Experiment 4: Data Collection. Student-X. Lab Partner: Student-Y. Date Performed: 4 Feb 09; 1010-hours. PHY 211 C11

Transcription

1 Experiment 4: Data Collection Student-X Lab Partner: Student-Y Date Performed: 4 Feb 09; 1010-hours. PHY 211 C11

2 Section 1: Experiment and Observation A. Objective Students will make predictions involving the speed of a thrown baseball and the motion of a bowling ball across a level surface. These predictions will then be tested by performing simple experiments using balls and collecting data on the balls velocities (speeds). B. Equipment Used C. Data LabPaq lab manual Computer with Excel 2003 Lab Partner Measuring tape Baseball Stopwatch Bowling ball (my laboratory partner owns one) Tape (to mark distances) Data Table 1 shows my pitching speed data along with the data of three other students. The values for average time, average speed in meters per second and average speed in miles per hour were manually calculated in this table. In each case, the numbers used in calculations were not rounded to the appropriate number of significant figures until the last step. Name Distance (m) Data Table 1 t 1 (s) t 2 (s) t 3 (s) Avg. t (s) Avg. speed (m/s) Avg. speed (miles/h) Student-X Student-A Student-B Student-C Predicted speed of my pitch = 50 miles per hour

3 Data Table 2 shows my pitching speed data along with the data of three other students. The values for average time, average speed in meters per second and average speed in miles per hour were calculated using Excel in this table. Name Distance (m) Data Table 2 (spreadsheet calculations) t 1 (s) t 2 (s) t 3 (s) Avg. t (s) Avg. speed (m/s) Avg. speed (miles/h) Student-X Student-A Student-B Student-C Whole group Predicted speed of my pitch = 50 miles per hour Data Table 3 shows the data from the horizontal motion experiment using a bowling ball (on a flat smooth surface). This data table includes the average time for the three trials at each distance. Data Table 3 Time: 2-m Distance Time: 4-m Distance Time: 6-m Distance Trial s 2.94 s 4.53 s Trial s 3.05 s 4.67 s Trial s 2.84 s 4.37 s Average time: 1.42 s 2.94 s 4.52 s Data Table 4 shows the average speed of the bowling ball at each distance during the horizontal motion experiment. Notice that the speed does decrease slightly as the ball rolls. Data Table 4 Average Speed (m/s) 2-m Distance m Distance m Distance 1.33

4 Section 2: Analysis A. Calculations Calculating the average of a set of numbers (data) is a good way to find the value that the numbers (data) center around. The average of a set of numbers is the sum of the numbers divided by the number of numbers that are in the set. Average times were calculated for both the pitching experiment and the horizontal motion (bowling ball) experiment. Average = 1 N N yi = 1 i = 1 N ( y ) 1 + y 2 + y y N 1 + y N The average time for the three times I threw the baseball in procedure part 2 (see Data Table 1) was calculated like this: 1 (0.67 s s s) = 0.68 s 3 To see how fast I threw the ball (on average), the average speed of the ball has to be calculated (for part 2 of the procedure). This calculation was performed for all the different pitchers (see Table 1). The average speed of the ball for the three trials can be calculated by dividing the distance traveled (which is the same for all three trials) by the average time for the three trials. Average speed calculations were also performed for procedure part 4 (see Data Table 4). Average speed = Δd Δ t ( average) The average speed for my ball in procedure part 2 was: 10 m = 15 m/s 0.68 s Since my prediction for the speed of my pitched ball was in miles per hour, it is necessary to convert my ball s average speed from meters per second to miles per hour (this conversion was also used on the other average speeds from procedure part 2). The conversion was done in the following way: m s 1 mile 1609 m 3600 s 1 hour = miles hour I converted my speed like this: m/s 1 mile 1609 m 3600 s 1 hour = 33 miles per hour (two significant figures)

5 The percent difference between my predicted pitch speed and the actual average speed of my pitches in the three trials will be calculated in order to see how close my prediction was. Percent difference is calculated like this: % difference = E E 1 2 x 100 % E 1 + E 2 2 The percent difference of my predicted pitch speed and the actual average speed of my three pitches was calculated in the following way: 50 miles per hour 33 miles per hour x 100% = 41% 50 miles per hour + 33 miles per hour 2 Note: The calculations in Data Table 2 were performed using a spreadsheet program (Excel 2003). Where is the standard deviation computation? You need this to provide a descriptive narrative on uncertainty in the RESULTS Section. You can do this any time you have multiple trials. B. Graphs Note: The procedure implies that multiple graphs should be made for the data in Table 3, so I made graphs for each trial and for the average times. All of the graphs in this section demonstrate a similar linear relationships between distance traveled and the time that the bowling ball was rolling (the ball does slow down by a small amount, but the relationship is still essentially linear in the time period that was measured). Figure 1 shows the relationship between the distance traveled by the bowling ball and time in trial one in Table 3.

