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Statistics / Statistics for Engineers and Scientists 4 / Chapter 3.2 / Problem 6E

Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi

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A cylindrical hole is bored through a steel block, and a

Chapter 3, Problem 6E

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QUESTION:

A cylindrical hole is bored through a steel block, and a cylindrical piston is machined to fit into the hole. The diameter of the hole is \(20.00\pm0.01\mathrm{~cm}\), and the diameter of the piston is \(19.90\pm0.02\mathrm{~cm}\). The clearance is one-half the difference between the diameters. Estimate the clearance and find the uncertainty in the estimate.

Equation Transcription:

$20.00\pm{}0.01\ cm$

$19.90\pm{}0.02\ cm$

Text Transcription:

20.00{+/-}0.01 cm

19.90{+/-}0.02 cm

Questions & Answers

QUESTION:

A cylindrical hole is bored through a steel block, and a cylindrical piston is machined to fit into the hole. The diameter of the hole is \(20.00\pm0.01\mathrm{~cm}\), and the diameter of the piston is \(19.90\pm0.02\mathrm{~cm}\). The clearance is one-half the difference between the diameters. Estimate the clearance and find the uncertainty in the estimate.

Equation Transcription:

$20.00\pm{}0.01\ cm$

$19.90\pm{}0.02\ cm$

Text Transcription:

20.00{+/-}0.01 cm

19.90{+/-}0.02 cm

ANSWER:

Answer:

Step 1 of 1:

In this question, we are asked to estimate the clearance and find the uncertainty in the estimate.

Let assume $X$ is the diameter of hole = $20.00\ \pm{}0.01\ cm$

And $Y$ is the diameter of the piston = $19.90\ \pm{}0.02\ cm$

The clearance is one-half the difference between diameters.

Hence estimate of clearance $P$ = $\frac{1}{2}(X\ -\ Y)$

$P\ =\frac{1}{2}(X\ -\ Y)\$

= $\frac{1}{2}(20.00\ -\ 19.90)$

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