Suppose the quantities A = 1, B = 2 and C = 3 have been measured with an Absolute Error of EA = 0.1, EB = 0.2, EC = 0.03 respectively. The quantity D is calculated by the following equation: Report: D = ( )

MDC PHY2048L
EXTRACREDIT ASSIGNMENT 2 (9 points)
Comment
The completion of this assignment is a good preparation for the Test 2.

Exercise 1 (3 points)
⦁ If the quantity which should be reported results from a calculation by using an equation where are involved measured quantities, the error of the quantity is determined by a procedure called PROPAGATION of ERROR.
⦁ Suppose the quantity D = f(X, Y, Z) is a function of the measured quantities X, Y, Z and Ex , Ey , Ez are the Absolute Error of the quantities X, Y, and Z respectively.
⦁ In the Theory of Errors, the Absolute Error of the quantity Z is related with the Absolute Error of the quantities X and Y by using the following equation (it is assumed that Ex and Ey are independent):

ED = ((dD/dX)2 Ex2 + (dD/dY)2 Ey2 + (dD/dZ)2 Ey2)0.5 (1)

It is very important to know some simple situations which simplify the work with more complex situations. Attention: the equations for EZ in this situations were derived by suing the equation (1)
⦁ Z = X + Y or Z = X – Y
EZ = (Ex2 + Ey2)0.5

Suppose Z = X + Y – M
EZ = (Ex2 + Ey2 + Ez2)0.5

⦁ Z = X Y or Z = X / Y

EZ = Z [(Ex /X)2 + (Ey /Y)2]0.5

Suppose Z = XY/M
EZ = Z [(Ex /X)2 + (Ey /Y)2 + (EM /M)2]0.5

⦁ Z = constant X

EZ = Z (Ex /X)

⦁ Z = Xn

EZ = n Z (Ex /X)

The rules of thumb in reporting the data with absolute error is:
⦁ The Absolute Error should contain only 1 significant digit
⦁ The number of decimal places of the value of the measurement quantity should be the same than the number of decimal places of the Absolute Error. If the Absolute Error doesn’t have decimal places, round the measured value to the ones.
Example
Suppose the quantities A = 1, B = 2 and C = 3 have been measured with an Absolute Error of EA = 0.1, EB = 0.2, EC = 0.03 respectively. The quantity D is calculated by the following equation:

⦁ Solution:

⦁ D = 243.4

⦁ If we apply strictly the equation (1), we get

ED = [9(A2B/(C+B))2EA2 + (A3C/(C+B))2EB2 + (-A3B/(C+B)2 +5C4)2EC2]0.5 (give a try!)

ED = 0.62289

Report: D = (243.4 0.6)

Now is your turn

⦁ Suppose the quantities A = 1, B = 2 and C = 3 have been measured with an Absolute Error of EA = 0.1, EB = 0.2, EC = 0.03 respectively. The quantity D is calculated by the following equation:

Report: D = ( )

⦁ Suppose the quantities A = 1, B = 2 and C = 3 have been measured with an Absolute Error of EA = 0.1, EB = 0.2, EC = 0.03 respectively. The quantity D is calculated by the following equation:

Report: D = ( )

Exercise 2 Write below the following equations with the Word equation editor (3 point)

The Equation should be beautiful:
⦁ the subscripts and superscripts should be correctly shown
⦁ the partial derivative should be clearly shown

2.1 ED = [9(A2B/(C+B))2EA2 + (A3C/(C+B))2EB2 + (-A3B/(C+B)2 +5C4)2EC2]0.5

It should look like this

2.2 ED = ((dD/dX)2 Ex2 + (dD/dY)2 Ey2 + (dD/dZ)2 Ez2)0.5

The equation should look like this

Exercise 3 Submit an excel document with the data 1 and data 2 you can find below plotted in the SAME GRAPH (3 points)

DATA 1 DATA 2
Mass (kg) Torque (Nm)
1 4
2 12
3 20
4 30
5 32
6 41
Time (s) Length (m)
10 300000
20 100000
30 70000
40 50000
50 20000
60 10000

Your graph should look exactly as the one in the picture to be considered beautiful and receive full credit. Attention to the colors of scatters and lines. Attention to the shape of the scatters. Attention to the right logarithmic axis, etc, etc, etc

Graph Beautiful Features
⦁ The graph area has not border
⦁ The axes have to have black color
⦁ The font of axes labels is New Time Roman, 12 p or 14 p
⦁ The labels of the axes must include units
⦁ The font of the axes numbers is New Time Roman and 12 p
⦁ Major tick mark in the axis should be visible and outside
⦁ Graph title (any) with font New Time Roman, 14 p, capital letter.
⦁ The graph must include only scatters, no line plus scatter. Size of the scatter: 10
⦁ The fitting (linear, exponential, etc) should be added as requested.
⦁ The equation of the fitting equation must be included as well as the Determination factor (R2) which informs about the quality of the fitting. Format : Time New Roman, 12p or 14p.
⦁ If are plotted to quantities with respect the same independent variable, two axis with label must be included.
⦁ Legend mandatory. Format: Time New Roman and 14 p. The edition of the Legend is mandatory. It should clearly explain what the scatters and lines represent in the graph.

Last Completed Projects