Data and Motion - Understanding About Relationships Between the Measured Quantities - Random and Systematic Uncertainties - Physics Assignment Help

Assignment Task:

Data and Motion
Introduction
Most experiments in physics center on measuring some sort of motion, and all experiments generate data. In physics this data is usually quantitative, and so we are often interested in understanding two critical aspects of the data: what trends exist in the data that might lead us to understanding about relationships between the measured quantities, and what uncertainties exist in the data themselves, or in quantities we calculate from the data. We know that generally uncertainties can generally be broken down into random and systematic uncertainties. It is important that we understand both types of uncertainties and how to detect them. Systematic uncertainties can take the form of “errors” introduced in the experiment due to things like poor calibration of an instrument. Systematic uncertainties can also take the form of limitations in precision introduced by the instrument. For example a ruler that reads to the nearest millimeter will always have a minimum systematic uncertainty of ±0.5 mm. You can never make a measurement to the nearest micrometer with such an instrument. In the case of errors introduced by calibration or improper usage, we can and should correct the error. However, there will always remain uncertainty associated with the resolution, the physical limit of the instrument. In many cases we must determine this systematic uncertainty by estimation (you may find, when looking carefully that it is significantly higher than just half the lowest increment of the scale, unlike in the simple case above). Random uncertainties are evident by performing “repeated measures”, that is to say, by measuring the same quantity over and over again. When we do this we arrive at a mean value, which we use for our measured value, and we should determine a value that describes the spread, or variance in the data.

Experiment 1: Random Error
In this experiment we are going to explore the idea of random uncertainty and statistical distributions of data. To do this we will use a random number generator: three dice. When rolling three fair dice we can obtain values between 3 and 18, but with different probabilities. For two dice, the most likely roll is 7 because there are 6 ways to get seven (1 & 6, 6 & 1, 2 & 5, 5 & 2, 3 & 4 and 4 & 3), more than any of the other possible rolls. There are 62 = 36 possible outcomes, so the probability of rolling a 7 is 6/36=16.66...%. What about three dice though? The goal of this experiment is to theoretically calculate the most probably roll value for 3 dice, then experimentally test it and finally to get an error bar on that measurement.

• Equipment
• three dice
• Microsoft Excel or other spreadsheet programs

Procedure
1. Using logic like we applied above determine what the most likely roll will be based on the possible combinations you can roll. This is easily googleable, do not do that. Figure it out. What is the probability of rolling this value? Explain your reasoning clearly, using complete sentences.
2. Roll the three dice 50 times. Make a column in Excel for each die, and record the value of that die for each of the 50 rolls in that column. Make a fourth column in which you have Excel calculate the sum. When you are making a table in Excel or doing other computer work you do not need to additionally copy it by hand into your log book, but you should include a printout of your work in your logbook, or, if this is not possible, be sure to turn in your the relevant files along with your lab notebook entry. Make sure to include enough description and explanation in your logbook that the spreadsheet, or other files will be clear and easy to interpret.
3. Calculate the mean value of this fourth column. Qualitatively, how does this value compare with the most likely value you calculated in step 1?
4. Calculate the standard deviation of the values in the fourth column. You can do this using the equation above, but you can also use Excel’s function STDEV. If you wanted to calculate the standard deviation of ten cells from A1 to A10 you would just type “=STDEV(A1: A10)” into the cell where you want the standard deviation. Is the post probably value within the one standard deviation of the mean value you calculated in step 3?
5. Calculate the standard error for your fourth column. Is the most probable value within one standard error of the mean value?
6. Draw a histogram in the logbook of your data. If you do not know what a histogram is, ask your instructor. Mark the mean value on the histogram, and the standard deviation. Sketch what you imagine the histogram might look like if you took a very large number of data points, say 10,000.

 Experiment 2: Trends
In this experiment we are going to look at the plotting of data, identifying trends, and estimating uncertainty in situations where we cannot use statistics to determine the uncertainty. The motion we’re going to analyze is the motion of coffee filters as they are dropped from a fixed height.

• Equipment
• Coffee filters
• Tape measure, cell phone stopwatch

Procedure
1. Use the tape measure to measure the height of a fixed reference, relative to the floor, that you can use to repeatedly drop your coffee filters. A good reference might be the top of a door, or door frame. As you do this, look at the tape measure and pay note to how you are measuring this length. Estimate the uncertainty in the distance you are measuring. Record height and uncertainty.
2. You may need to practice this a few times: Using one hand, raise a single coffee filter to the reference point. Hold your phone in stopwatch mode in the other hand. Simultaneously release the filter and start the stopwatch. Hit stop as the filter hits the ground. Repeat this step 5 times and record all five-time values. This set of five measurements is what we will call a “trial”.
3. Repeat the previous step using two coffee filters nested together, then three, four, up to about 10-12 filters. Then do a trial with all your coffee filters. Record all ?ve time values for each of these.
4. Calculate the meantime for each of your trials, and the standard deviation. Are there any systematic errors you need to consider? Write them down.
5. Calculate the average speed for each of your trials. Use the error propagation relation to figure out the error bar on your speed values.
6. Use Excel to make a plot of the average speed vs. a number of coffee filters. There is no uncertainty in the number of coffee filters, so we need no horizontal error bars. There is uncertainty on the speed, so we do need vertical error bars. Make sure you include all the other things we normally expect in a graph (e.g. axis labels, units). If your graph looks linear include a trendline (have Excel include the equation of the trendline). If your graph does not look linear, describe it qualitatively.

 Questions & Comments

• How do you think the width of your histogram in the first experiment would change as a function of the number of trials. Could you take enough to make it a really narrow spike all centered on the most likely value? How does the standard error change as you take more values?
• Why do you think your graph looks as it does? What factors influence the motion of the coffee filter?

This Physics Assignment has been solved by our Physics Experts at My Uni Paper. Our Assignment Writing Experts are efficient to provide a fresh solution to this question. We are serving more than 10000+ Students in Australia, UK & US by helping them to score HD in their academics. Our experts are well trained to follow all marking rubrics & referencing style.

Be it a used or new solution, the quality of the work submitted by our assignment experts remains unhampered. You may continue to expect the same or even better quality with the used and new assignment solution files respectively. There’s one thing to be noticed that you could choose one between the two and acquire an HD either way. You could choose a new assignment solution file to get yourself an exclusive, plagiarism (with free Turnitin file), expert quality assignment or order an old solution file that was considered worthy of the highest distinction.