M9c: Free Fall Acceleration Introduction: Gravity represents one of the central concepts of physics. In fact, two of the most well known names in physics found their fame in dealing with gravity. If one were to ask people the first name that pops into their mind when they hear the word "physics", most likely it will be Sir Isaac Newton (and his allegorical apple falling from the tree), or Albert Einstein (whose theory of relativity modifies and extends Newton). The main objective for this experiment is to calculate the acceleration "g" of a free falling object manifested due to the force of gravity. In addition to this objective, this experiment will also determine if mass or the distance that an object falls influence the gravitational acceleration that object experiences. The question of whether or not heavier objects fall faster will be answered yet again, determining if Galileo's experiments at the Leaning Tower of Pisa were right. This all will be accomplished first by dropping a silver colored metallic sphere from several pre-established heights. Measuring how long it takes the sphere to fall, it is then possible to calculate gravitational acceleration. The effects (if any) of mass on gravitational acceleration are tested by dropping a second sphere, different from the first, and measuring how long it takes to fall. One final component of this lab, found within the Discussion section, will be the demonstration of how the application of key concepts within physics can lead to the derivability of any number of equations, which is a very useful aspect of the study of physics. Apparatus: 1 long solid rod (1 to 3 meters in length) w/ table clamp 1 right angle clamps 1 holder arm/ gate one 1 impact sensor / gate two 2 metal spheres laboratory balance > 2 meter measuring stick computer timing system Figure 1Discussion: With physics, if one is given a concept (such as kinematics); then this Kinematic Definitions concept in turn points towards a set of definitions (such as the definitions of Acceleration a =- a = - -V velocity and acceleration). These At -t definitions finally will yield up a base set of equations that approximate a Ar velocity - Vitys physical relationship, and with these Vavg At 2 1 , - t ; equations, it is then possible to derive new sets of relationships that can correlate to your experiment. This Figure 2 derivability of equations gives the equation needed to calculate the acceleration due to gravity. In order to derive the equation necessary to calculate the acceleration due to gravity, it is first necessary to consider the two most basic and fundamental concepts of Kinematics (the study of motion): acceleration and velocity. Now, in order to simplify calculations, and because it correlates with this experiment's setup, acceleration and velocity can be considered as representing Motion in only One Dimension. In light of this fact , the definitions for acceleration and for velocity are defined within Figure 2 as being dependent on the initial and final velocities ( v,, vy ), the initial and final times (t;, t, ), and the initial and final positions (17, "). Now, consider the diagram provided in Figure 3, representing this experiment's setup. The different t's, r's, and v's with their different subscripts (of 1 and 2) represent the different points of observation: the holder at the top of the apparatus, and the impact sensor at the bottom. Collected Data t = computer time interval d = distance between timing gates t = time r = position For the experiment, the following equation may be a=g v = velocity surmised, working under the original definitions provided in Figure 2, where a has been replaced by g. and ty -t; and ry -7, have been changed according to t2 - t1 = t Figure 3's equations and relationships: 12 - 1 = d g = 12 - M - and Mit V/2 2 Now, by assuming that v, is equal to 0 (since the sphere is being dropped from a resting position, this is a valid assumption), it is possible to see that 2d g = - and v2 = -, which, in turn gives the final Figure 3 equation for acceleration due to gravity for this 2d experiment: g = -Data Sheet: M9c: Free Fall Acceleration NAME: DATE: Object 1: mass= 0.016107 (kg) weight= (Newtons) distances Trial 1.545 (m) 1.485 (m) 1.375 (m 1.215 (m) 1.005 (m) t (s) g (m/s2) t S g (m/s2) t (s g (m/s2) t (S g (m/s2) t S g (m/s2) 0.56234 0.55176 0.52928 0.50097 0.45632 N 0.56148 0.55150 0.53153 0.49954 0.45541 3 0.56423 0.55064 0.52967 0.49786 0.45557 Mean g (m/s2) Overall Mean g (m/s2): Standard Deviation (m/s2): %Error: Object 2: mass= 0.02778 (kg) weight= (Newtons) distances Trial 1.545 (m) 1.485 (m) 1.375 (m) 1.215 (m) 1.005 (m) t (s) g (m/s2) t (s) g (m/s2) t (s) g (m/s2) t (s) g (m/s2) t (s) g (m/s2) 0.56174 0.55072 0.52944 0.49833 0.45116 N 0.56179 0.55067 0.53024 0.49859 0.45415 3 0.56109 0.54536 0.52884 0.49815 0.45298 Mean g (m/s2) Overall Mean g (m/s2): Standard Deviation (m/s2): %Error