Lab Report about Gravity and Wind Resistance.

Introduction Thid week's laboratory will deal with the physics of falling objects. In the first section of the lab, you will measure the acceleration due to gravity of an object. Because of the size, shape, and mass of the object, wind resistance will be negligibly small. In the second part of the experiment, you will investigate the effects of wind resistance on a light object falling under the influence of gravity. In the first part of the experiment, you will measure the acceleration due to gravity of three different balls, each of a different mass. You will then analyze whether the acceleration due to gravity depended in a systematic way on the mass. In the second part of the experiment, we will be dropping very light coffee filters under the influence of gravity. Because of their size relative to their mass, the coffee filters will experience appreciable wind resistance effects. In fact, they will very rapidly achieve a terminal velocity where the force of wind resistance balances their weight, causing them to fall with a constant velocity. Some detailed analysis of the situation using calculus shows that the terminal velocity is expected to be, VI mg b where m is the mass of the falling object, g is the acceleration due to gravity, and b is a constant that depends on the properties of air and the shape of the object falling. Procedure We will begin the today's experiment by measuring the acceleration due to gravity of three different balls of different mass. The computer program that we will be using to make this measurement is called LoggerPro. It is an interface that is connected to our motion sensors that takes the data and helps you organize it. We begin by holding one of the balls beneath the motion sensor, but not too close. We release the ball and the computer plots a velocity vs. time graph for you on the screen corresponding to the motion of the ball. We find the region of the graph where the ball is falling freely under the influence of gravity. Since the slope of a velocity vs. time graph gives the acceleration, you can extract the acceleration due to gravity from this data. Record this number. We will repeat this procedure ten times for each ball. Below is an example image of one of the trials: Logga PuL01A21Wocity Graphiambil Ele Edr. Experiment Data Analyze insert Sabons Page Lep Bege 1 2 ANOM Collect 10 - near Fittoratet Velocity Verb m/Stoper 1015 mbi binlercepti: 2.734 ms CH 0.9993 1 EMRE 00-05 6- (31) Kapoor 1 2- 05 1.0 00 (A10.158 Av.0.26) Time (s) We extract the slope for all 10 trials for each of the 3 balls. The data are summarized in the three tables below (each slope is in m/s?: Ball with a mass of 54.8g: 10.62 9.84 10.65 10.01 10.66 9.25 9.50 10.21 10.15 9.36 Ball with a mass of 198.2g: 9.41 10.19 9.47 8.97 9.79 10.66 9.91 9.61 10.34 10.65 Ball with a mass of 406.4g: 9.35 8.52 10.96 9.72 9.38 9.63 10.26 10.07 10.10 9.93 Calculate the average acceleration for each ball and use the standard deviation in those ten values as the uncertainty in the acceleration for each ball. Is there any systematic variation in the acceleration due to gravity for each ball due to the mass of the ball? Make a plot of the acceleration as a function of the mass of the ball. Please include your uncertainties as error bars. In the next part of the experiment, you will investigate the effects of wind resistance. To do so you will be dropping coffee filters from beneath the motion sensor. Start out by dropping one coffee filter and plotting its velocity vs. time graph. We then attempt to find an interval of time when the coffee filter has a basically constant velocity, its terminal speed. We then use statistical analysis to determine the mean and the variation in the terminal velocity, as shown in the dialog box shown in each plot below: Figure 1: One Coffee Filter Logger Pro-L0A2-1 [Ve ocity Giphsxmb File Edi Experiment Data Analye at patium Pegu up SBPage 1 A eV, MOR Collect 3- M Statistics for Latest Viaty min: 1433 1032 maic 1272 a 1.465 mean 1204 median: 1.203 std dev: 0.04018 samples 17 Ay 155 Velocity (mis) 1 05 10 1.5 00 (At 0.574 Av.0.061) Time (5) Figure 2: Two Coffee Filters Legger Pro L04A2.1 (Velocity Graphs amb File Edit Experient Data ruly mat plium Page Exp HAPage - AurP121/MOR Cellett 2- Statistics for Latest Velaty min: 1.767 09324 mac 1.670 at 1190 mean. 1827 medan: 1.823 sid dev: 0.03284 samples: 12 Av 0100 Velocity (mis 05 10 15 00 (0879, 0.672) (A:0 385 Av0 783) Time (5) Figure 3: Three Coffee Filters 1 0 X Logger Pro-L0A2-1 ve ocity Graphsxmb File Edin Experiment Data Analyer mat Option Page Fup Page 1 AQQINDS AIM OD Collect Statistics for Latest Velocity min: 2.025 1 199 mac 217 21.132 mean. 2.079 medan.2.UTT sid dev: 0.02733 samples: 10 Av 092 Velocity (mis) 1 0 00 (A0.335 AVD. 117) 0.5 1.0 1.5 Time (5) Figure 4: Four Coffee Filters Logger Pro-LUTA2-TV ocity Gaphsxmbr File Edit Esperiment Data Analye ncert Options Page tep Page 1 ARQ22.1/ Collect 3 2 Velocity imis 0- 0.5 1.0 1.5 0.0 (1 093.2373) (Ar: 141 A 0039) Time (5) Record the mean value and the standard deviation of the highlighted velocity for each trial. Plot the terminal velocity as a function of the number of filters (which is proportional to the mass of the system). Please include your uncertainties as error bars. Do you find a systematic variation in the terminal velocity as a function of mass? Is it what you expected from the theory presented