Textbook Notes
(363,062)

United States
(204,388)

Arizona State University
(495)

Physics
(238)

PHY 122
(8)

Dolenko
(8)

Chapter

# Lab 2 Density 72 out of 85.docx

Unlock Document

Arizona State University

Physics

PHY 122

Dolenko

Spring

Description

Lab 2: Diameter, Mass and Density
By:
T.A:
Monday at 2:00 p.m
Abstract:
This experiment was performed in order to demonstrate how density is related to mass and
diameter and how mathematical models can be made to model real life scenarios. The diameter
was measured six times for six spheres of different sizes and the mass was measured once for the
ρ=ρ ∇ρ
spheres (all made of the same material). The density was found using averag+/- ,
6m
ρ= 3 ∇ ρ
where π∗d and is the error propagation for the density equation. The
g
density was found to be 1.67 +/- .02 cm3 .Then, the density of the sphere was
approximated by comparing how fast it sunk to other objects with known densities. After
plotting diameter cubed versus the mass a best fit line and the slope of the line (of graph one in
the appendix) was found which determined the ρaverageρ respectively. The same approach
was used for the ln graph model and the density was found, using that model, to be 1.78 +/- .02
g . g
cm 3 For the ln plot, the density was equa1.65 +/- .05 cm 3 . These results show that
using any of the models will give you a fair estimate for what the density of an object is. The
results also suggest the ln plot more fairly represented the actual density.
Objective: The goal of this lab is to find the density of spheres of clay and then find a model function for the
relationship between mass versus diameter using both a linear and a ln-ln plot.
Equipment:
The equipment used in this lab was a scale to measure the weight, a Vernier caliper to measure
the diameter of the spheres and a container with water to test how fast different objects sank
when placed in water.
Procedure:
The diameters of each of the six spheres were recorded six times using the Vernier caliper. The
mass of each sphere was measured once using the scale. A qualitative experiment was then done
to approximate the density. The qualitative experiment was conducted by dropping objects with
known densities in a container of water with the unknown density of the clay. The clays’ speed
was compared to the other objects to get a rough estimate of the density of the clay. Using
graphical analysis, two different plots (one that compared the mass to the diameter cubed and
one that compared the ln(mass) versus the ln(diameter)) were made that simulated the
relationship between the mass and diameter of the clay spheres. This was then checked with the
qualitative experiment to verify that the results obtained were reasonable. Results
Part 2:
As several different shapes with different densities were dropped into a tank of water, it was
g g
found that the density of the clay should be between 1.07 3 and 7.3 3
cm cm
Part 3&4:
Figure 2:
Figure 3: DataAnalysis:
Part 1:
ρ
Density ( ρ ) = average+/- ∇ ρ
ρ = 6m
averagπ∗d 3 *mass is the average mass and d is the average diameter
ρ
Example Calculation averagfor sphere 3:
ρ average∗95.34 =1.67 g
π∗4.782 3 cm3
m n
∇ρ given the equation f =cx ∗y :
∇F 2 ∇x 2 ∇y 2
( f ) = m ∗( x ) + n∗( y )
2 2
∇ρ=∇F=f∗ ∣m∣∗(∇x ) ∣n∣∗(∇ y )
√ x y
∇F =the error propagation in the density; f= the average density; m=expon=error in
mass; x=average mass of the sphere; =standard deviation of mean for the diameter; y=average
diameter
∇ ρ
Example calculation for for sphere 3:
.01 2 .026 2 g

More
Less
Related notes for PHY 122