\fSince the steel ball gains speed (accelerates) as it fails it witl achieve its maximum velocity just before it strikes floor. We can combine equations [4] and [5] to derive a useful equation for estimating the maximum velndty of the hall (where d- y: distance the hall dropped) _ Vmu = 2 Ay ' [7] . .L.' ' , , t ' And the average velocity is one-half the maximum velocity: = A!- :81 Viva l , 7 , use that velocity (v) is a measure or how fast the falling object changes its position, and :: acceleration a (or g in this case) is a measure of how fast the object's velocity changes. In this experiment you 'll nd the time t required for a steel bait to fall from various heights. Using your measured time, you will also calculate the experimental vatue of g the acceleraho'n' due to gravity. , .___ ;Some questions to ponder before you begin: 1. is the acceleration of the falling steel ball constant? If the acceleratioo' Is constant then what' ts the value of the acceleration? 2 3; Is it the same for all objects. or does it vary with the mass andror the size of the shied? ' ' ' 4 7 Do heavier objects fall faster than lighter ones? PROCEDURE "9 \"COLLECT DATA 1. Drop a metat ball (or similar) from a height of 0. 5m (use 2 feet if using a yardstick}. Usino a ._ . stopwatch measure the time it takes for the ball to drop from this distance. Record this time as t1 7 Repeat the time measurement four more times disregarding any erroneous measurements and ' ._. record your resutts as values t2 through ts '2. Calculate the average of the tive values and record your result as tug. Then compute two\". T" ' 3. Repeat Steps 1 8r 2 for six different values of d (suggestion. 0. 75m. 1. 0m 125m 1 5m 1. 15m , - 2 .,iJrn higher if possible). (The actual heights need not be exactly these vatues, just be sure to record the measured value and use it for your caldulations ) Note that d= Ay in the equations- . . . I 4. Calculate the accepted value of time. 1m, using Equation [4] for each measured y and record it in ,, ' . ' I the table under tag: in Table 2. I 5. 'Using Equation [7] and your distance (y) and lime (rm) data ll In the values for v..." in Table 2 [5. For each height y and your average time tug, calculate the experimental acceleration due to gravity gm, from Equation [4] and record it In Table 2 as igup. ' I 7. Calculate the % difference for each value of g .I' , I ' , \"B. in Table 3, re- enter your 'y' and 'lavg 'values from Table 1 in the appropriate columns. Then calculate . 'Ir 7'. " I ' the ll-in columns tor '2y' (that's2times y) and 't; 1'. - ' IIIV w -- I ' ' . I ' I . I - 9. To determine your experimenter g', graph 2y (on the y) and 'tm?' (on the it). Note that this is just re ' \"' ' I arreuror '19 t. quat ion 4 and so who tor \"9 U .e- a scatter plot and add a linear tondlinelcurVB-t \"no. I - I l , Enter the slope of the line next to Table 3 TABLE 1 - EXPERIMENTAL DATA teva ( m) ( s) (8 ) ( 8 ) ( 8 ) (8) TABLE 2- CALCULATING GRAVITY 'g' taoc Vmax gexperimental !accepted % Difference (m) (m/s) (m/s?) (m/s?) 9.8 9.8 3.8 IN THE SPACE BELOW, SHOW ONE CALCULATION FOR EACH OF THE FOLLOWING VALUES IN YOUR TABLES ABOVE: Lace CS Scanned with CamScanner Vmax goxpertmental % differenceTABLE 3 -GRAPHICAL DETERMINATION of GRAVITY *g' 2 y tava tava? (m) (m) (s) (82) Slope of 2y vs to graph WRITE-UP Fill in ALL data tables, SHOW WORK for ONE calculation set, and answer the questions below CS the space provided, Show all work to receive credit. Attach the graph to the file before uploadit SHOWING the TRENDLINE from which you round the SLOPE above