Measurement (Exam 98, Question 4)

Usage notes

The Measurement-Quiz consists of parts a to d.
Part c will be visible, when you solved a and b successfully.
Part d will be visible when solved c
Please fill in each entry-field. Otherwise later parts of the quiz won't work as expected.
As long as a Hint-button is visible, further hints are available.

a: The problem

A weight of 1000 kg is suspended from two walls separated by 2 m, as shown in the sketch below:

There are spring-scales on both wires, which are accurate to about 1 kg, and the distance from the left wall to the support of the weight is measured with a ruler which is accurate to 1 mm.

Denoting by f1, f2 and d the exact values of the observed quantities, and by f1_hat, f2_hat and d_hat the measured values, you have the following readings:

	f1_hat := F1/g = 813 kg
	f2_hat := F2/g = 706 kg	
	d_hat = 0.783 m

Please calculate in these units!

The goal of the whole exercise is to determine the angle a from these data using a least squares approximation.

First define the measurement errors to be minimized by least squares:

e1 = ___________________
e2 = ___________________
e3 = ___________________

b: Constraints and Least Squares"

Write down equations derived from the geometry and the forces which relate f1, f2, a, b, c, d and h. To avoid numerical values use m for the mass of the weight and w for the distance between the two walls.

m = 1000
w = 2
f1_hat = 813
f2_hat = 706
d_hat = 0.783
e1 = ?
e2 = ?
e3 = ?

___________________
___________________
___________________
___________________
___________________

Now write down the expression to be minimized as a function of the errors e1, e2 and e3, using the actual standard deviations given in the problem description:

___________________

What would be your next steps for solving this problem?
It is already solved.

Solve all equations in terms of b, c.

Solve all equations in terms of d, h.

Solve all equations in terms of e1, e2.

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