a Estimate v and determine the uncertainty in the estimate b

(a) Estimate v, and determine the uncertainty in the estimate.

(b) Of the uncertainties in w, a, and b, only one has a non-negligible effect in the uncertainty in v. Which one is it? Show the mathematical proof to support your claim.

Solution

v = a+bw

a varies from 2.4 to 2.6 mm

b from 0.04 to 0.06

and w = 1.1 to 1.3 mm

a) v = a+Bw

Estimate for v depends on mean value of a,b and w

Hence v estimate = 2.5+0.05(1.2)

= 2.5+0.006 = 2.506

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b) v=a+bw, a can vary only upto 0.2 in total hence negligible

In bw if w is constant w varies from 1.1 to 1.3 hence maximum variation for b only

but

v=a+bw

Find partial derivatives wrt a, b and w

v_a = 1

v_b = w and v_w =b

w is the maximum of these three as even minimum of w = 1.1 mm.

Hence b, having the highest derivative, has non negligible effect.