ap physics formal lab examplejhband things to do i dont even know hahahahahah whatever lolz

7/30/2019 AP Physics Formal Lab Examplejhband things to do i dont even know hahahahahah whatever lolz

1/13

AP Physics Formal LabFinding g Using a Free Fall ApparatusPaul Greeney and Gardner Friedlander

October 1, 2013

Abstract

The acceleration due to gravity,g, was measured by dropping a mass with a paper tapeattached. A constant-frequency buzzer put constant time interval dots on the tape as it

was pulled past, and analysis of these dots allows the experimenters to find a value for

the acceleration of the object.

Theory

If the only force on an object is gravity, the object will accelerate atg:

F = ma

mg= mag= a

Thus, the acceleration should be constantg= 980 cm/s2. If this is the case, then the

constant acceleration formulas derived in class

v = vo + at andx = xo + vot + at

2

should be valid. As well, the graph of velocity versus time should be a straight line witha slope equal to the acceleration,g. See the Error section below for cautions on applyingthis theory.

Equipment setup diagram and description

The equipment was set up in

the manner described in the

2000 AP Physics Lab Manualand as pictured at right. For

the discussion in Procedurebelow, note the difference

between what is called aninterval and a position

measured from zero, both

illustrated by using the fifthpoint. Also note the end of

the tape called the trailing

end.

The Dot Timer was a PASCO Model ME-9283 Tape Timer, which was labeled with a

sticker B3 so that the identical unit could be used for all runs.

.

Mass

Dot TimerB3

Tape-trailing end

Stand

.

Fifthinterval

Zero pointthe first clearly separated dot

Position of fifth point, measured from zero

.

.

.

.

.

.

.

.


2/13

The mass pictured is the control mass, a fifty-gram hanger. For a heavier mass, a stack of

22 twenty-gram plates and one ten-gram plate was placed on the fifty-gram hanger (totalmass 500 grams). For a small mass, a 50-gram hooked mass was used.

Procedure and Analysis

The following discussion assumes that the reader has read the instructions to the

laboratory (Experiment #1 in the 2000 AP Physics Lab Manual.) This discussion is about

changes and enhancements made to the basic procedure described there.

For each run, the tape was held by its trailing end (by one of us standing on the table) to

keep it straight, minimizing flapping of the tape and the resulting friction (but, see below

under error analysis.)

The displacement intervals were measured (using a transparent ruler) by setting the 0.00

mark (which was not at the end of the ruler) at the center of the first dot, and then

estimating the location of the center of the second dot. The center was used rather thanone of the edges because it was noted that as the tape moved faster, the dots spread out.

Consistently using the leading edge would result in an increasingly low intervalcompared to using the center, and using the trailing edge would result in an increasingly

high interval. It was decided to accept the inherent increase in uncertainty involved in

finding the center of the dot rather than to introduce a systematic error that would be hard

to take into account. A magnifying glass was used for all of the readings to lessen theuncertainty involved.

The initial tape was measured six times (by each of us on three separate days) so that wewould have an independent confirmation of our uncertainty measurements. As a

crosscheck, the position of the 15th point measured from zero was also measured (using avariety of meter sticks and tapes) each time, which gave us a crosscheck on the accuracy

of the plastic ruler by summing the first 15 intervals. The Error Analysis below willemploy this crosscheck as a correction for a possible systematic error.

The details of analyzing this tape are shown below in the Data, Calculations, Graphs and

Results section. For the other three tapes, each lab partner measured each interval once,and the average of these two measurements is included in the data table. As shown by

the example of the first tape, differences in measurement (excluding blunders, which

were corrected by the continuing crosscheck with the lab partner and not even recorded)

were minor.

Different masses were attached to the tape to test the relative importance of air friction on

the masses and surface friction with the apparatus. In order to separate the two effects,three different masses were used: a control used for most runs (50 grams with a 4.1-cm

diameter cross section), a heavy mass (500 grams with the same 4.1-cm cross section),

and a small mass (50 grams with a 1.8-cm cross section). See the Results section for the

outcomes, and the Error section for an analysis.


3/13

A typical calculation (the acceleration of the seventh data point) involves five different

time and position measurements to calculate a single acceleration. See the spreadsheets

below:Point Time Position Velocity accel.

Number (s) (s) (cm/s) (m/s/s)

5 0.125 6.61

6 0.15 9.53 128.3

7 0.175 13.02 150.8 945.5

8 0.2 17.07 175.6

9 0.225 21.80

B I J K L M

# Average Time Position Velocity Interval

(s) (s) (cm/s) accel.

