the spark tape Calculate the last three columns using a spread sheet program The distance time column may be determined theoretically by dividing y t yielding y g vo t 3 t 2 which is the equation of a straight line with a y intercept of vo and a slope of g 2 7 With the data entered into a spread sheet calculate the last three columns Analysis 1 Plot a graph of distance in meters vs time in seconds Fit a quadratic polynomial order 2 to the data points What is the shape of the curve Is the graph and equation of the trendline consistent with theory What value of g is indicated by the fit to the data 2 Plot a graph of average speed y t vs time and determine its y intercept and slope using a linear trendline Is the shape of the curve consistent with theory The acceleration of gravity can be determined from the slope of the graph what is this value 3 What is the meaning of the y intercept on the graph plotted in step 2 of the analysis What is its value What does this value tell you about the motion of the plummet 4 How does the value of g compare with the standard value of g given in these instructions