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Measuring density lab report, Lab Reports of Physics

Measuring density lab report with a 20/20 final score.

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Group#4: Hachim-Jeongho-Wasim-Cado
PHYS 3A
Professor Rosa Alvis
9/7/2021
Lab 1: Measuring Density
Objective:
The purpose of this experiment is to utilize both high and low precision instruments to
measure a given metal cylinder’s mass and dimensions and use the data to calculate its
volume and density. Ultimately, we ought to observe the discrepancy between the two
precision instrument types. The measurements will be noted by the four assigned group
student members.
Procedure:
In this experiment, we need to read and understand the measurements of a metal
cylinder. An object’s mass and dimensions can be measured utilizing a variety of tools
including, but not limited to, low precision kitchen scale (13g uncertainty), a high
precision digital scale (0.05g uncertainty), a low precision metric ruler (0.05cm
uncertainty), and a high precision Vernier caliper (0.010cm uncertainty).
Length is generally measured by using a meter ruler and the least count of the meter
ruler is 1.0mm. Consequently, meter rulers are only limited to measure length
increments no larger than 1mm. On the other hand, high-precision instruments such as
the Vernier caliper can measure length segments as small as 0.02 mm.
The figure below shows an image of the Vernier caliper. There are two scales in the
caliper. The main scale provides the main number(s) plus one decimal place to the
reading, and the vernier scale provides two additional decimal places to the reading,
which gives the scale its high precision capability.
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Group#4: Hachim-Jeongho-Wasim-Cado PHYS 3A Professor Rosa Alvis 9/7/ Lab 1: Measuring Density Objective : The purpose of this experiment is to utilize both high and low precision instruments to measure a given metal cylinder’s mass and dimensions and use the data to calculate its volume and density. Ultimately, we ought to observe the discrepancy between the two precision instrument types. The measurements will be noted by the four assigned group student members. Procedure : In this experiment, we need to read and understand the measurements of a metal cylinder. An object’s mass and dimensions can be measured utilizing a variety of tools including, but not limited to, low precision kitchen scale (13g uncertainty), a high precision digital scale (0.05g uncertainty), a low precision metric ruler (0.05cm uncertainty), and a high precision Vernier caliper (0.010cm uncertainty). Length is generally measured by using a meter ruler and the least count of the meter ruler is 1.0mm. Consequently, meter rulers are only limited to measure length increments no larger than 1mm. On the other hand, high-precision instruments such as the Vernier caliper can measure length segments as small as 0.02 mm. The figure below shows an image of the Vernier caliper. There are two scales in the caliper. The main scale provides the main number(s) plus one decimal place to the reading, and the vernier scale provides two additional decimal places to the reading, which gives the scale its high precision capability.

To use the scale properly, make sure the object is placed firmly between the two jaws. To read Vernier’s scale:

  1. Read the main scale. Look for the last whole increment visible before the 0 (zero) mark.
  2. Read the secondary scale (Vernier) measurement. This is the division tick mark that lines up best with a mark on the main scale.
  3. Add the two measurements together. Data: Low precision readings: m(g)±δ d(cm)±δ l(cm)±δ Hachim (100±13)

Jeongho (100±13)

Ahmer (100±13)

High Precision Experiment: Vernier caliper, digital scale Average value Average uncertainty Mass (g) 108.80 0. Diameter (cm) 2.548 0. Length (cm) 7.595 0. Density (g/cm^3 )

Calculations: Average value: 𝑥 = Σ𝑥 𝑁 Average uncertainty: δx= δx 1 )^2 + (δx 2 )^2 + (δx 3 )^2 + (δx 4 )^2 ] 1 𝑁 [( Density equations: ⍴ = ; where ⍴, m and V are the density, mass, and volume of the 𝑚 𝑉 given sample, respectively. V = π* r^2 *l = π*( )^2 * l; where V, r, d, and are the volume, radius, diameter, and length of 𝑑 2 𝑙 the sample, respectively. ⍴ = 4𝑚 π𝑑^2 𝑙 Uncertainty equation: δ⍴ = ⍴ ( δ𝑚 𝑚 ) 2

  • ( δ𝑙 𝑑 )^ + (^ δ𝑙 𝑙 ) 2 Fractional Uncertainty: 𝝳𝑥 |𝑥| Sample Calculations: Average low precision mass value: 𝑚 = = = 100g Σ𝑚 𝑁 100100100* 4 Average low precision mass uncertainty calculation:

Given δm of the kitchen scale = 13g As all mass measurements were taken using the same kitchen scale: δm 1 = δm 2 = δm 3 = δm 4 δm= δm 1 )^2 + (δm 2 )^2 + (δm 3 )^2 + (δm 4 )^2 ] 1 𝑁 [( δm= [(13g)^2 +(13g)^2 +(13g)^2 +(13g)^2 ] 1 4 δm= = = 6.5 ≅7g 4 * 4 13 2 δm = m ± δm = (100 ± 7)g Low precision density calculation: ⍴low = = = = 2.60g/cm^3 4(100𝑔) π(2.55𝑐𝑚)^2 (7.54𝑐𝑚) 400𝑔 ᴨ49.02885𝑐𝑚^3 400𝑔 154.02867𝑐𝑚^3 Low precision uncertainty calculation: δ⍴low = 2.60g/cm^3 = 2.60g/cm^3 = 7𝑔

2

2(0.03𝑐𝑚

2

0.03𝑐𝑚

2

  1. 00546.. 0.19g/cm^3 δ⍴low = (2.6 ± 0. 2)g/cm^3 High precision density calculation: ⍴high = = = = 2.809g/cm^3 4(108.80𝑔) π(2.548𝑐𝑚)^2 (7.595𝑐𝑚) 435,20𝑔 ᴨ49.3090488𝑐𝑚^3 435.20𝑔 154.9089...𝑐𝑚^3 High precision uncertainty calculation: δ⍴high = 2.809g/cm^3 = = 0.030𝑔

2

2(0.005𝑐𝑚

2

0.005𝑐𝑚

2

  1. 809𝑔/𝑐𝑚3 0. 00001... 0.01 g/cm^3 δ⍴high = (2.81 ± 0.01) g/cm^3 Fractional low precision uncertainty = (0.2/2.6) = ±0. Fractional high precision uncertainty = (0.01/2.81) = ±0. Discrepancy test: