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UW-Madison PHYSICS 207 - Lab Worksheet

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M-4: Acceleration in Free Fall Name_______________________ Lab Worksheet Group member names__________________________________ This sheet is the lab document your TA will use to score your lab. It is to be turned in at the end of lab. To receive full credit you must use complete sentences and explain your reasoning clearly. Follow the directions in the lab manual to obtain a tape marked by sparks as it is pulled down by a mass in free fall. The sparks occur at equal time intervals of 1/60 of a second. Ignore the first dot made at the beginning before the bob was released. Place the meter stick on edge so the graduations touch the marks on the tape. It does not matter where you locate 0 mm and you will be asked to repeat this step with the meter stick in a different position. (See 4, 5, and 6 on page 29 of your lab manual.) In the table at right record the position of every other dot to 0.1 mm being very careful not to bump the meter stick as you work. Every other dot is a 1/30 second time interval. Taping down the meter stick may help. Shift the meter stick’s position and measure the same set of dots again, recording the values in the 2nd column. It is the differences in these measurements that matter so before continuing check that both sets of data produce similar differences. Suggested Procedure (build you own application): Now open up Excel and follow the instructions below. This will save you the time of doing all these individual calculations by hand. Enter a header row as on page 30 of your lab manual. Enter the units you want to use for each quantity in the next row. As illustrated below at right, enter a few numbers in the spark interval column then drag a box around them. Now by dragging the square dot at the lower-right corner of the box down, Excel will automatically fill in a sequence of numbers. This click-and-drag feature works with the formulas you will enter next. You will need to format the rest of the cells to number with any decimal places you wish as Excel keeps track of them all anyway. Enter “=A3/30” as shown below and drag this corner down to fill the column with times. Enter the data from the table of positions (either column) then enter formulas for average velocity and average time (s) 1st measurement 2nd measurement 0 1/30 2/30 3/30 4/30 5/30 6/30 7/30 8/30 9/30 10/30 11/30 12/30 13/30 14/30M-4: Acceleration in Free Fall Name_______________________ Lab Worksheet 2 acceleration in the second cell down from the top and drag to fill as before. Be careful make sure your numbers to match your units. Excel can make many different plots with your data and you should make one of r, v, and a vs. time. Add a “linear regression line” to the velocity plot. Print these and attach them to this sheet. Alternative procedure (use the pre-built version): Click on the “Speadsheet application MC4” which will down an Excel application with the necessary formulas already set to go. All you have to do is to enter you own position data. In this case you should perform a single trial calculation by hand in your notebook to make sure you understand the process. Be careful make sure your numbers to match your units. Excel can make many different plots with your data and you should make one of r, v, and a vs. time. Add a “linear regression line” to the velocity plot. Print these and attach them to this sheet. ERROR ANALYSIS: The points on your velocity plot we calculated with differences in position measured with a meter stick. 1) By considering how well you can use the meter stick, quote a value of your uncertainty in this data. δr = _______ 2) Using your uncertainty value above quote a value for the uncertainty in the calculated average velocity. Assume there is no uncertainty in ∆t. Show clearly how you determined this value. Do what you think you should first then check your reasoning with your TA. δv = _______ 3) Make an estimate of the uncertainty in the slope of the velocity graph by placing error bars on your average velocity plot. That is, what is the max and min slope consistent with the data given the uncertainty in the average velocity? Show clearly how you made this estimate.M-4: Acceleration in Free Fall Name_______________________ Lab Worksheet 3 Using your uncertainty value above quote your average acceleration value and the value for the uncertainty in the acceleration. Assume there is no uncertainty in ∆t. Show clearly how you determined this value. Do what you think you should first then check your reasoning with your TA. a = _______ δa = _______ EQUIVALENCE OF GRAVITATIONAL AND INERTIAL MASS Repeat the above experiment for the lightweight bob of the same shape. Enter the new data (just one measurement is fine this time) into your spreadsheet and print the same plots as before. Since this experiment is done the same way as the previous one the uncertainty in the acceleration need not be calculated again—it should be the same. 1) Quote values for the average acceleration and its uncertainty below. a = _______ δa = _______ 2) Comment on whether or not this data is strong or weak evidence of the equivalence principle. Standard deviation and standard deviation of the mean revisited Write the average value of you three measurements on the white board. When enough groups are done (six or more) than calculate the mean and standard deviation of the mean for the class g. Does your value agree or disagree with the nominal “accepted” value of 9.81 m/s2. Explain your reasoning σM = _______ std. dev. of the mean = _______ time (s) 1st measurement 0 1/30 2/30 3/30 4/30 5/30 6/30 7/30 8/30 9/30 10/30 11/30 12/30 13/30


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UW-Madison PHYSICS 207 - Lab Worksheet

Documents in this Course
Syllabus

Syllabus

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Lecture 3

Lecture 3

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Lecture 3

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Lecture 8

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Lecture 1

Lecture 1

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Fluids

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Lecture 9

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Lecture 5

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Lecture 5

Lecture 5

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Lecture 5

Lecture 5

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Lecture26

Lecture26

11 pages

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