# LAB REPORT Measurement of a table

ABSTRACT:

The purpose of this experiment was to determine the value of the acceleration of a free falling object and to describe the range of experimental values. Within the experiment the items used to help provide the conclusion that 2/3 or our values fell within the 9.62m/s^2- 9.78m/s^2 range was a Vernier data-collection interface, Logger Pro Application and the apparatus Photogate. The results found within the 30 trial periods were all precise. It was believed that the data would not be exact to the actual acceleration of gravity but would be precise with a low percentage of error, the results showed to be true to what was expected.

OBJECTIVE:

To determine the mean value, the standard deviation of the mean and significant figures through measured values. Also to gain an understanding of propagation of errors while enhancing knowledge of precision and accuracy.

PROCEDURE:

Within the lab a 20cm wooden cylinder is provided to measure the length and then the width of the lab table. The group was to measure the length and the width of the table a total of twenty times; with a group a four each individual measured the table length and width a total of five times each. Once all measurements are calculated, the provided values were entered into the system LoggerPro for visual analysis of the data.

RESULTS:

Table 1.Data From Experiment

#

Length(cm)

Width(cm)

#

Length(cm)

Width(cm)

1

183 cm

92cm

11

179 cm

94 cm

2

195 cm

94 cm

12

179 cm

90 cm

3

165 cm

87 cm

13

170 cm

85 cm

4

187 cm

93 cm

14

160 cm

80 cm

5

184 cm

89 cm

15

170 cm

85 cm

6

182 cm

90 cm

16

164 cm

90 cm

7

182 cm

90 cm

17

167 cm

88 cm

8

173 cm

93 cm

18

160 cm

89 cm

9

160 cm

96 cm

19

169 cm

90 cm

10

140 cm

82 cm

20

163 cm

82 cm

GRAPH-1.Data From Experiment

GRAPH-2.Data From Experiment

DATA ANALYSIS:

This section analyzes the results of the experiment.

Mean:

Mean Equation:

The sum of all values divided by the quantity of values in the list. Mean Sample Calculation for LENGTH:

183+195+165+187+184+182+182+173+160+140+179+179+170+160+170+164+167+160+169+163/20= 171.6cm Standard Deviation of the Mean:

Standard Deviation of the Mean Equation:

In order to find the Standard deviation of the mean you want to take you mean and subtract it from each value in the list. Then square each value that you get and add them all together. After adding them together divide them by one less than the number of values in the list and then find the square root of your answer to find the Standard Deviation of the Mean. Mean Sample Calculation LENGTH:

Starting with the Mean/ 171.6 from the above equation: (183cm-171.6 cm) then^2 +(195 cm -171.6 cm)then^2+(165 cm -171.6 cm)then^2+(187 cm -171.6 cm) then ^2+(184 cm -171.6 cm) then ^2+(182 cm -176.1 cm) then ^2+(182 cm -176.1 cm) then ^2+(173 cm -176.1 cm) then ^2+(160 cm -176.1 cm) then ^2+(140 cm -176.1 cm) then ^2+(179 cm -176.1 cm) then ^2+(179 cm -176.1 cm) then ^2+(170 cm -176.1 cm) then ^2+(160 cm -176.1 cm) then ^2+(170 cm -176.1 cm) then ^2+(164 cm -176.1 cm) then ^2+(167 cm -176.1 cm) then ^2+(160 cm -176.1 cm) then ^2+(169 cm -176.1 cm) then ^2+(163 cm -176.1 cm) then ^2/19 = 155.3705263 cm square rooted = 12.26cm Total Error:

Total Error Equation:

The square root of standard error in the measuring device squared plus standard mean deviation squared Total Error Sample Calculation for LENGTH:

Square root of (0.03) ^2 + (2.7) ^2 = 7.3cm

Uncertainties:

Uncertainties Equation:

Standard Mean +/- Standard Deviation of the Mean

Uncertainties Sample Calculation for LENGTH:

2.7cm +/- 171.6cm

Area of a table:

Area of a table Equation used:

(A+/-change A) x (B+/- change B) = C+/- change C

Then C=A*B and

Change C =C * square root of (change A/a) ^2+ (change B/b)^2 Area of a table Calculation for...

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