in the introduction? Introduction Thid week's laboratory will deal with the physics of falling objects. In the first section of the lab, you will measure the acceleration due to gravity of an object. Because of the size, shape, and mass of the object, wind resistance will be negligibly small. In the second part of the experiment, you will investigate the effects of wind resistance on a light object falling under the influence of gravity. In the first part of the experiment, you will measure the acceleration due to gravity of three different balls, each of a different mass. You will then analyze whether the acceleration due to gravity depended in a systematic way on the mass. In the second part of the experiment, we will be dropping very light coffee filters under the influence of gravity. Because of their size relative to their mass, the coffee filters will experience appreciable wind resistance effects. In fact, they will very rapidly achieve a terminal velocity where the force of wind resistance balances their weight, causing them to fall with a constant velocity. Some detailed analysis of the situation using calculus shows that the terminal velocity is expected to be, VI mg b where m is the mass of the falling object, g is the acceleration due to gravity, and b is a constant that depends on the properties of air and the shape of the object falling. Procedure We will begin the today's experiment by measuring the acceleration due to gravity of three different balls of different mass. The computer program that we will be using to make this measurement is called LoggerPro. It is an interface that is connected to our motion sensors that takes the data and helps you organize it. We begin by holding one of the balls beneath the motion sensor, but not too close. We release the ball and the computer plots a velocity vs. time graph for you on the screen corresponding to the motion of the ball. We find the region of the graph where the ball is falling freely under the influence of gravity. Since the slope of a velocity vs. time graph gives the acceleration, you can extract the acceleration due to gravity from this data. Record this number. We will repeat this procedure ten times for each ball. Below is an example image of one of the trials: Logga PuL01A21Wocity Graphiambil Ele Edr. Experiment Data Analyze insert Sabons Page Lep Bege 1 2 ANOM Collect 10 - near Fittoratet Velocity Verb m/Stoper 1015 mbi binlercepti: 2.734 ms CH 0.9993 1 EMRE 00-05 6- (31) Kapoor 1 2- 05 1.0 00 (A10.158 Av.0.26) Time (s) We extract the slope for all 10 trials for each of the 3 balls. The data are summarized in the three tables below (each slope is in m/s?: Ball with a mass of 54.8g: 10.62 9.84 10.65 10.01 10.66 9.25 9.50 10.21 10.15 9.36 Ball with a mass of 198.2g: 9.41 10.19 9.47 8.97 9.79 10.66 9.91 9.61 10.34 10.65 Ball with a mass of 406.4g: 9.35 8.52 10.96 9.72 9.38 9.63 10.26 10.07 10.10 9.93 Calculate the average acceleration for each ball and use the standard deviation in those ten values as the uncertainty in the acceleration for each ball. Is there any systematic variation in the acceleration due to gravity for each ball due to the mass of the ball? Make a plot of the acceleration as a function of the mass of the ball. Please include your uncertainties as error bars. In the next part of the experiment, you will investigate the effects of wind resistance. To do so you will be dropping coffee filters from beneath the motion sensor. Start out by dropping one coffee filter and plotting its velocity vs. time graph. We then attempt to find an interval of time when the coffee filter has a basically constant velocity, its terminal speed. We then use statistical analysis to determine the mean and the variation in the terminal velocity, as shown in the dialog box shown in each plot below: Figure 1: One Coffee Filter Logger Pro-L0A2-1 [Ve ocity Giphsxmb File Edi Experiment Data Analye at patium Pegu up SBPage 1 A eV, MOR Collect 3- M Statistics for Latest Viaty min: 1433 1032 maic 1272 a 1.465 mean 1204 median: 1.203 std dev: 0.04018 samples 17 Ay 155 Velocity (mis) 1 05 10 1.5 00 (At 0.574 Av.0.061) Time (5) Figure 2: Two Coffee Filters Legger Pro L04A2.1 (Velocity Graphs amb File Edit Experient Data ruly mat plium Page Exp HAPage - AurP121/MOR Cellett 2- Statistics for Latest Velaty min: 1.767 09324 mac 1.670 at 1190 mean. 1827 medan: 1.823 sid dev: 0.03284 samples: 12 Av 0100 Velocity (mis 05 10 15 00 (0879, 0.672) (A:0 385 Av0 783) Time (5) Figure 3: Three Coffee Filters 1 0 X Logger Pro-L0A2-1 ve ocity Graphsxmb File Edin Experiment Data Analyer mat Option Page Fup Page 1 AQQINDS AIM OD Collect Statistics for Latest Velocity min: 2.025 1 199 mac 217 21.132 mean. 2.079 medan.2.UTT sid dev: 0.02733 samples: 10 Av 092 Velocity (mis) 1 0 00 (A0.335 AVD. 117) 0.5 1.0 1.5 Time (5) Figure 4: Four Coffee Filters Logger Pro-LUTA2-TV ocity Gaphsxmbr File Edit Esperiment Data Analye ncert Options Page tep Page 1 ARQ22.1/ Collect 3 2 Velocity imis 0- 0.5 1.0 1.5 0.0 (1 093.2373) (Ar: 141 A 0039) Time (5) Record the mean value and the standard deviation of the highlighted velocity for each trial. Plot the terminal velocity as a function of the number of filters (which is proportional to the mass of the system). Please include your uncertainties as error bars. Do you find a systematic variation in the terminal velocity as a function of mass? Is it what you expected from the theory presented in the introduction