Jennifer Chen

Phys-130 Lab

Prof. Stark

Feb. 22, 2006

Objective:       To prove density is an intrinsic property of materials.

Intrinsic (adj.) 1. Of or relating to the essential nature of a thing; inherent; belonging to a thing by its very nature. 2. Situated within or belonging solely to the organ or body part on which it acts; "intrinsic muscles."

Theory:           We know the volume of a cylinder is V =  π * R^2 * (l) where V = volume, R = radius, π = 3.14, and l = length.

We know the radius of a circle is R = D/2, where D = diameter.

We know the density is the mass of a substance contained in unit volume, where D = M/V, where M = Mass (grams), and V = volume (cm^3).

We know the density of wood falls between 0.4 – 0.8 g/cm^3.

We know the density of copper is 8.9 g/cm^3.

Procedure:      First we measured three objects – one wood and two metal (copper) cylinders from the base to the top, excluding the hook to get the length (in cm) using a ruler. Then we measured the diameter from the circular base. Then we zeroed the scale and measured the weight of each cylinder (in grams) and made our calculations from our data.

Data:               See table.

Analysis:         See table.

Sources of error:  Sources of error in this experiment can be due to human error. For example, while measuring the cylinder with the ruler, the human eye could have read an inconsistent reading, depending on the angle at which the ruler was viewed or the way the ruler was held.  While making calculations, the numbers may have been rounded off inconsistently, or a mathematical error could have been made.  Also, the scale might not have been accurately zeroed, or the hook attached to a hole in the cylinder could have altered the weight.

Data Table                                                                                                                 Jennifer Chen

<-------------DATA---------------- > < -------------Derived Data ------------------- >

 Sample Length (l) (cm) Diameter (D)  (cm) Mass (M) (grams) Radius (R ) (D/2) Volume (V) (π*R^2*l) Density (M/V) 1. Wood cylinder 10.1 cm 0.75 cm 3.5 g (0.75cm/2) = 0.375cm (3.14*(0.375cm)^2*10.1cm) = 4.46 cm^3 (3.5g/4.46cm^3) = 0.785 g/cm^3 2. Copper cylinder 1 2.45 cm 1.8 cm 60.9 g (1.8cm/2) = 0.9cm (3.14*(0.9cm)^2*2.45cm) = 6.23 cm^3 (60.9g/6.23cm^3)= 9.78 g/cm^3 3. Copper cylinder 2 2.45 cm 1.8 cm 62.8 g (1.8cm/2) = 0.9cm (3.14*(0.9cm)^2*2.45cm) = 6.23 cm^3 (62.8g/ 6.23cm^3)= 10.08 g/cm^3

Percent Error %

│Accepted value – Measured value│     X 100%

Accepted value

1. Wood cylinder │0.8 g/cm^3 – 0.785 g/cm^3 │ = │0.015  g/cm^3  =          1.875 % error

0.8 g/cm^3                               0.8g/cm^3

1. Copper cylinder #1 │8.9 g/cm^3 – 9.78 g/cm^3│ = │0.88 g/cm^3│ = 9.89 % error

8.9 g/cm^3                        8.9 g/cm^3

3. Copper cylinder #2 │8.9 g/cm^3 – 10.08 g/cm^3│ =        │1.18 g/cm^3│ = 13.26 % error

8.9 g/cm^3

Conclusion

The density is an intrinsic property of a material.  Every object has its own unique density, as shown in this experiment using wood and copper cylinders.  The densities calculated did not exactly match the accepted density values due to human and mechanical errors.