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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/ 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:
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
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
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