9 =B8+1 =AVERAGE(C9:H9) =J8+0.025 =K8+I9

10 =B9+1 =AVERAGE(C10:H10) =J9+0.025 =K9+I10 =(K11-K9)/(J11-J9)

11 =B10+1 =AVERAGE(C11:H11) =J10+0.025 =K10+I11 =(K12-K10)/(J12-J10) =(L12-L10)/(J12-J

12 =B11+1 =AVERAGE(C12:H12) =J11+0.025 =K11+I12 =(K13-K11)/(J13-J11)13 =B12+1 =AVERAGE(C13:H13) =J12+0.025 =K12+I13

Data, Calculations, Graphs, and Results

The actual paper tapes used in each run have been saved and are available for checking

under our names in the top-right-most drawer in the AP Lab room. The following tables

are imbedded Excel spreadsheets and charts; double-clicking on them allows for

exploration of formulae, etc. To see details of the calculations and formulas shown, seebelow in the Uncertainties section.


4/13

Analysis of run #1

# Length of intervals, measured in cm Time Position Velocity Interval

Run 1, with control mass, measured 6 times Average (s) (s) (cm/s) accel.

0 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.000 0.00

1 0.21 0.23 0.21 0.23 0.22 0.21 0.22 0.025 0.22 18.7 (m/s/s)

2 0.71 0.73 0.73 0.71 0.71 0.71 0.72 0.050 0.93 40.8 9193 1.32 1.30 1.34 1.30 1.33 1.32 1.32 0.075 2.26 64.7 924

4 1.91 1.91 1.89 1.92 1.91 1.90 1.91 0.100 4.17 87.0 854

5 2.44 2.45 2.44 2.43 2.42 2.44 2.44 0.125 6.61 107.4 826

6 2.92 2.90 2.92 2.92 2.90 2.90 2.93 0.150 9.53 128.3 868

7 3.49 3.48 3.49 3.50 3.48 3.51 3.49 0.175 13.02 150.8 946

8 4.05 4.05 4.05 4.04 4.07 4.05 4.05 0.200 17.07 175.6 953

9 4.72 4.71 4.73 4.72 4.72 4.74 4.73 0.225 21.80 198.4 855

10 5.19 5.17 5.17 5.20 5.19 5.20 5.19 0.250 26.99 218.3 813

11 5.72 5.73 5.71 5.72 5.73 5.72 5.72 0.275 32.72 239.1 886

12 6.24 6.26 6.24 6.23 6.26 6.26 6.23 0.300 38.95 262.6 967

13 6.90 6.88 6.88 6.89 6.92 6.90 6.90 0.325 45.85 287.4 927

14 7.47 7.47 7.49 7.45 7.45 7.47 7.47 0.350 53.32 309.0 85615 7.96 7.96 7.96 7.95 7.95 7.95 7.98 0.375 61.30 330.2 870

16 8.51 8.50 8.53 8.49 8.51 8.53 8.53 0.400 69.83 352.5 889

17 9.22 9.22 9.21 9.21 9.20 9.23 9.09 0.425 78.92 374.7 889

18 9.62 9.61 9.62 9.63 9.60 9.60 9.65 0.450 88.57 396.9

19 10.05 10.06 10.07 10.04 10.03 10.03 10.20 0.475 98.77

sum 61.25 61.22 61.27 61.20 61.26 61.29 10.76

positi 61.33 61.32 61.34 61.34 61.35 61.32 11.31

Average 890

As mentioned above, the tape of the first run was independently measured six times. For

each interval, there seems to be about a 0.02 cm. uncertainty, with no evident pattern

based on day or the person doing the measuring. This justifies taking the average of thesix measurements as values accurate to within the precision given, and validates the

method used for the other data, as well.

In the table and graph that follow (Table 1 and Graph 1, as they were called in the

original experiment), the Position column was found by adding each displacement

interval sequentially.Table 1 and Graph 1

Point Time Interval PositionNumber (s) (cm) (cm)

1 0.000 0.22 0.002 0.025 0.72 0.723 0.050 1.32 2.044 0.075 1.91 3.955 0.100 2.44 6.396 0.125 2.93 9.327 0.150 3.49 12.818 0.175 4.05 16.86


5/13

Graph 1 shows the position versus time graph. Note that the quadratic curve fit is near-

perfect, (R2=1.000), another indication of self-consistent data.

However, note that the sum of the first 15 intervals does not match the position of the 15th

dot as measured directly in the cross-check. This is true of all of the runs; the sum of the

intervals is consistently lower, by .06 to .18 cm. This indicates the possibility of asystematic error, which will be addressed in the Error section below.

9 0.200 4.73 21.5910 0.225 5.19 26.7811 0.250 5.72 32.5012 0.275 6.23 38.7313 0.300 6.9 45.63

14 0.325 7.47 53.1015 0.350 7.96 61.0616 0.375 8.51 69.5717 0.400 9.22 78.7918 0.425 9.61 88.4019 0.450 10.06 98.46

measured 15 61.35

Position (cm) as a function of Time (s)

y = 440.93x2

+ 20.195x - 0.0697

R2

= 1

-20.00

0.00

20.00

40.00

60.00

80.00

100.00

120.00

0.000 0.100 0.200 0.300 0.400 0.500

Time (s)

Position(cm)


6/13

Graph 2, below, plots velocity versus time. Note that the erratic behavior of the last three

points is again visible, but they average near the best-fit line anyway. Graph 2a shows

the same data without the last three points.Graph 2

Point Time VelocityNumber(s) (cm/s)

1 0.0002 0.025 40.83 0.050 64.64 0.075 87.05 0.100 107.46 0.125 128.47 0.150 150.88 0.175 175.69 0.200 198.4

10 0.225 218.211 0.250 239.012 0.275 262.613 0.300 287.414 0.325 308.615 0.350 329.416 0.375 354.617 0.400 376.618 0.425 393.419 0.450 402.4

Graph 2a

Note that this graph (without the last three

data points) has a slightly larger slope,indicating that the erratic behavior may be

partially an artifact of the experimental

process and partially due to a real effect.

More on this in the Error analysis below.

Velocity as a function of time

y = 890.71x + 18.71R2 = 0.9998

0.0

100.0

200.0

300.0

400.0

500.0

0.000 0.100 0.200 0.300 0.400 0.500

Time(s)

Velocity(cm/s)

Velocity as a function of time

y = 877.16x + 20.852

R2

= 0.9989

0.0

100.0

200.0

300.0

400.0

500.0

0.000 0.100 0.200 0.300 0.400 0.500

Time(s)

Velocity(cm/s)


7/13

Comparing the data runs to each other

Plotting the displacement intervals themselves is equivalent to plotting the velocities,

although without the smoothing process of taking two intervals at once. To convert

intervals to velocities, we would divide by 0.025, the time interval. If this were done forall of the points, we would have a velocity versus time graph as we had with Graph 2, and

the slope would be the acceleration.

Interval#

Time Length of intervals, measured incm

(s) Average 1 Run 2,heavy

Run 3,small

Run 4 Run 5 Run 6

1 0.025 0.22 0.84 0.51 3.27 0.66 0.662 0.050 0.72 1.44 1.12 3.81 1.21 1.203 0.075 1.32 2.08 1.72 4.42 1.81 1.804 0.100 1.91 2.66 2.25 4.79 2.17 2.155 0.125 2.44 3.29 2.83 5.53 2.92 2.906 0.150 2.93 3.91 3.41 6.02 3.40 3.387 0.175 3.49 4.48 3.99 6.67 4.06 4.058 0.200 4.05 5.09 4.54 7.31 4.69 4.689 0.225 4.73 5.71 5.07 7.81 5.20 5.1710 0.250 5.19 6.30 5.68 8.09 5.48 5.4811 0.275 5.72 6.95 6.26 8.96 6.35 6.3312 0.300 6.23 7.46 6.84 9.54 6.93 6.9113 0.325 6.90 8.16 7.37 9.67 7.07 7.0614 0.350 7.47 8.74 8.18 10.29 7.67 7.6415 0.375 7.96 9.45 8.42 10.84 8.23 8.2016 0.400 8.51 9.93 9.28

sum of15

61.28 76.56 68.19 107.02 67.85 67.63

position15

61.35 76.89 68.39 107.72 67.97 67.76

To convert intervals to velocities, we would divide by 0.025, the time interval. If this were done for all of

the points, we would have a velocity versus time graph as we had with Graph 2, and the slope would be the

acceleration. Thus, the slopes (and intercepts) in the trend line equations (listed to the right of the graph for

each run) in the graph below can be converted to accelerations by dividing them by 0.025 seconds. This is

y = 24.2x + 0.25

y = 22.7x - 0.00

y = 22.2x - 0.35

y = 21.8x + 2.77

y = 21.9x + 0.16

y = 21.8x + 0.15

0

2

4

6

8

10

12

14

0.000 0.100 0.200 0.300 0.400 0.500

Time

Interval

Run 1averageRun 2(Heavy)Run 3(small)Run 4

Run 5

Run 6

Linear (Run


8/13

done for the following table.