6 Figure 1: Distance traveled by the bowling ball versus time for trial 1 in Table 3 distance (m) time (s) Figure 2 shows the relationship between the distance traveled by the bowling ball and time in trial two in Table 3. distance (m) Figure 2: Distance traveled by the bowling ball versus time for trial 2 in Table time (s) Figure 3 shows the relationship between the distance traveled by the bowling ball and time in trial three in Table 3.

7 Figure 3: Distance traveled by the bowling ball versus time tor trial 3 in Table 3 distance (m) time (s) Figure 4 shows the relationship between the distance traveled by the bowling ball and time for the average times in Table 4. distance (m) Figure 4: Distance travled by the bowling ball versus time for the average times in Table time (s) C. Error Analysis The error analysis for this laboratory exercise was a percent difference calculation comparing my predicted pitch speed and the actual average measured speed of my three pitches in procedure part 2. This percent difference calculation shows how close my predicted and actual pitch speeds were to each other. The calculation (see calculations section) showed that the difference between my predicted and actual pitch speeds was 41%. This is a fairly significant difference. I predicted that I could throw the baseball 50 miles per hour, but I was only able to throw it 33 miles per hour. It is clear that I greatly overestimated how fast I could throw a baseball while making my prediction. The error causing this large percent difference really just involved making a somewhat unreasonable predicted (I don t play any sports that involve throwing a ball, so I should not have predicted that I could throw the ball very fast). Since this error does not really involve the procedure with which measurements were taken or the measuring devices that were used, it is not really systematic or random (it was just a bad prediction).

8 Section 3: Discussion and Conclusions A. Discussion: This laboratory exercise is important because it gives students practice gathering, organizing and performing calculations with data involving the speed of real world objects. Data collection is an important process for both physics students in physicists. Proper data collection is essential to the success of any experiment. If data is collected or analyzed incorrectly, the results of an experiment will not be valid. In this experiment, proper data collection and analysis insured that the results describing the speed of a baseball and the motion of a bowling ball were correct. I would have to say that this experiment met my expectations. I expected to collect data and analyze it in a pretty straightforward fashion, and that is pretty much how things worked out. I was able to measure the speed of the baseball in procedure part one fairly easily and my data for the bowling ball experiment turned out to look pretty good (liner) when it was graphed. Question (in the procedure): Part 1: A. What is the fastest that you think that you can comfortably pitch in miles per hour? I think that I can pitch a baseball fifty miles per hour without much trouble. B. What are the reasons for your prediction? Top professional pitchers can throw a baseball at about one hundred miles per hour. I am reasonably athletic, so I think that I can throw a ball at least half that fast without much trouble (so I predicted fifty miles per hour). C. Would you call your prediction a guess, a hypothesis, or something in between? Explain why. I would say that my prediction is something in between a guess and a hypothesis. My prediction is based (in part) on some relevant information on how fast top pitchers can throw a baseball, so it is not a complete guess. However, my prediction is not really based (in any precise fashion) on my physical abilities, so it probably would not be called a hypothesis (it is really just half of the speed that a top professional pitcher can throw a baseball). Part 2: D. Compare your results to your predictions in Section 1. How well did you predict?

