Physics Lab

Purpose: The purpose of this experiment was to measure the velocity of various objects in freefall. Upon completion of this lab one will be able to calculate the values for acceleration and the effect of air resistance. Apparatus: 2m clear plastic tube Acculab sonic ranger (speed of sound = 343 m/s period = 0.03 seconds) SensorNet software Macintosh computer with system 6.07 or later Blank 3.5 HD Macintosh formatted disk Electronic mass scale, calipers Various objects to drop Procedure For the first part of Experiment 1 we dropped three objects of the same shape, but of varying mass. To promote accuracy, we performed three trials for each object. The first object we dropped was a 301 gram ball of radius 1.85 cm, followed by a 225 gram ball with radius 1.82 cm, and finally a 20 gram ball of radius 1.81 cm. From this information we were able to derive the mass densities of the objects. mass density = mass/((4/3)pR3 ) We recorded the relevant data and evaluated the average acceleration by means of the slope of the velocity graph. From the following equation we determined the magnitude of the net force acting on the object: Force net = mass x acceleration = Force gravity + Force air resistance Next, we calculated the errors and uncertainties: mean = 1/N [t1 + t2 + ... + tN] º 1/N S ti s = [1/N S (mean - ti )2]1/2 For the next part of Experiment 1, we simply conducted three trials for a ping pong ball of mass 20 grams and radius 1.81 cm. We followed the same basic procedure as above. Upon completion of three trials, we compared the data collected for the light object with that of a heavy object. The method used in Experiment 2 is a lot like that used in the previous experiment. Only now we are concerned with the velocity and acceleration during a jump. It took us several attempts to finally achieve three data samples in which the ball did not hit the wall of the tube. We evaluated the acceleration at several different key points and recorded our data. Then we calculated the errors using the equations stated above. Relevant Data On the following page are three representative samples of raw data from one trial for each of the experiments we conducted. The slope of the velocity graph, which can be calculated by the computer, is equivalent to the average acceleration. The mass density was calculated using the equation stated in the Procedure. The mean values of the slope for the three combined trials is calculated using the mean formula. The standard deviation is found using the standard deviation formula. Sample Calculations (using Mass = 301 g; Radius = .0185 m) Mass Density mass density = mass/((4/3)pR3 ) mass density = 301 g/((4/3)p(.0185)3 ) mass density =1.13 ´ 107 Mean Average Acceleration mean = 1/N [t1 + t2 + ... + tN] º 1/N S ti mean = 1/3 [14.605 + 6.394 + 5.634] º 8.877 Standard Deviation of the Mean s = [1/3 S (8.877 - {14.605, 6.394, 5.634})2]1/2 s = 2.344 Average Acceleration average acceleration = mean average acceleration ± standard deviation average acceleration = 8.877 ± 2.344 m/s2 Experiment 1.1 Mass = 301 g Radius = .0185 m Mass Density = 1.13 ´ 107 Mean of the Acceleration = 8.877 s = 2.344 Time (s) Distance (m) Dist (vel) Dist (accel) Vel (m/s) 1.32 0.562 2.922 2.922 1.35 0.663 3.368 14.887 3.368 1.38 0.773 3.647 9.304 3.647 1.41 0.889 3.889 8.064 3.889 1.44 1.014 4.168 9.304 4.168 1.47 1.144 4.317 4.962 4.317 1.5 1.285 4.708 13.026 4.708 1.53 1.433 4.913 6.823 4.913 1.56 1.595 5.415 16.748 5.415 1.59 1.767 5.732 10.545 5.732 1.62 1.95 6.104 12.406 6.104 Mass = 225 g Radius = .0182 m Mass Density = 8.91 ´ 106 Mean of the Acceleration = 12.617 s = 1.392 Time (s) Distance (m) Dist (vel) Dist (accel) Vel (m/s) 0.69 0.585 2.922 2.922 0.72 0.686 3.35 14.267 3.35 0.75 0.8 3.815 15.507 3.815 0.78 0.909 3.647 -5.583 3.647 0.81 1.033 4.131 16.128 4.131 0.84 1.168 4.503 12.406 4.503 0.87 1.307 4.615 3.722 4.615 0.9 1.458 5.024 13.647 5.024 0.93 1.62 5.415 13.026 5.415 0.96 1.791 5.713 9.925 5.713 0.99 1.97 5.936 7.444 5.936 Mass = 20 g Radius = .0181 m Mass Density = 8.05 ´ 105 Mean of the Acceleration = 13.672 s = 1.593 Time (s) Distance (m) Dist (vel) Dist (accel) Vel (m/s) 0.57 0.555 2.903 2.903 0.60 0.650 3.182 9.304 3.182 0.63 0.755 3.480 9.925 3.480 0.66 0.868 3.759 9.304 3.759 0.69 0.988 4.020 8.684 4.020 0.72 1.069 2.680 -44.661 2.680 0.75 1.066 -0.093 -92.424 -0.093 0.78 1.100 1.154 41.560 1.154 0.81 1.108 0.242 -30.395 0.242 0.84 1.728 20.675 681.087 20.675 0.87 1.903 5.825 -494.998 5.825 Experiment 1.2 Lead Ball Mass = 225 g Radius = .0182 m Mass Density = 8.91 ´ 106 Mean of the Acceleration = 12.617 s = 1.392 Time (s) Distance (m) Dist (vel) Dist (accel) Vel (m/s) 0.69 0.585 2.922 2.922 0.72 0.686 3.35 14.267 3.35 0.75 0.8 3.815 15.507 3.815 0.78 