The Scientific Method, Measurements and the Art of Discovery (1)

General Physics I Laboratory (PHY2053L) The Scientific Method, Measurements, and the Art of Discovery Name: _ Date: ______________________________________________________________________________ Introduction Vernier Caliper In this laboratory, we will use different tools to measure physical quantities. One of these tools is the Vernier Caliper, which has a precision of 0.1mm. The Vernier caliper can be used to measure the inner diameter, outer diameter or length of an object. The following figures show how to read a Vernier Caliper. 0 Vernier scale Main scale 1) Take the reading on the left of this mark: 41mm 3) Add both readings: 41mm + 0.3 mm = 41.3 mm 2) Count the number of divisions on the Vernier scale until you get to the division that lines up with the main scale and multiply by 0.1mm: 3 × 0.1 mm = 0.3 mm

Volumetric Density The density, of a substance ( ρ is the lowercase Greek letter rho) is defined as its mass per unit volume: ρ = m V Where m is the mass of a sample of the substance and V is the volume. The SI unit for density is kg/m 3 . The following table show the density for different substance. Material Density ( kg / m 3 ) Air 1.00 Alcohol 0.79 × 10 3 Water 1.00 × 10 3 Mercury 13.60 × 10 3 Concrete 2.30 × 10 3 Aluminum 2.70 × 10 3 Zinc 7.00 × 10 3 Iron and Steel 7.80 × 10 3 Brass 8.30 × 10 3 Copper 8.90 × 10 3 Lead 11.30 × 10 3 Materials: Black box, probe, meter stick, cylindrical object, digital scale, Vernier caliper, drafting compass and graph paper. Method Part I: Density 1. List the precisions of your measurement tools. (5 points) _Vernier Caliper (0.1mm), Ruler/meter stick (1cm & 1in), Digital scale (0.1g). _________________________________________________________________________ ______________________________________________________________________________ 2. Use the digital scale to measure the mass and the Vernier caliper to measure the dimensions (diameter and height) of the cylindrical object. Record your results in table 1. 2

Measurement Diameter (m) Height (m) mass (kg) Volume (m 3 ) Density (kg/m 3 ) 1 0.183 m 0.352 m 0.08647 9.26 x 10 -6 9.338 x 10 3 2 0.183 m 0.353 m 0.08646 9.28 x 10 -6 9.317 x 10 3 3 0.183 m 0.353 m 0.08647 9.26 x 10 -6 9.338 x 10 3 4 0.183 m 0.352 m 0.08646 9.28 x 10 -6 9.317 x 10 3 5 0.183m 0.352 m 0.08646 9.28 x 10 -6 9.317 x 10 3 6 0.183 m 0.352 m 0.08646 9.28 x 10 -6 9.317 x 10 3 7 0.183 m 0.352 m 0.08647 9.26 x 10 -6 9.338 x 10 3 8 0.183 m 0.352 m 0.08647 9.26 x 10 -6 9.338 x 10 3 9 0.183 m 0.353 m 0.08646 9.28 x 10 -6 9.317 x 10 3 10 0.183 m 0.352 m 0.08646 9.28 x 10 -6 9.317 x 10 3 Average 0.183 0.3523 0.08646 9.27 x 10 -6 9.325 Table 2 1 0 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 1 0 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 1 0 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 1 0 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 1 0 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 1 0 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 1 0 10 10 10 10 10 10 10 10 10 10 10 10 9 10 10 1 0 10 10 10 10 10 10 10 10 10 9.7 9.8 9. 8 9.9 10 10 1 0 10 10 10 10 10 10 10 10 9.5 9.9 9.5 9. 7 9.6 10 10 1 0 10 10 10 10 10 10 10 10 9.5 9.7 9.7 9. 8 9.8 10 10 1 0 10 10 10 10 10 10 10 10 9.4 9.9 9.7 9. 8 9.8 10 10 1 0 10 10 10 10 10 10 10 10 9.9 9.6 9.9 9. 9 9.7 10 10 4

1 0 10 10 10 10 10 10 10 10 9.8 9.7 9.9 9. 6 9.8 10 10 1 0 10 10 10 10 10 10 10 10 9.8 10 10 10 9.9 10 10 1 0 10 10 10 10 10 10 10 10 10 10 10 10 9.7 9 10 1 0 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 Table 3 Black box Wall thickness = 0 m (m) Object texture: Metallic Number of objects: 1 Objects composition: Metal Objects shape: Springy or Bouncy Table 4 Measurement Length (m) Width (m) Height (m) Volume (m 3 ) Diagonal (m) Black Box 0.1 m 0.1 m 0.1 m 0.001 m 3 0.1 m 5