The following table summarizes the results of the six runs, with the slope and theintercept converted to acceleration and initial velocity respectively:

Run intercept slope Vo acceleration discrepancy comment

# (cm) (cm/s) (cm/s) (cm/s2)1 .35 22.2 21 888 9.39% The most precisely measured run.

2 .25 24.2 10 968 1.22% Run with a heavy mass.

3 0.0 22.7 0 908 7.34% Run with a small mass.

4 2.77 21.8 110 872 11.0% Fastest run (largest Vo)

5 .16 21.9 6.4 876 10.6%

6 .15 21.8 6 872 11.0%

(The negative intercept for run#1 is troublesome and will be mentioned in the error

analysis.)

Uncertainty estimates

The precision of the dot timer was not given. After some discussion, and at our request,

the lab instructor ran a test on the sound given off by the timer. Based on evidence of anFFT analysis which measures the frequency, it was found that a reasonable guess for

the frequency was 40.0 0.5 Hz, or about 1% uncertainty. Thus an uncertainty of 1%

(0.00004 s) for any time interval was used in the following analysis. (Data from themanufacturer lists the precision as 0.1%.)

Based on our repeated measurements of Run #1, an uncertainty of any one displacementinterval should be about 0.02 cm, which means that any one position interval would

have about 0.03 cm uncertainty.

Uncertainty propagation for a typical interval (the acceleration based on calculating the 7th acceleration

point for the average Run#1 data.)Here is the original calculation:

Point Time Position Velocity accel.


5 0.125 6.61

6 0.15 9.53 128.3

7 0.175 13.02 150.8 945.5

8 0.2 17.07 175.6

9 0.225 21.80 With the first time raised by the uncertainty amount (+0.00004 s, which is + 4 x 10

-5s),

the result drops 2 cm/s2

from the original 945.5 cm/s2

as shown below:Point Time Position Velocity accel.

Number (s) (s) (cm/s) (m/s/s)5 0.12504 6.61

6 0.15 9.53 128.4

7 0.175 13.02 150.8 943.5

8 0.2 17.07 175.6

9 0.225 21.80


9/13

With the second time raised by the uncertainty amount (+0.00004 s, which is + 4 x 10-5

s), the result rises 0.8 cm/s2




5 0.125 6.61

6 0.15004 9.53 128.3

7 0.175 13.02 150.9 946.3

8 0.2 17.07 175.6

9 0.225 21.80 With the third time raised by the uncertainty amount (+0.00004 s, which is + 4 x 10

-5s),

the result rises 4.9 cm/s2




5 0.125 6.61

6 0.15 9.53 128.2

7 0.17504 13.02 150.8 950.4

8 0.2 17.07 175.7

9 0.225 21.80With the fourth time raised by the uncertainty amount (+0.00004 s, which is + 4 x 10-5 s),

the result drops 0.7 cm/s2




5 0.125 6.61

6 0.15 9.53 128.3

7 0.175 13.02 150.7 944.8

8 0.20004 17.07 175.6

9 0.225 21.80 With the fifth time raised by the uncertainty amount (+0.00004 s, which is + 4 x 10

-5s),

the result drops 2.8 cm/s2


as shown below:

Point Time Position Velocity accel.Number (s) (s) (cm/s) (m/s/s)

5 0.125 6.61

6 0.15 9.53 128.3

7 0.175 13.02 150.8 942.7

8 0.2 17.07 175.4

9 0.22504 21.80 With the first position raised by the uncertainty amount (+0.03 m), the result rises 12.0

cm/s2




5 0.125 6.64

6 0.15 9.53 127.77 0.175 13.02 150.8 957.5

8 0.2 17.07 175.6

9 0.225 21.80


10/13

With the second or fourth position raised by the uncertainty amount (+0.03 m), the result

remains unchanged from the original 945.5 cm/s2

as shown below (this can be explained

mathematically by the way we calculated the acceleration):Point Time Position Velocity accel.


