PHYS 2425 – Engineering Physics I

Density and Random Uncertainty

 

Equipment Needed


Calipers, Digital

 

Cylinder Set, Density

Scale, Digital


Introduction

      In this brief activity we will use a determination of the density of several materials to help us investigate the propagation of random error through an experiment and the comparison of a measured value with estimated uncertainty to an accepted value.  The density of a material is given by r = m/V where m is the mass of the object and V its volume.  The SI units for density is kg/m3.  These units give values that are quite large.  For instance, in SI units the density of water is 1000 kg/m3 so often units such as g/cm3 or g/ml are used for convenience.

 

Objectives

Ø      Understand the difference between systematic error and random error.

Ø      Learn how to correctly write the results of a measurement or calculation (includes significant figures and propagation of error).

Ø      Learn how to correctly use a digital caliper.

Ø      Learn how to measure the density of objects.

 

Procedure

1.      Carefully make one measurement of the mass of each object using the electronic balance

2.      Measure the radius and length of each object.

3.      Correctly record all data in the table below (with units and correct significant figures).

4.      Calculate the density of each object in grams per cubic centimeter (g/cm3) and in kilograms per cubic meter (kg/m3).


 

Cylinder

mass (g)

length (cm)

radius (cm)

Density (g/cm3)

Density (kg/m3)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

5.  Often the accuracy of an instrument is specified, but sometimes it is the job of the experimenter to characterize the accuracy.  A simple way to characterize the accuracy of a digital instrument is to assume the instrument is accurate to ½ of the least significant bit (LSB).  The least significant bit is the smallest digit given by the instrument.  For instance the electronic scale reads to the nearest 0.1 gram.  An estimate of its uncertainty then is ½ of .1 g or .05 g.  Thus when we use the electronic balance we can record masses as m ± .05 g.  Modify the entries in your data table to show this uncertainty.

 

6.  Make a similar estimate for the uncertainty in the caliper reading.  Modify your data table.

 

7.  Taking the density as r = m/(pr2h), derive an expression for dr. 

 

 

 

8.  Use your measured values and estimated uncertainties to estimate the experimental uncertainty in your densities.  Record your results with uncertainties in the table below.

Cylinder

Measured Density

Accepted Value

 

 

 

 

 

 

 

 

 

 

 

 

9.  For each cylinder does your measured density agree with the accepted value?  Justify your answer.

 

 

10.  If for any of the cylinders the values didn’t agree within random error, then there was a systematic error.  Describe any systematic errors that may have occurred in this lab.  Be specific.  Don’t use catchalls like “human error” or “equipment error”.  If you did something wrong – describe it.  If blue sparks came shooting out of the caliper, then say so.