9 The actual average speed of my three pitches was 33 miles per hour (see Data Table 1) and my predicted pitch speed was 50 miles per hour. These values have a percent difference of 41% (see calculations section). This difference is fairly large. I definitely overestimate how fast I can comfortably pitch a baseball. I am definitely more impressed with the pitching speeds of professional baseball players now that I have calculated how fast I can pitch a baseball. Part 3: E. How do the average times and speeds calculated by your spreadsheet program compare to the manual calculations you made on the same data in Part 2? If they differ in any way try to explain why. My manually calculated average times and speeds in Data Table 1 differ slightly in some cases from the values calculated using an excel spreadsheet in Data Table 2. For example, the manually calculated average speed of my pitches was 33 miles per hour, while the value calculated by the spreadsheet program was 34 miles per hour. The reason for these differences is that I did not round to two significant figures until the end of my calculations, while the spreadsheet program used the values (for average time and speed in m/s) that were already rounded to two significant figures in the table to calculate the subsequent answers. The differences between Data Tables 1 and 2 are quite small and none of the average speeds in Data Table 2 differ by more that one mile per hour from the corresponding average speeds in Data Table 1. Part 4: A. What do you predict will happen to the distance the ball moves as a function of time? Will the ball move at a steady speed, speed up, or slow down after it leaves the bowler's hand? Why? I would predict that the distance that the ball moves will increase but at a slower and slower rate as time progresses. This means that the ball will slow down after it leaves the bowler s hand. I made this prediction because no surface (and definitely not the one that will be used in this experiment) is completely frictionless, so friction will slow the ball down as it rolls. Part 5: Note: These images were taken from Physics 1 Lab Manual of Experiments for the Independent Study of Physics by Peter Jeschofnig, Ph.D.

10 B. Results: A. Compare the shape of the graphs you produced in Section 4 with the sketches shown above. Would you say that the distance increases with time? Decreases with time? Is it a linear function of t? Is it proportional to t? Explain. The graphs produced using the data from procedure part 4 (figures 1 through 4) show a strong linear relationship between distance traveled by the bowling ball and time. The distance traveled by the bowling ball increases with time. The line of best fit for each graph very nearly passes through the origin of each graph, so I would have to say that my graphs most closely resemble the graph on the right in the sketch shown above (where distance is proportional to time). It should be pointed out that even though the graphs (figures 1 through 4) appear to show a strictly linear relationship between distance and time, the ball does actually slow down slightly in all three trials (see Data Table 3 and 4), so distance is not exactly proportional to time (but the ball slows down by so little during the measured time interval that the difference is not really noticeable on the graphs). B. How do the results compare with the prediction you made in Part 4? Were you surprised? When I first made the graphs in figures 1 through 4, I was surprised that the distance traveled by the bowling ball in each trial appeared to be proportional to time, but when I examined the data in Data Tables 3 and 4 more closely, I noticed that the ball did slow down by a small amount as it rolled. The ball slowed down by so little during the time interval that was measured (because of friction) that you cannot really see the difference in the graphs. So my prediction that the ball would slow down was correct, but the ball did not slow down nearly as much during the measured time interval as I thought it would (the difference in speed was so small that it was barely noticeable). I think that it would be much easier to see the ball slowing down (due to friction) on the graphs if a longer time interval was measured (so friction would act on the ball for more time). C. What do you think would happen to the slope, m, of the graph if the ball had been rolled faster? Would it increase? Decrease? Stay the same? If the ball had been rolled faster, the rate of change in distance during a given time interval would increase for the ball, so the slope (m) on the graphs (which plot distance traveled by the ball versus time) would increase if the ball had been rolled faster. This laboratory exercise taught me how to collect data involving the speeds of real-world objects. I also gained experience organizing and performing calculations on data involving the seed of objects. This data collection laboratory exercise is very important to the physics of speed and velocity because the speed and velocity of an object cannot be accurately determined if the necessary data is not appropriately gathered and analyzed. Proper data collection is very important to the results of any physics experiment (not just those involving velocity), and mistakes made while collecting data can make the results of an experiment invalid.

