A cylindrical wire of radius R elongates when subjected to a tensile force F. Let L0 represent the initial length of the wire and let L1 represent the final length. Young’s modulus for the material is given by

Assume that F = 800 ± 1 N, R = 0.75 ± 0.1 mm, L0 = 25.0 ± 0.1 mm, and L1 = 30.0 ± 0.1 mm.

a. Estimate Y, and find the uncertainty in the estimate.

b. Of the uncertainties in F, R, L0, and L1 only one has a non-negligible effect on the uncertainty in Y. Which one is it?

Answer:

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In this question we are asked to estimate the Young’s modulus of cylindrical wire of radius and the uncertainty in the estimate.

Young’s modulus for the material is given by

…………….(1)

Given parameters:

Tensile force = 800N

Radius = 0.750.1 mm

Initial length mm

Final length 0.1 mm

The quantity which we are estimating has several measurements. In this question we are measuring the radius , tensile force , Initial length and Final length . These quantity mentioned here is uncertain and independent measurements.

So here we can use the following basic formula.

……………...(2)

Where , ,........, are independent measurements and uncertainties are , ,.........,

Equation 2 is called the multivariate propagation of error formula.