Average value = 9.26 x 10 -6 +9.26 x 10 -6 +9.26 x 10 -6 + 9.26 x 10 -6 + 9.28 x 10 -6 +9.28 x 10 -6 +9.28 x 10 -6 +9.28 x 10 -6 +9.28 x 10 -6 + 9.28 x 10 -6 / 10 A = 9.27 x 10 -5 The material for the cylindrical object seems to be copper, since it is the closest in Density (kg/m 3 ). 2. Calculate the standard deviation of the mean ( σ = √ ∑ i = 1 N ( x i − x ) 2 N ( N − 1 ) ) for the density. Include a sample of your calculations below. (5 points) Mean= 9.325 σ = (9.338 – 9.325) 2 +(9.338 – 9.325) 2 +(9.338 – 9.325) 2 +(9.338 – 9.325) 2 +(9.317-9.325) 2 + (9.317-9.325) 2 +(9.317-9.325) 2 + (9.317-9.325) 2 +( 9.317-9.325) 2 + (9.317-9.325) 2 = (0.000169)+ (0.000169)+ (0.000169)+ (0.000169)+(0.000064)+ (0.000064)+ (0.000064)+ (0.000064)+ (0.000064)+ (0.000064) = √0.00106/10-1 = √0.00106/9 σ = 0.01085 Part II: Black Box 7

3. Draw the object(s) contained in the black box using the distance measurements from table 2- 4, and other information from the Method section. (5 points) 4. What is the shape of the object(s) inside the black box and its dimensions? (5 points) -The shape of the object inside the black box is round with parts of the coming out like springs. The shape is quite odd and not definite. The dimensions are 3.5cm in Width x 3.6 in Length, and 4.6 cm in Height. 5. Calculate the diagonal of the black box? Show your calculations in detail and write the average value of the diagonal. (5 points) Hint: not a square diagonal! √Length 2 + Width 2 + Height 2 The box dimensions 10Wx10Lx10H √10 2 +10 2 +10 2 = 17.321 Part III: Measuring π graphically 6. Using your area and diameter measurements for both circles (in terms of number of squares), determine the experimental value of π E using the following formula: π E = 4 A D 2 . Include a sample of your calculations for each circle. (5 points) Circle 1 (inner circle): diameter =11.5, area =103 π E = 4 A D 2 = 4(103)/11.5 2 =412/132.25 = 3.1153 8

gathered by counting the number of squares within each circle and counting the squares across. Thus, concluding the experimental value to be 3.12 and 1.19 for each circle. When calculating the percent error, the values came out as 0.637 and 62.102. The results for all tasks completed seemed to be manipulated possibly by the materials used. Although, it could have also been the calculation part of the tasks. __________ ______________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ In the second paragraph, you must show once how your measuring tools produce a quantified experimental error and discuss its implications for your results. The measuring tools used for the different task were a vernier caliper, protractor, ruler, and a measuring scale. When measuring the cylindrical object, the actual objects size differed throughout since it was old and used before multiple times. The vernier caliper measured the object precisely but the scale used could have had incorrect measurements when the object was placed on the scale. When measuring each hole in the black box there were difficulties in measurement when placing the stick in between each hole. As well as the measurements done to try and find the size of the object made it hard because we were only using cm to measure each hole. Which could have caused an improper measurement conclusion about the object in the box. Lastly for the drawing of the concentric circles the protractor was difficult to use when attempting to draw precise circles. Although, the center for each circle was the same, the protractor created not very uniformed circles which could have messed with calculation when trying to find area and diameter. ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ In the third paragraph, you may discuss any other experimental errors qualitatively that may have influenced your results. The other kinds of experimental errors that I came across were calculations when trying to find the diagonal of the box and the dimensions of the object inside the box. I believe I did them right but there was slight hesitation if they were performed correctly. Another one I came across was calculating the standard deviation of the cylindrical object density. The average value from table 10

1 was used in my calculations but I believe the calculations may have or not been written correctly. For the most part the procedures were done smoothly and as precise as possible. _______________________________________________________________________ _______ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ _____________________________________________________________________________ 11