EXPERIMENT 1: Experimental Errors and Uncertainty

Objective: To gain an understanding of experimental errors and uncertainty.

Name of author: Matthew Martin

Date and time experiment was performed: 03/02/2011 12:00pm

Course Name/Number: PHYS-171-DL1

Equipment and Material used:

Pen and pencils Paper, plain and graph

Computer and spreadsheet program

No LabPaq supplies are required for this experiment.

Data:

The data table (Lab Manual, p. 55) that follows shows data taken in a free-fall experiment. Measurements were made of the distance of the fall (Y) at each of the four precisely measured times.

Time, t (s)

Dist, y1 (m)

Dist, y2 (m)

Dist, y3 (m)

Dist, y4 (m)

Dist, y5 (m)

σ

t2

0

0

0

0

0

0

0

0

0

0.5

1.0

1.4

1.1

1.4

1.5

1.3

0.2

0.25

0.75

2.6

3.2

2.8

2.5

3.1

2.8

0.3

0.56

1.0

4.8

4.4

5.1

4.7

4.8

4.8

0.3

1.0

1.25

8.2

7.9

7.5

8.1

7.4

7.8

0.4

1.56

Procedures:

From the above data perform the following Tasks.

Task 1. Complete the table.

Results 1:

In the table we have the values of four precisely measured times – t(s) and for each of them we have five measured quantities of the distance of the fall – y(m). When measurement is repeated several times we need to measure the mean and the standard deviation in order to record the data most accurately. The mean is the central value, the average of all recorded measurements. We calculate it according to the formula:

=1/N.(y1+y2+……+yn-1 +yn)

N is the number of measured values, which in our case is equal to 5. When the time is equal to 0.5 seconds, we calculate according to the formula:

=1/5(1.0+1.4+1.1+1.4+1.5)

=6.4/5

=1.3

Applying the same rule we calculate all the values of for each of the measured times and complete the column of the table above. The standard deviation is the spread of deviation of the measured values about the mean. It is presented with the symbol σ. Using the formula for standard deviation, with known values of N and , we can calculate σ for each set of measured distances (which EXCEL calculated) and fill out the column of the table. The last column is referred to the square of t(s), which is calculated for further use in the graphing process.

Task 2. Plot a graph versus t (plot t on the abscissa, i.e., x-axis).

Results 2:

Using the data from the table above we create another table (located on the Excel spreadsheet on sheet2- table2). In the first column we put the values of t, which will go on the abscissa, and in the second- the values of , which go on the ordinate. Using Excel we create the graph of versus t, which shows the proportion between time and distance in a free fall starting from rest. t is independent variable, which values are precisely measured. Y is the dependant variable, which increases in value as the time increases. This proportion is also supported by the formula: y = ½ gt2, which is a quadratic equation, and the bigger the time value, the bigger is the distance.

Task 3. Plot a graph versus t2 (plot t2 on the abscissa, i.e., x-axis). The equation of motion for an object in free fall starting from rest is y = ½ gt2, where g is the acceleration due to gravity. This is the equation of a parabola, which has the general form y = ax2.

Results 3:

On the Excel file – sheet3-table3 we have the squared values of t in the first column and the values of in the second column. The graph shows the LINEAR relations between time and distance in a free fall starting from rest.

Task 4. Determine the slope of the line and compute an experimental value of g from the slope value. Remember, the slope of this graph represents ½ g.

Results 4:

To determine the slope of the line we use the Trendline feature on Excel and as we see on the graph (on sheet3) the equation shown is y=4.950x. In this equation x represents the square value of t: x=t2 and the value of the...