Problem 6E

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 ± 0.01 cm, and the diameter of the piston is 19.90 ± 0.02 cm. The clearance is one-half the difference between the diameters. Estimate the clearance and find the uncertainty in the estimate.

Answer:

Step 1 of 1:

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

Let assume is the diameter of hole =

And is the diameter of the piston =

The clearance is one-half the difference between diameters.

Hence estimate of clearance =

=

=

Hence the estimate of clearance is .

Uncertainty in the estimate:

If are independent measurements and are constants, then

Uncertainty in the measurement …(1)

uncertainty in the diameter of hole =

uncertainty in the diameter of the piston =

=

=

=

Hence uncertainty in the estimate is .

We can therefore express the clearance