mechanical engineering

University of New Haven Tagliatela College of Engineering

Department of Mechanical & Industrial Engineering MECH3316 Mechanics Lab

To: MECH3316W Sec 02 Students

From: S. Daniels, PhD, PE

Re: Uncertainty Problems

Date: February 4, 2019

Due Date: February 11, 2019

Please complete the following problems by hand on green paper, NOT in Excel.

You may use Excel to do the statistic calculations but show steps on the paper. Please follow the

regular homework format with a title, problem statement, calculation section, results &

interpretation section. All assignments will be turned in electronically as pdf files on blackboard.

Use “Camscanner” or similar program or ask Ms. Roth/Dr. Daniels to scan your work. I will not

accept paper copies. If you have an accommodation you may use Excel but must still follow the

same format.

1. The volume of a cylinder is to be determined from measurements of the diameter and length. If the length and diameter are measured at four different locations by means of a

micrometer with an uncertainty of 0.75% of reading, determine the uncertainty in the

measurement.

Diameter,

in

Length,

in

3.9875 4.4950

3.9892 4.4985

3.9935 4.5150

3.9995 4.5265

2. A tube of circular section has a nominal length of 125 cm +/- 1.5 cm, an outside diameter of 25cm +/- 0.08cm, and an inside diameter of 20cm +/- 0.08cm. Determine the

uncertainty in calculated volume.

3. A cantilever beam of circular section has a length of 8 ft and a diameter of 5 in. A concentrated load of 500 lbf is applied to the beam end, perpendicular to the length of the

beam. If the uncertainty in the length is +/- 2.5 in., in the diameter is +/- 0.15 in., and in

the force +/- 10 lbf, what is the uncertainty in the calculated maximum bending stress?

4. From a sample of 250 marbles having a mean diameter of 10 mm and a standard deviation of +/- 5.8 mm, how many marbles would you expect to find in the range from

10 to 15 mm?

University of New Haven Tagliatela College of Engineering

Department of Mechanical & Industrial Engineering MECH3316 Mechanics Lab

5. In order to determine whether the use of a rubber backing material between a concrete compression sample and the platen of a testing machine affects the compressive strength,

six samples with packing and six without were tested. Determine if the packing material

has any effect. Use a 99% confidence level. Use the t-test comparison of two samples.

Tensile Strength, MN/m2

Sample # With

Packing

Without

Packing

1 2.56 2.25

2 2.85 2.55

3 2.80 2.30

4 2.85 2.05

5 2.75 2.15

6 2.70 2.30

6. Spacer blocks are manufactured in quantity to a nominal dimension of 1.25 mm. A sample of 9 blocks were selected and the following measurements made. Using Student's

t-test, determine the upper and lower tolerance values within which the population mean

may be expected to fall with a significance level of 10%.

Spacer Block Dimensions,

mm

1.28 1.26 1.26

1.26 1.23 1.23

1.24 1.29 1.29