Lab 1 (Error Analysis)

7/31/2019 Lab 1 (Error Analysis)

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Error Analysis Lab

Data Collection

Qualitative Data:

Metal A is a lustrous silver cylindrical metal.

Metal B is a dull bronze cylindrical metal.

Quantitative Data:

Table 1: Mass of Metal A and B using Electronic Balance

Trial/unit (0.001g) Mass/g (0.001g)

Metal A 1 18.601

2 18.599

3 18.599

4 18.597

Average Mass of Metal A 18.599

Metal B 1 28.861

2 28.862

3 28.861

4 28.858

Average Mass of Metal B 28.861

Table 2: Volume of Metal A and B Measured Using a Graduated Cylinder

Trial/unit Initial Volume/ml (1.0ml) Final Volume/ml (1.0ml)

Metal A 1 30.0 36.5

2 30.0 36.83 30.0 36.3

4 30.0 36.5

Average Final Volume of Metal A 36.5

Metal B 1 30.0 33.5

2 30.0 33.6

3 30.0 34.0

4 30.0 33.2

Average Final Volume of Metal B 33.6


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Table 3: Volume of Metal A and B Measured Using a Caliper

Trial/unit Height/cm (0.001cm) Diameter/cm (0.001cm)

Metal A 1 5.114 1.278

2 5.113 1.280

3 5.112 1.274

4 5.114 1.268

Average 5.113 1.275

Metal B 1 2.562 1.270

2 2.560 1.268

3 2.560 1.270

4 2.563 1.270

Average 2.561 1.270

Data Analysis

Method 1: Graduated Cylinder

Metal A:

Volume = Vfinal Vinitial

Volume = Average of Vfinal Average of Vinitial

Volume = 36.5 30.0

Volume = 6.5 ml (2 s.f.)

Uncertainty = 1.0 + 1.0

Uncertainty = 2.0 ml

Average Volume of Metal A = 6.5 2.0 ml (2 s.f.)

Density = Mass / Volume

Density = 18.599 / 6.5

Density = 2.861384615 g/ml (2 s.f.)% uncertainty of mass = (uncertainty / mass) x 100%

% uncertainty of mass = (0.001 / 18.599) x 100%

% uncertainty of mass = 0.0053766332%

% uncertainty of volume = (2.0 / 6.5) x 100%

% uncertainty of volume = 30.76923077%

Actual Uncertainty = sum of % uncertainties x value

Actual Uncertainty =30.77496843% x 2.9

Actual Uncertainty = 0.880590212 g/mlDensity of Metal A = 2.9 0.9 g/ml (2 s.f.)


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Metal B:

Volume = 33.6 30.0

Volume = 3.6 ml (2 s.f.)

Uncertainty = 1.0 + 1.0

Uncertainty = 2.0 ml

Average Volume of Metal B = 3.6 2.0 ml (2 s.f.)

Density = 28.861 / 3.6

Density = 8.016944444 g/ml

% uncertainty of mass = (0.001 / 28.861) x 100%



% uncertainty of volume =55.5555556%

Actual Uncertainty = 55.55902044% x 8.0

Actual Uncertainty = 4.454135802 g/ml

Density of Metal B = 8.0 4 g/ml (2 s.f.)

Method 2: Caliper

Metal A:Volume = rh

Volume = x (average diameter / 2) x average height

Volume = x (1.275 / 2) x 5.113

Volume = 6.528088653 (4 s.f.)

% uncertainty of radius = (uncertainty / diameter) x 100%

= (0.001 / 1.275) x 100%

= 0.784313725%

% uncertainty of height = (uncertainty / height) x 100%% uncertainty of height = (0.001 / 5.113) x 100%

% uncertainty of height = 0.0195579894%

Actual Uncertainty = sum of % uncertainties x value


Actual Uncertainty = 0.011516902

Average Volume of Metal A = 6.528 0.01 cm (4 s.f.)


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Density = 18.599 / 6.538

Density = 2.844753747 g/cm





Actual Uncertainty = 0.0044956539 g/cm

Density of Metal A = 2.845 0.004 g/cm (4 s.f.)

Metal B:

Volume = x (1.270 / 2) x 2.561

Volume = 3.244194635 (4 s.f.)

% uncertainty of radius = (0.001 / 1.270) x 100%

= 0.0787401575%

% uncertainty of height = (0.001 / 2.561) x 100%

% uncertainty of height = 0.0390472472%


Actual Uncertainty = 0.0063769158

Average Volume of Metal A = 3.244 0.006 cm (4 s.f.)

Density = 28.861 / 3.244

Density = 8.896732429g/cm




Actual Uncertainty = 0.1879568343% x 8.897Actual Uncertainty = 0.0167225195 g/cm

Density of Metal B = 8.897 0.02 g/cm


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Results

Density (g/cm)

Metal A Metal B

Method 1 2.9 0.9 8.0 4

Method 2 2.845 0.004 8.897 0.02

(1ml = 1cm)

Data Evaluation

The objective of this lab was to determine the density of two different metal cylinders by

as many different methods possible. Through method 1, using a graduated cylinder, the

density of metal A was found to be 2.9 0.9 g/cm and the density of metal B, 8.0 4

cm. Through method 2, using a caliper, the density of metal A was found to be 2.845

0.004 g/cm and the density of metal B, 8.897 0.02 g/cm. The accepted density of

metal A, which is aluminum, is 2.70 g/cm and the accepted density of metal B, which is

copper, is 8.96 g/cm.

The % error = (l (Known value experimental value) l / known value) x 100%

% error for Method 1, Metal A:l (2.70 2.9) l / 2.70 x 100% = 7.407%

The % uncertainty was 30.77496843%

% error for Method 1, Metal B:l (8.96 8.0) l / 8.96 x 100% = 10.714%


% error for Method 2, Metal A:

l (2.70 2.845) l / 2.70 x 100% = 5.37%


% error for Method 2, Metal B:

l (8.96 8.897) l / 8.96 x 100% = 0.703%



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Sources of Error Effect on Result Suggestion for Improvement

The table is not parallel to

the floor.

The reading of the

meniscus is not

completely accurate

Several more trials on different

surfaces would eliminate

systematic uncertainty.

The balancesometimes

becomes uncoordinated.

When uncoordinated, the

balance doesnt start

from 0g but from -0.001g

or -0.002g.

I should not hurry to place the

metal on the balance right

after a previous one but

should wait for the numbers

to go down to 0g and check

that it is not set on -0.1g

When reading the meniscus,

the table the graduated

cylinder was set upon was

wobbling.

The wobbling could have

changed the volume even

by 0.1ml.

I can move the graduated

cylinder to a steadier table.

Also, by doing several more

trials, I can increase the

accuracy and precision of my

results.

The caliper readings are

easily misread.

The uncertainty will thus

be increased and thus the

results will become lessprecise.

Doing several trials on one

caliper reading, before moving

on to the next, would be agood idea.


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Bibliography

Hoadley, Rick. "Density of Metals." Magnet Man. 1998-2011. Web. 23 Aug. 2011.

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Documents

Lab 1 (Error Analysis)