Measurements_Report (1)

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Physics I Laboratory Faculty of Science, UOIT Report PhyI-01: Measurement and Evaluation of Physical Parameters Student’s name: Bryanna Bowers-Delsol CRN 11602 Date : 22/May/2019 TA Signature_____________________ Partner’s name _________________________ Experiment #1: Length, Diameter and Volume Hypothesis What method do you think will be more precise for measuring the object’s volume (a) using calipers to measure linear dimensions and then calculate the volume or (b) just measuring the volume of water displaced by the object? Why do you thing so? Measurements Shape of the regular-shaped object: cuboid Table 1.1. Measurements, linear in cm and volume in ml ( cm 3 ) Object Height of cylinder or block, h, cm Diameter of cylinder, d , or width of block, w, cm regular-shaped object. 4.87 0 4.85 5 4.82 5 4.88 0 4.890 1.500 1.505 1.510 1.590 1.595 irregular-shaped object N/A N/A Object Length of block only, l , cm Displaced volume, V D , ml (cm 3 ) regular-shaped object 3.16 0 3.15 0 3.12 5 3.15 5 3.140 25.0 25.1 25.2 25.3 25.4 irregular-shaped object N/A 25.8 25.9 26.0 26.1 26.2 Report PhyI-01: Measurement and Evaluation of Physical Parameters The more precise method for measuring an objects volume is using the direct method ( using calipers ) to measure linear dimensions and then calculating the volume. The reason for this is because water displacement has more discrepancies, sources of error and only considers three significant figures. However, for an object that is irregular, the water displacement method would be more precise since its linear dimensions cannot be accurately measured.

Physics I Laboratory Faculty of Science, UOIT Experiment #2: Mass and Densit y Measurements Table 2.1. Measurements Object Mass m , g regular-shaped object 65.6g irregular-shaped object 66.5g Report PhyI-01: Measurement and Evaluation of Physical Parameters 2

Physics I Laboratory Faculty of Science, UOIT Experiment #1: Analysis Regular-shaped object: Table 1.2: Analysis Mean (average) value, ¯ x Instrumental uncertainty, σ x,inst Statistical uncertainty, σ x, stat Absolute uncertainty, σ x Height, h 4.864cm 0.005cm 0.011cm 0.012cm Diameter of cylinder or width of block, d/w 1.540cm 0.005cm 0.022cm 0.023cm Length of block only, l 3.146cm 0.005cm 0.006cm 0.008cm Volume calculated, V B/C 23.56 cm 3 N/A N/A 0.36 cm 3 Volume displaced, V D 25.2 cm 3 0.5 cm 3 0.1 cm 3 0.5 cm 3 Volume of the regular-shaped object V B/C = 23.56 cm 3 Volume of the regular-shaped object V D = 25.2 cm 3 Irregular-shaped object: Mean value, ¯ x Instrumental uncertainty, σ x,inst Statistical uncertainty, σ x, stat Absolute uncertainty, σ x Volume displaced, V D 26.0cm 3 0.5 cm 3 0.1 cm 3 0.5 cm 3 Volume of the irregular-shaped object V D = 26.0cm 3 Report PhyI-01: Measurement and Evaluation of Physical Parameters 3

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Physics I Laboratory Faculty of Science, UOIT Experiment #2: Analysis Table 2.1. Measurements Object Mass m , g Instrumental uncertainty, σ m ,inst , g Absolute uncertainty, σ m , g regular-shaped object 65.6g 0.05 g 0.05 g irregular-shaped object 66.5g 0.05 g 0.05 g Table 2.2. Analysis Object Volume, V, cm 3 Absolute uncert., σ V , cm 3 Mass, m , g Absolute uncert., σ m , g Density, ρ exp , g/cm 3 Absolute uncert., σ ρ , g/cm 3 regular-shaped object, indirect volume equation method 23.56 cm 3 0.36 cm 3 65.6g regular-shaped object, direct displaced volume method 25.2 cm 3 0.5 cm 3 65.6g irregular-shaped object, direct displaced volume method 26.0cm 3 0.5 cm 3 66.5g Density of the regular-shaped object ρ exp = ____________ Material: _____________, ρ ref = ____________ Density of the irregular-shaped object ρ exp = ____________ Material: _____________, ρ ref = ____________ Conclusion and Error Analysis To determine the volume of the two shapes we used two methods the method we used to calculate the volume of the shapes was calculating the volume based on the volume of displaced water from an Report PhyI-01: Measurement and Evaluation of Physical Parameters 4

Physics I Laboratory Faculty of Science, UOIT overflow container. For the regular shaped object we measured the dimensions and calculated the volume based on my measurements. according to my measurements the regular shaped object had a volume of about 23.56 cm 3 .When using the overflow container the volume of the regular'shaped objectwas also 25.2 cm 3 .The measurements showed no uncertainty for the volume. ! /lthough my measurements showed no difference in uncertainties% I’d imagine the measuring method was more precise! The uncertainties for the methods were reasonable% as they were the same! If there were any errors% the sources of these errors could arise from two places! The first is the human error caused by the operator of the tools! 7or e8ample% when measuring% if the measurer was not perfectly parallel with the edge they are measuring then the measurement would be larger! 7urthermore% if the measurer misread the measurement then% of course% the measurement would be inaccurate! Then there is the systematic errors caused by the tools themselves! 9ach tool and method had its own designated error to it! While we did multiple trials to slim down this error% an error could still e8ists! 7or e8ample% calipers had an error of +!++3 cm% this would mean that each measurement (even if take as best as humanly possible) would have its own inherent uncertainty! The displaced volume method is what I would define as a rough e8periment because of two reasons! 7irstly% it was the least accurate! :econdly% the accuracy was in the fact that themeasurement method had large inherited uncertainties! This would make it nearly impossible to be very accurate! The way we calculated density was threw calculation! We weighed the pieces and then divided their weight by their volume to get their density in g.cm 1 % which we could then reference to find out what material we were dealing with! We determined the density through calculation! This calculation was based on the measured volume and the weighed weight! When comparing our density with that of true /luminum% we find that our density is at the most +! g.cm  1 off of the referenced density! I believe that this is a successful e8periment to come so close to the real density considering the conditions! This lab was carried out in an open environment! The metal was vulnerable to wear% warp% o8idi;ation% and was handled by first time students! The sources of errors are from the error in volume (calculated and presented in part one of the lab)% the error in the weight (displayed on scale)% and human error! We could have weighted it wrong% or misread the weight! The obtained uncertainty values are very reasonable! To come so close to the actual density% I have no doubt that these uncertainty values are too small to allow the consideration that the metal was not /luminum! The general purpose of this lab was to teach students how to calculate uncertainties and to find out what material the mystery metal pieces were made out of% by referencing deduced densities with the theoretical values! Report PhyI-01: Measurement and Evaluation of Physical Parameters 5

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