Katrina Washington

Brittany

Kristen

Experiment 1

Measurements and Experimental Uncertainty

PHYS-101-04X

May 22,2012

Objectives:

The purpose of this lab was to observe experimental uncertainty in measurements, show

various experimental results to the correct number of significant figures, and gather the accepted

values of measured results by calculating percentage errors.

Theory:

Types of Error: There are two types of experimental errors. Statistical errors that are

random and unpredictable and systematic errors due to the instrument or techniques used.

Accuracy: how close a measurement is to the true value

Precision: the agreement among repeated measurements.

Least Count: Smallest subdivision on the instrument scale

Significant Figures: For a measured value, the number of significant figures includes all

numbers measured directly from the instrument plus one estimated number, which is a

fraction part of the least count. When performing calculations with measured values the

results must be rounded according to the rules of significant figures. In general, the

accuracy of the results cannot increase after performing mathematical operations.

Rules of rounding: If the first digit to be dropped is 0-4, leave the preceding digit by one.

Percentage error:[ |A-E|/a]x100%

Percentage Difference: [|E1-E2|/average]x100%

Equipment and Materials:

Measurement disks:

Ruler:

Graduated cylinder:

Mass Balance:

Digital Vernier Caliper:

Digital Micrometer:

Instrument Least Count

Meter Stick or Ruler 1mm

Vernier Caliper 1mm

Micrometer .001mm

Mass balance 1g

Graduated Cylinder 0.2ml

Data:

Part A: Least Count of Instruments

Part B: Discover pi

Disk # Circumference(cm) Diameter(cm)

1 16.4 5.11

2 19.9 6.32

3 27.7 8.85

4 31.3 9.96

Part C: Volume and Density Calculations

Object Wire Rod Sphere Rectangle

TrialDiameter

(cm)Length(cm)

Diameter(cm)

Length(cm)

Diameter(cm)

Length

(cm)

Width(cm)

Thickness(cm)

1 .32 9.42 1.27 5.08 1.90 4.75 2.54 1.27

2 .33 9.43 1.27 5.08 1.90 4.75 2.53 1.27

3 .32 9.42 1.26 5.08 1.89 4.74 2.54 1.26

4 .32 9.42 1.27 5.07 1.90 4.75 2.54 1.27

object Mass(g)

Wire 6

Rod 8

Sphere 28

Rectangle 42

Irregular 27

Calculations:

Part B:

Pi=Circ/Diam

o Disk #1: 16.4/5.11= 3.15

o Disk #2: 19.9/6.32=3.15

o Disk #3: 27.7/8.85=3.13

o Disk #4: 31.3/9.96=3.14

o Accepted π:3.14

o Experimental Average: 3.142

o % Error: 0.06%

Part C:

ObjectVolume

(cm3)Density=M/V

(g/cm3)

Acc. Density(g/cm3)

%Error

Wire [3.14(0.322)(9.42)]/4=0.75 6/0.75=8.00 7.86 0.51%

Rod [3.14(1.272)(5.08)]/4=6.43 8/6.43=1.24 2.70 53.9%

Sphere [314(1.903)]/6=3.58 28/3.58=7.80 7.86 0.76%

Rectangle (4.75)(2.54)(1.27)=15.3 42/15.3=2.74 2.70 1.48%

Irregular 17.4-14.6=2.8 27/2.8 11.3 15.0%

Volume of a Cylinder= πD2L/4

Volume of a Sphere=πD3/6

Volume of a Rectangle=LxWxH

Volume of an Irregular object= Vf-Vi

Conclusions:

Experimental Value for π= 3.14

Experimental Value for Volume (cm3):

Wire=0.75

Rod=6.43

Sphere=3.58

Rectangle=15.3

Irregular=2.8

Experimental Value for Density(g/cm3):

Wire=8.00

Rod=1.24

Sphere=7.80

Rectangle=2.74

Irregular=9.64

The Experimental data agreed with the accepted data for the most part. The only part that had

a very big error was the density of the rod and the irregular object. The reason the rods density is

so high is because we most likely made a mistake in the actual measurements. The calculations

are correct so must have measured the rod incorrectly. I believe the percent error was high in the

irregular object because the volume was off. It had to be the volume because the mass was very

accurate. From this lab I learned how to actually calculate significant figures correctly. I also

enjoyed finding π physically.

Sources of Error:

In the Rod I believe the source of error came from our actual measurements because my

calculations are correct. In the Irregular object I believe the source of error came from the

volume measurements because the mass is correct.

Resources:

Cutnell, John D., and Kenneth W. Johnson. Physics. Hoboken, NJ: Wiley, 2009. Print.

Lab Handouts

"Discover Pi Set." PASCO : (10 Pack). Web. 29 May 2012.

<http://pasco.com/prodCatalog/ME/ME-6819_discover-pi-set-10-pack/>.