5 0.125 6.61

6 0.15 9.56 128.3

7 0.175 13.02 150.2 945.5

8 0.2 17.07 175.6

9 0.225 21.80 With the third position raised by the uncertainty amount (+0.03 m), the result drops 24.0cm/s

2from the original 945.5 cm/s

2as shown below:

Point Time Position Velocity accel.


5 0.125 6.61

6 0.15 9.53 128.9

7 0.175 13.05 150.8 921.5

8 0.2 17.07 175.09 0.225 21.80 With the fifth position raised by the uncertainty amount (+0.03 m), the result rises 12.0

cm/s2




5 0.125 6.61

6 0.15 9.53 128.3

7 0.175 13.02 150.8 957.5

8 0.2 17.07 176.2

9 0.225 21.83

The total possible variation due to the estimated uncertainty is then2 + .8 + 4.9 + .7 + 2.8 + 12.0 + 24.0 + 12.0 = 59.2 cm/s

2, or about 60 cm/s

2

with most of this coming from the uncertainty in position. Since the uncertainties are

very possibly not independent from each other, there is no a priori reason to use the RSS

calculation (which would give 30 cm/s2).

This analysis explains only in part why the interval acceleration jumped around so much.

For the first sixteen intervals, the acceleration for Run 1 ranged from 813 to 967 cm/s2, or

about 890 70 cm/s2, in good agreement with the variation predicted in the analysis

above (we may have slightly underestimated either the time or displacement uncertainty).

Analysis of the average requires us to divide the uncertainty by the square root of thenumber of trials, = 60/ 16 = 15 cm/s

2. Comparing the four control runs (runs 1,4,5,

and 6) done with the same falling mass, we have results of 888, 872, 876, and 872 cm/s2,

which can be summarized as 877 11 cm/s2, even somewhat better agreement than our

uncertainty analysis would lead us to expect. Note however that the other runs, withresults of 908 and 968 cm/s

2, lie much further away, which indicates that a real effect is

at work. See below, under Error Analysis.


11/13

Error analysis

Three major systematic errors were noticed: friction, air friction, and a distance

measuring inaccuracy. There may be a systematic error in the time interval as well, but

an oscilloscope test (FFT analysis) run by the lab instructor at our urging was somewhatinconclusive due to the large uncertainty in the frequency measurement. Data from the

manufacturer indicates an accuracy of better than one percent in the time measurement.

The effect of a constant force of frictionfon a falling mass m would be to lower the

acceleration by an amount equal tof/m. Thus the effect on a large mass would be less

than on a small mass in inverse proportion to the quantity of mass. In comparing the

control runs (#1,4,5, and 6) with the run using the heavy mass (#2), we find this to be thecase. The control mass had an average discrepancy of 10.5%, over eight times as large as

the heavy mass. Theoretical analysis would predict ten times larger, but it seems that

friction between the tape and the timer may account for most of the discrepancy. If a

correction factor for a frictional force of 4000 dynes (the weight on 4 grams) is added toeach result, the corrected results are as follows:

Run acceleration discrepancy mass Friction Correction Corrected result

# (cm/s2) (cm/s ) (cm/s )

1 888 9.39% 50 g + 80 968

2 968 1.22% 500 g + 8 976

3 908 7.34% 50 g + 80 988

4 872 11.0% 50 g + 80 952

5 876 10.6% 50 g + 80 956

6 872 11.0% 50 g + 80 952

To see if this was reasonable, we tried a run (with the timer running!) with a falling massof 5 grams, and we found that friction did not stop the fall, but it did just stop the fall of a

falling mass of only 4 grams. Thus the frictional correction seems to be of a reasonable

amount. The corrected values are now close to being in agreement (within uncertainty

limits of15 cm/s2

) with the accepted value of 980 cm/s2

. Further fudging of thiscorrection factor would bring the corrected results even closer to the accepted value, but

it seemed unwarranted to us.

Air friction would not be constant. It would decrease with a smaller cross-sectional area,and it would increase with a larger speed. Comparing the control runs and the third run

(with a smaller area), we see that the smaller area reduced the discrepancy by about 2%

or 3%, and put the corrected result well within the range of the accepted value. Thefastest run (#4) was the furthest off of all the runs, but since the relatively slow run #6

was off by just as much, this may not have much meaning. Another place we might

expect to see a speed effect is in the graphs of each individual run. We would expect the

high-velocity points to lag below the best-fit line, especially in cases of low mass. Adetailed analysis of each of the graphs shows that the last point indeed does lie below the

trend line for each of the runs, indicating that there is a noticeable speed effect.


12/13

Run acceleration Friction Correction Air friction correction Corrected result

# (cm/s2) (cm/s

2) (cm/s

2) (cm/s

2)

1 888 + 80 +20 988

2 968 + 8 +2 978

3 908 + 80 +0 (?) 988

4 872 + 80 +20 972

5 876 + 80 +20 9766 872 + 80 +20 972

These corrected results have an average of 979 cm/s2, and the expected uncertainty (15

/ 6 = 6 cm/s2) is very close to the observed range.

The final systematic error was noticed in comparing the sum of the first fifteen intervals

with the position of the fifteenth point as measured directly. The position was measured

by several different meter sticks and tapes and each measurement was in agreement to

within the expected 0.03 cm. uncertainty. The sum of the intervals is always short ofthe position, by an amount ranging from 0.1% to 0.6%. Either the method used to

measure the intervals had a consistent tendency to under-measure, or the ruler used tomake the measurement was inaccurate by 3 parts out of 1000. In any case, the effect ofthis error on the experiment is swamped by the first two errors noted (each of them ten to

a hundred times as large) as well as by the uncertainty (also about ten times as large).

Answers to Questions

a. For each of the two graphs, briefly explain the shape of the trendline that fits this graph.The graph of the position-time graph is a parabola, and the velocity-time graph is a straight line.

b. For each of the two graphs, what to the terms (the numbers) in the equation of the trendline represent?As mentioned in the Theory section, two of the constant-acceleration equations are:

v = vo + at and

x = xo + vot + at2

Rearranging these so that the higher-order exponent of t comes first, and matching these with the

equations fitted to the curve, it can be seen that in theory,

For Graph 1 (position versus time), the first number is half the acceleration, the second one is the

initial velocity, and the third one is the initial position.

For Graph 2 (velocity versus time), the first number is the acceleration and the second one is the initial

velocity. However, see the answer to question c.

c. Why doesnt the line for Graph 2 go through the origin?Because we did not use the mass of overlapping dots as the origin for position, it is clear that the

paper had a downward velocity at the time designated as time zero. Thus, we would expect a positive

y-intercept on the velocity versus time graph. However the intercept of the best-fit line was negative in

one case and zero in another. This shows that there is an artifact in the way data was collected and

graphed.

d. Does your acceleration agree with the accepted value? If not, what is the percent difference? Explainsome of the sources of this difference.

No. There is a discrepancy of from 1% to 11%, with the experimental number always lower than the

theoretical one. Friction between the tape and the timer is the primary source of error, with air friction

being a secondary one. A systematic measurement error was also found. See the Error section for a

further discussion.


13/13

e. Comment briefly on how this procedure may have introduced error and how it could be improved toachieve more accurate and precise results without needing different equipment.

Friction slowed the acceleration. The use of heavier masses for all runs would have lessened this

effect. The use of a different ruler might have eliminated the need to correct for the ruler we did use.

See the Error section for a further discussion.

Extensions to the labTaking more runs, especially with heavy masses, and better measuring the precision and

accuracy of the dot timer are the two most obvious extensions that should be done. Using

a variety of rulers and meter sticks for each measurement might help eliminate the needto correct for the systematic measurement error we found, but that correction would be

minor.

Who did what:

The Abstract and Conclusion were written by Greeney.

The Procedure, Equipment Setup, and Diagram were written by Friedlander.

The majority of the data was taken jointly, but the last three runs were done aloneby Greeney. As noted above, each partner made each measurement

independently.

The first set of calculations were done independently by both of us (Greeney on aspreadsheet, Friedlander on a calculator). The rest of the calculations and graphs

were done by Greeney.

The Uncertainty and Error analyses were done by Greeney.

The Questions were discussed between us, but the section was written byFriedlander.

The rest of the sections, and the final collating and proofreading, were done byGreeney.

Conclusion

The acceleration of gravity was measured as a six-run average of 900 15 cm/s2. The

discrepancy of 80 cm/s2

is not covered by the uncertainty, but corrections needed to

account for friction between the tape and the timer and a smaller effect due to air friction

(and other less major effects discussed in the Error Analysis section) do explain the

discrepancy. The corrected results have an average of 979 6 cm/s2, in excellent

agreement with the accepted value of 980 cm/s2.

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