Freefall Lab Equipment Freefall Timer & Apparatus Clamp, 90 Steel Ball (2 different sizes) Meter Stick w/ 2 post clamps Ring Stand, 120cm Graphical Analysis Software . .... . . .. .' . . .- Figure 1 Photo and Schematic of Freefall Apparatus Overview You will measure the time it takes for a steel ball to fall from various heights. From this data you will be able to calculate the acceleration due to gravity, g. By repeating the experiment with a second steel ball of different mass, you can see if the mass of the ball noticeably influences the measured acceleration due to gravity. Introduction An object dropped near the Earth's surface will fall with an acceleration of g, independent of its mass. This was the famous observation of Galileo. This is true specifically when air resistance effects are negligible. Thus in a vacuum, a feather falls as quickly as a stone. The kinematic equation that describes the vertical position of an object at any time if it is dropped from rest is: y = 2812. (1 )For this particular formulation, y is taken to be positive in the downward direction and its initial position is taken to be zero. Thus, as time goes by the object is at greater positive values of y. If we plot y vs. t for this equation, then the resulting graph will be that of a parabola. So in order to produce a linear graph we will need to plot y vs. ". Remembering that the general formula for a straight line is: y = mx +b, (2) we can match equation (1) to this form by letting x = 1 , m = 1/2*g & b=0. Notice that the slope of the line would be half the acceleration due to gravity, so we would have to find the slope and then double our value. However, if we were to plot y vs. 2t2 then when we match this to the formula for a straight line we find that: m = g (3) b= 0 Notice that in this case the slope of the line for this plot is identically the acceleration due to gravity! This is preferable to the previous situation, so we will make plots of y vs. It to analyze for our lab. You are to experimentally determine the parameters m and b in equation set (3). You will accomplish this by measuring y and t for various heights of fall for a steel ball. After your data has been acquired you will plot y vs. x, where x takes on the value shown in equation (3). The slope of your best-fit line will be your value of g, and the intercept will be a further check on the validity of equation set (3). You will then repeat this for a second steel ball of a different mass. Procedure 1. Set up the ball release mechanism on a vertical stand that will allow various heights y to be arranged for the mechanism. 2. Place the steel ball in the mechanism and set the tightening screw so that the ball is secure. 3. Place the stop timer directly underneath the ball. 4. Measure the height y as shown in Figure 1. 5. Reset the timer. Release the ball. Record y and t for the fall. Repeat two more times. 6. Repeat at different heights for a total of five data points. 7. Repeat the data taking process for the second ball.DATA Trial Height Time 1 Time 2 Time 3 Median time (s) 1 (m) (s) (s) t2 (s) 2 (s 2) 0.38 0.2786 0.2788 0.2788 0.2787 0.0388 2 0.45 0.3039 0.3038 0.3041 0.3039 0.0462 3 0.54 0.3336 0.3336 0.3334 0.3335 0.0556 4 0.65 0.3758 0.3755 0.3756 0.3756 0.0705 5 0.77 0.3986 0.3973 0.3973 0.3977 0.0791\fData Analysis 1. For each trial determine the median value of your three measured times. It will be the middle value when you arrange them in ascending order. 2. You should then square the median value and then divide it by two in order to obtain a value for 2 2. 3. Make a high quality, full-page graph of your measured values of Height versus It for each ball. Make sure that your graph has an appropriate title and that the axes are labeled and indicate their units. You may do this either with a graphing program or on graph paper. If you use a computer make sure that the regression line and regression equation are both shown on the printout. If you use graph paper draw a best-fit straight line with a straight edge and calculate the slope of this line on the graph. You should also draw in an acceptable steepest/shallowest lines and calculate their slopes in order to obtain an uncertainty for your value of the acceleration due to gravity. Show your calculation on the graph page. Freefall - small ball position (m) [1/2]t2 ($2) Time Page 3 of 4 RVS Labs4. The slope of your best-fit line will be your value for "g". Determine the acceleration due to gravity with uncertainty for each ball. Remember to use the appropriate rules for uncertainties. 5. Finally you should strive to answer the following questions in your Results and Conclusions section of your lab report: Is the accepted value of "g" within the range . of uncertainty for each measurement that was made? What is the percent difference of your values for g for each measurement from the accepted value of 9.80 m/s2? Do the values that you obtained for the two different balls experimentally agree with each other? Did you experimentally verify Galileo's observation that all objects fall at the same rate? 6. You should also note if there are any trends in the data that you have taken and/or analyzed values