Error and measurement - A full completed physics lab report. All of the labs remain the same each year. PDF

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A full completed physics lab report. All of the labs remain the same each year. ...

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Measurement and Error

PHYS 223, Section 04 Wednesdays 9am-10:50am Due Date: September 5, 2019 Date Submitted: September 5, 2019

1. Introduction: The true value of an object is defined as the value that would be obtained by a perfect measurement in an ideal world. In a realistic world, measurements that are made vary from the true value of an object because it is impossible to make an exact measurement. This is known as error. There are two different kinds or errors: systematic, which describes error as a result of a faulty instrument, human error, or improper techniques, and random error, which describes unknown and unpredictable changes in

the experiment. Since error cannot be avoided, there are several techniques that can be implemented to combat this. These techniques include repeating the measurements several times to increase the sample size. Once the sample size is increased, the average (or mean) value can be taken, allowing for a more accurate number that is closer to the true value. Correspondingly, the data can be plotted to create a normal distribution curve that shows how the values deviate from the mean value. This is known as standard deviation, and it states that for a normal distribution curve, 68.3% of values are focused around the mean. Another measurement of deviation is probable error, which specifies that half of the values from the distribution will lie within the interval and half outside. 2. Objective: The objective of this experiment was demonstrate that it is impossible to make an exact measure while utilizing the mean, standard deviation, probable error, and histograms to get closer to the true value. 3. Questions & Analysis: Part 1:

Mean Standard Deviation Probable Error % Probable Error

29.96 6.29 4.25 14.19

5. The mean value of my data set is 29.96. The tens unit number is 30. The mean value came very close to the tens unit number; it was only 0.04 less. 6. The histogram does not approach that of a normal distribution. In a normal distribution, most of the values would have been concentrated around the mean, but in my histogram most of the values are concentrated in the beginning intervals. Part 2: Mean Standard Deviation Probable Error % Probable Error

3.19 0.133 0.090 2.82

5. My histogram depicts a normal distribution. Majority of the values are concentrated around the mean which is a characteristic of a normal distribution. 6. All of the measurements in the part did not come out the same due to systematic error. Only one person in my group took time for the ball. She could have started the timer too slow or too fast which resulted in incorrect time measurements. Only one person was rolling the ball as well. This person could have released the ball too slowly or may have pushed the ball upon release, resulting in incorrect time measurements. Even though an apparatus was provided for us to set up the experiment, the person setting up the experiment could have set up the apparatus at an angle that caused the ball to roll slightly faster, producing faster time measurements. There could have been an error with the instrument as well. Sample Calculations:

4. Conclusions In conclusion, we gained knowledge on the concepts of measurement and error. The mean, standard deviation, and percent error was calculated for all the data. As stated, error is inevitable when measuring. The mean of the dice experiment was 29.96 which was 0.04 away from the original value. The standard deviation was 6.29 and the percent probable error was 14.19%. The mean of the ball experiment was calculated to be 3.19 with a standard deviation of 0.133 and a percent probable error 2.82%. Human error could have caused the variation in the data obtained in the both experiments....