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Measurement of density

1) Introduction to the vernier caliper

Dimensions of the order of tenths of a millimeter (0.1 mm or 0.01 cm) can be measured using a
vernier caliper. It consists of a main scale and a movable vernier scale. The main scale is calibrated
in centimeters with a millimeter least count, and the vernier scale has 10 divisions that cover 9
divisions on the main scale. The left most mark on the vernier scale is the zero mark, which is
often unlabeled.

A measurement is made with the vernier caliper by closing the jaws on the object to be measured
and then reading the position where the zero line of the vernier falls on the main scale. The
fractional part of a main scale division is obtained by noting which line on the vernier coincides
with a line on the main scale. Visit this vernier web site and learn how to use a vernier caliper.

2) Introduction to the micrometer

Dimensions of the order of hundredths of a millimeter (0.01 mm or 0.001 cm) can be measured
using the micrometer. It has a movable spindle that is advanced by a rotating thimble. The
ratchet allows slippage of the screw mechanism when a small and constant force is exerted on the
jaw. This permits the jaw to be tightened on an object with the same amount of force each time.
The axial main scale is calibrated in millimeters and the thimble is calibrated in 0.01 mm.

The micrometer should be checked for a zero error, for it may not read zero when the jaws are
completely closed. In such cases a zero correction has to be applied to every reading. The zero
error may be either positive or negative. The zero correction is always made by subtracting the
zero reading from the final reading.

The micrometer is read by noting the position of the edge of the thimble on the main scale which
gives the nearest whole main scale division. The position of the axial line on the circular thimble
scale gives the fractional part of the main scale. Visit this micrometer web site and learn how to
use a micrometer.

In this experiment the mass will be measured using an electronic balance.

A. Rectangular Solids

Purpose: To determine the densities of various rectangular solids by measuring their dimensions and mass.

Apparatus: Electronic balance, foot ruler, vernier caliper, micrometer,
rectangular solid metals- Al, Cu, Brass, and Fe; sheet metal, and acrylic block.

Theory: Density = Mass/Volume, Volume = Length x Width x Height.

Data: Rectangular Solids

	Mass	Length	Width	Height
Al	-	-	-	-
Cu	-	-	-	-
Fe	-	-	-	-
Brass	-	-	-	-
Sheet metal	-	-	-	-
Acrylic block	-	-	-	-

Enter the above data in Excel spread sheet and calculate the volumes and densities. Also enter the accepted densities and calculate the %Error. Save your data table.

Accepted densities (in gm/cm^3):

Aluminum = 2.70    Copper   = 8.90     Iron     = 7.85        Brass    = 8.40
Steel    = 7.80        Gold       =19.30     Lead     =11.30     Nickel   = 8.75
Platinum =21.54    Silver      =10.5       Zinc      = 7.10        water    = 1.00
Wood = 0.64        Acrylic    = 1.2

B. Cylinders

Purpose: To determine the densities of various cylinders by measuring their dimensions and mass.

Apparatus: Metal cylinders: Cu, Fe, Steel, Brass, and Al; wood cylinder, length of Cu wire, electronic balance, foot ruler, vernier caliper, and micrometer.

Theory: Density = Mass/Volume, Volume = (Pi x d^2 x h)/4.

Data:

Cylinder	Mass	Height, h	Diameter, d
Al	-	-	-
Steel	-	-	-
Cu	-	-	-
Brass	-	-	-
Fe	-	-	-
Wood	-	-	-
Cu wire	-	-	-

Enter the above data in Excel below your earlier Data Table, and calculate the volumes and densities. Also enter the accepted densities and calculate the %Error. Print a hard copy of the data tables sheet in landscape orientation.

D. Density of Water

Purpose: Investigate the density of water.

Apparatus: Graduated cylinder, electronic balance, and water.

Theory: Density = Mass/Volume

Procedure:

1. Measure the mass of a graduated cylinder in grams (use the electronic balance), and record it
on the data table.

2. Fill a small amount of water and measure the mass of graduated cylinder and water.

3. Determine the volume of water by reading the water level in the graduated cylinder.

4. Repeat 1-3, by adding water, 9 more times.

DATA

Mass of the graduated cylinder = ______________

Mass of cyl + water	Volume of water
-	-
-	-
-	-
-	-
-	-
-	-
-	-
-	-
-	-
-	-

5. Enter the above data in excel and create a column for the mass of water and calculate it.

6. Plot an XY scatter chart and obtain the density of water from the graph. Print a hard copy of your graph.

7. Density of water from your graph:______________________

D. Density of a penny

Calculate the density of a penny by measuring its mass, diameter, and thickness.

Data:

Year of penny________________

Measured mass of penny __________

Measured diameter of penny________

Measured thickness (or height) of penny ________

Calculated volume of penny__________

Calculated density of penny____________

Visit this penny composition website and calculate an accepted density for your penny. Also comment about the metal composition of your penny.

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