0.909 3.647 -5.583 3.647 0.81 1.033 4.131 16.128 4.131 0.84 1.168 4.503 12.406 4.503 0.87 1.307 4.615 3.722 4.615 0.9 1.458 5.024 13.647 5.024 0.93 1.62 5.415 13.026 5.415 0.96 1.791 5.713 9.925 5.713 0.99 1.97 5.936 7.444 5.936 Ping Pong Ball Mass = 2 g Radius = .0180 m Mass Density = 8.18 ´ 106 Mean of the Acceleration = 9.862 s = 2.955 Time (s) Distance (m) Dist (vel) Dist (accel) Vel (m/s) 0.81 0.511 2.456 2.456 0.84 0.600 2.977 17.368 2.977 0.87 0.694 3.145 5.583 3.145 0.90 0.799 3.480 11.165 3.480 0.93 0.908 3.629 4.962 3.629 0.96 1.024 3.889 8.684 3.889 0.99 1.151 4.206 10.545 4.206 1.02 1.280 4.317 3.722 4.317 1.05 1.416 4.522 6.823 4.522 1.08 1.559 4.764 8.064 4.764 1.11 1.709 5.006 8.064 5.006 1.14 1.859 5.006 0.000 5.006 1.17 1.985 4.206 -26.673 4.206 Experiment 2 Tennis Ball on way down first time Average Acceleration = 9.367 m/s2 Time (s) Distance (m) Dist (vel) Dist (accel) Vel (m/s) 0.84 0.575 2.810 2.810 0.87 0.678 3.424 20.470 3.424 0.90 0.779 3.387 -1.241 3.387 0.93 0.893 3.796 13.647 3.796 0.96 1.014 4.020 7.444 4.020 0.99 1.147 4.429 13.647 4.429 1.02 1.283 4.541 3.722 4.541 1.05 1.426 4.764 7.444 4.764 1.08 1.579 5.099 11.165 5.099 1.11 1.742 5.452 11.786 5.452 1.14 1.911 5.620 5.583 5.620 Tennis Ball just after hitting the floor Average Acceleration = -0.620 m/s2 Time (s) Distance (m) Dist (vel) Dist (accel) Vel (m/s) 1.20 1.911 -2.401 -2.401 1.23 1.796 -3.833 -47.763 -3.833 1.26 1.694 -3.387 14.887 -3.387 1.29 1.600 -3.145 8.064 -3.145 1.32 1.518 -2.717 14.267 -2.717 1.35 1.444 -2.494 7.444 -2.494 Tennis Ball near the top of its trajectory Average Acceleration = 14.577 m/s2 Time (s) Distance (m) Dist (vel) Dist (accel) Vel (m/s) 1.56 1.176 -0.577 -0.577 1.59 1.173 -0.093 16.128 -0.093 1.62 1.182 0.298 13.026 0.298 Tennis Ball on way down second time Average Acceleration = 9.361 m/s2 Time (s) Distance (m) Dist (vel) Dist (accel) Vel (m/s) 1.65 1.197 0.484 0.484 1.68 1.220 0.782 9.925 0.782 1.71 1.253 1.098 10.545 1.098 1.74 1.291 1.265 5.583 1.265 1.77 1.340 1.638 12.406 1.638 1.80 1.398 1.917 9.304 1.917 1.83 1.464 2.196 9.304 2.196 1.86 1.539 2.512 10.545 2.512 1.89 1.623 2.791 9.304 2.791 1.92 1.718 3.164 12.406 3.164 1.95 1.818 3.331 5.583 3.331 1.98 1.925 3.573 8.064 3.573 Analysis After analyzing our data we discovered some information concerning the relationships between different characteristics and properties of freefall. The graph of Acceleration vs. Mass, depicted on the following page, reveals no relationship between mass and acceleration. After completion of Experiment 1.1, our data showed that objects of lighter mass fall with a greater acceleration than those of greater mass. However, when we performed Experiment 1.2, our data for the ping pong ball did not follow the same trend as our data from Experiment 1.1. Upon careful evaluation, we discovered the relationship between mass density and acceleration. Objects of great density, such as the 301 gram ball, fall with less acceleration than objects of little density such as the ping pong ball. Experiment 2 revealed many things about acceleration. The acceleration downward is very close to the value of 'g', approximately 9.8 m/s2. This value of the average downward acceleration is constant for both the first time down and the second time down. We found the value of the average acceleration during the first descent to be 9.367 m/s2. This value is very close to the value we found for the second descent, 9.361 m/s2. The difference between these values and 9.8 m/s2 can be attributed to air resistance. We also found the value for the acceleration just after hitting the floor to be -0.620 m/s2. The value of the average acceleration near the top of the trajectory was found to be 14.577 m/s2. Discussion and Conclusion From this experiment, one learns how to measure the velocity of various objects in freefall. From this data, one can then calculate the values for acceleration and air resistance. This experiment relates directly to everyday situations. For example when one dribbles a basketball, the acceleration of the object becomes negative. Acceleration that at one time was direct towards the earth, is now directed in the opposite direction. From our calculations we concluded that as mass density increases, the average acceleration decreases and approaches 'g.' We also concluded that the downward acceleration is not related to air resistance. However we did find a relationship between velocity and the force of resistance. As the velocity of the object increases, the force of resistance decreases. We also found that the mass of an object has no effect on the downward acceleration of the object in freefall. From this experiment one discovers the relationships between different properties of an object.