11 The results for my average pitch speed and the average pitch speeds of three of my classmates (Data Table 1) show that simple distance and time measurements can be collected and used to determine the speed of an object. The average speed of the baseball in my three trials was 33 miles per hour. This value was substantially lower than my prediction of 50 miles per hour (there was a 41% difference between the two values), so my prediction was not very good. I probably should have considered my own physical abilities and the fact that the experiment was measuring how fast I could comfortably pitch a ball more carefully while I was making my prediction. The average speeds from my classmates trials from procedure part 2 were somewhat similar to my own. They all pitched at average speeds between 29 and 42 miles per hour (see Data Table 2). The graphical results from procedure part 4 (the bowling ball experiment) appear to show that the distance traveled by the bowling ball was proportional to the time that it had been moving. This is illustrated in figures 1 through 4 which show that the distance traveled by the bowling ball increased linearly with time (the lines of best fit very nearly go through the origin in each case). It should be noted that the bowling ball was not quite moving at a constant speed in procedure part 4. On average, the ball was moving 1.41 m/s at two meters and 1.33 m/s at six meters. The ball was slowed down slightly due to friction (see Data Table 4). This difference in speed was so small (and the time interval was so short) that the graphs in figures 1 through 4 still appear to show that the distance traveled by the ball was proportional to the amount of time that it had been rolling. In the absence of friction or any other external force on the bowling ball, it would indeed have a constant velocity and the distance traveled by the ball would have been proportional to time (but this was not the case in the experiment). The independent variable in procedure part 2 was the speed at witch the baseball was thrown (the thrower controlled this variable) and the dependent variable was the amount of time it took the baseball to travel the set distance (10 m in the case of my experiment. This is an inverse relationship because the time takes the ball to travel the measured distance goes down as the speed at which the ball was thrown is increased. In procedure part 4 (the bowling ball experiment) the independent variable was time and the dependent variable was the distance traveled by the bowling ball (see figures 1 through 4). The graphs in figures 1 through 4 show that distance traveled by the bowling ball increased as the amount of time that it had been rolling increased. The main problem with the procedure of this experiment was that there is not a good way to compare time measurements from different trials in procedure part 4 to analyze possible timing errors. The bowling wall was moving at different speeds in each trial, so it is difficult to analyze possible errors in the timing procedure. One possible way to get constant speed for procedure part 4 would allow the ball to roll the same distance down a simple ramp during each trial and then measure its speed after it has left the ramp and is rolling on a level surface. Such a procedure would allow students to compare time measurements from each trial to get an idea of the amount of error in the time measurements.

12 The procedure of this experiment did lead to some uncertainty. It was difficult to stop the watch at the exact instant that the baseball passed over the marked distance (the ball was moving at about 15 m/s after all), so there is probably some uncertainty in the time measurements in Data Table 1. However, my predicted pitching speed was 17 miles per hour faster than my actual pitching speed. This is a very significant difference, so minor timing errors probably did not lead to it. The main reason for the difference form the expected (predicted) value for my pitching speed and the measured value is that I overestimated how fast I could throw the ball and made a somewhat unreasonable prediction. The bowling ball was moving much slower (about 1.41 m/s) so stopping the watch when it reached each point was not as much of a problem. The friction of the floor did cause the bowling ball to slow down a small amount as it rolled, but this was expected (see my prediction in the discussion). So, the friction between the ball and the floor did not cause my results from the bowling ball experiment to deviate from what was expected. It should be noted that in an ideal frictionless environment with no external forces acting on the ball, its speed would not have changed after it was thrown. We were working with distances in meters, so the uncertainty of the measuring tape (+ or one mm) was not really too significant. The deviations in the measured times in Data Tables 2 and 3 were due to the fact that the balls (bowling ball and baseball) were moving at different speeds in each trial. The differences in the speeds appear to be quite random (because it was impossible to throw the ball at the exact same speed each time). It is also likely that some of the differences in the measured times were due to the uncertainty involved in the measuring process. The uncertainty of the stopwatch that was used was + or one hundredth of a second, but (as I mentioned previously) there is probably additional uncertainty involved in the timing process because it was difficult for the observer to stop the watch at the exact instant the baseball or bowling ball reached the distance markers. Repeated measurements usually decrease random error due to the uncertainty of measuring devices, but in the case of this experiment it may not be so simple because the balls are moving at different speeds in each trial (so it is impossible to tell how much of the difference is due to uncertainty and how much is due to tact that the ball is traveling at a different speed). However, I would have to say that repeated measurements would still probably help improve the uncertainty of the time measurements to some extent. As I have said before, the difference between my predicted pitching speed and actual pitching speed in procedure part 2 was mostly due to the fact that my guess was much too fast. The friction between the bowling ball and the floor is probably what caused the ball to slow down in procedure part 4. It is also possible that the floor was at a slight angle (which could have also caused the ball to slow down), but it seemed pretty flat to me. As I have mentioned previously, the main drawback to the procedure of this experiment was that the balls were moving at different speeds in each trial so there was no simple way to compare times to get a concrete idea of the error involved in the timing process. C. Interpretation of Results

13 The results in Data Table 1 show my average pitching speed (for three trials) and the average pitching speeds of thee of my classmates. These results show how fast the baseball was thrown on average (the average speed of my ball was 33 miles per hour). The average speed the baseball that I there was 17 miles per hour less than my predicted speed (a difference of 41%), so my prediction was not really very close to how fast I can actually throw a baseball. ). The results in figures 1 through 4 appear to show that the distance traveled by the bowling ball was proportional to the time that it had been moving. The distance traveled by the bowling ball appeared to increase linearly with time (the lines of best fit very nearly go through the origin in each case). However, the bowling ball was actually slowing down slightly over time in procedure part 4. On average, the ball was moving 1.41 m/s at two meters and 1.33 m/s at six meters. It can be inferred that the ball was slowed down slightly due to friction (see Data Table 4). This difference in speed was so small (and the time interval was so short) that it is not really visible in the graphs in figures 1 through 4. They still appear to show that the distance traveled by the ball was proportional to the amount of time that it had been rolling. In the absence of friction or any other external force, the bowling ball would have a constant velocity and the distance traveled by the ball would have been proportional to time. So the results of the bowling ball experiment are not quite consistent with the ideal results in a frictionless environment (many theories ignore friction, but it is in fact present in most real-world situations). The speed at which the baseball and bowling ball were thrown was in my control during this experiment because I was the one throwing them. This means, that the speed of the baseball and bowling ball was in my control for the most part. What was not in my control was the small amount of speed that was lost due to friction in the bowling ball experiment (I guess friction with the air slowed the baseball down too, but this was probably a very minor factor). The results were also influenced by the limitations of the person using the stop watch (he could only react so fast). Since the reaction time of my laboratory partner is not really something that I can control, such errors were beyond my control. All reasonable techniques were available to take the distance and time measurements necessary to get the results for this laboratory exercise. The only thing that was missing was a way to evaluate the error involved in the time measurements (because the ball was moving at different speeds in each trial). As I have mentioned previously, a procedure that ensured that the balls were moving at the same speed in each trial (such as using a ramp to get the ball moving in procedure part 4) would make such an evaluation of timing error possible. The results for procedure part 2 were not consistent with my original beliefs. It turns out that I cannot throw a baseball nearly as fast as I thought I could. I now gave a much greater appreciation for how fast professional baseball players can pitch. The results for procedure part 4 (the bowling ball experiment) were consistent with my original beliefs. I knew that the distance that the ball would travel would increase over time but at a slower and slower rate because of friction (the floor was obviously not completely

14 frictionless). The only thing that surprised me in procedure part 4 was that the bowling ball did not slow down by much in the distance that was measured (I thought that friction would have a greater effect). The average speed at which I threw the baseball (33 miles per hour) was comparable to the speeds of my classmates (their speeds were between 29 and 42 miles per hour), so I am pretty confident in my result even though it was quite a bit slower than my predicted pitching speed. The data from each of the three trials in procedure part 4 (the bowling ball experiment) was fairly consistent and the graphs in figures 1 through 4 show that the distance traveled by the bowling ball increased (nearly) proportionately with time, so I am very confident in my results from the bowling ball experiment in this laboratory exercise. D. Errors Sources and Why As stated previously, the main reason for the large percent difference (41%) between my predicted pitch speed and the actual measured value of my average pitch speed was that my prediction was higher than it probably should have been. The main source of error in procedure parts 2 and 4 (the pitching and bowling ball experiments) was human reaction time. The stopwatch that was used reported times to one hundredth of a second, but it is unlikely that my laboratory partner stopped the watch at the exact instant the baseball or bowling ball crossed the distance marker. A person just cannot be expected to consistently stop the watch at the exact instant the ball passes the distance mark (especially when the ball is moving 15 m/s), so the person taking the time measurements in each experiment introduces some uncertainty (it is unlikely that the measurements are actually accurate to one hundredth of a second). Also, the surface that the bowling ball was rolled across was not entirely smooth (frictionless), so the bowling ball did slow down by a (very) small amount during the horizontal motion experiment (I rolled the ball down a hallway in my residence hall). In the absence of friction (or any other force acting on the ball), the bowling ball s horizontal speed would have remained constant. Overall, I would have to say that the time values in the pitching experiment were fairly consistent and my graphs for the horizontal motion (bowling ball) experiments look pretty linear, so it does seem that Adrian (my laboratory partner) did a fairly good job taking the time measurements and that the friction involved in the horizontal motion experiment was a minor factor. So, the errors in this laboratory exercise did not cause any major deviation from the desired results. One drawback of the procedure in the horizontal motion(bowling ball) experiment was that there was no way to insure that the ball was moving at the same speed for each trial, so the measurements form each trail could not be compared to each other to analyze errors made measuring the time at each distance. If the speed was the same for each trail, the measured time the ball crossed each distance marker could be compared with other trials to evaluate timing errors.