Understanding lab | Physics homework help

3. Lab report on Experiment 1

(a) Tables 1 to 4 with analyzed data must be included in your lab report. (b) Answers to the questions #1 & #2 at the end of Exp 1 lab manual must be included in your lab report. (c) The required other contents and format for your lab report can be found in the syllabus. 1 2 3 4 5 average L (cm) 0.940 0.940 0.940 0.940 0.940 D1 (cm) 1.880 1.890 1.870 1.880 1.870 D2 (cm) 0.960 0.970 0.970 0.970 0.960 ( )2 2 1 2 4

L V D D

= − VVd iVi −= m (g) 5.720 5.720 5.720 5.720 5.720 (g/cm3) −= ii d % error between the measured Al and the accepted 3 3 :2.7 10 /Al kg m = Significant figures (sig. fig.)

Least Count: Smallest marked division of an instrument. Illustration:

Counting # of significant figures in a direct measurement: # of sig. fig in a reading = # of figures read directly from instrument + 1 for an estimate figure Illustration: Using a standard ruler, you measure some object’s length to be 2.5cm. But, actual length is between the 2.5cm and 2.6cm marks on ruler. So, real length = 2.5cm + (extra). You then eye estimate the (extra) to be 0.04cm. Then you have: final length reading = 2.54cm. Then this reading have 3 sig. fig., with the last ‘4’ as the estimate figure. Calculations with sig. fig. Multiplication and Division: The # of sig. fig. in calculated result is same as that in the measured number with the least # of sig. fig. Decimal place of last sig. fig in each factor is irrelevant. Illustration: If the sides of a rectangle are measured to be 2.03cm and 1.234cm, measured with different instruments. Then, if we calculate its area, then it can only have 3 sig. fig. Area= (1.234 × 2.03)cm2 = 2.5 0̄502cm2≃ 2.51cm2 Addition and Subtraction: The last significant decimal place in calculated result is same as that of the term with least # of sig. fig. after the decimal place. Total # of sig. fig. in each term is irrelevant. Illustration: Say we add Potential energy 1.234J with kinetic Energy 100.0 J, with correct sig fig each. Then total energy E is: E= (1.234+100.0)J = 101. 2̄34 J ≃ 101.2 J Calculations with sig. fig. (contd.) Sig fig. for constants: Constants do not contribute to determining # of sig. fig. A constant is assumed to have infinite # of sig. fig. and hence can be truncated at any necessary decimal place. Illustration: If the radius of a ring is measured to be r = 2.035cm , then its area is Area = π r2. Then we can choose value of as 3.142, as that is the number of figures in the radius. Then,π we have: Area= (3.142× 2.0352)cm2= 13.0 1̄172895 ≃ 13.01 cm2 About 0’s: Any 0’s on the left of 1st non-zero digit are not sig. fig. Any 0’s on the right of and in between non-zero digits are sig. fig. Illustration: 0.00010, 0.10 and 1.0 → all have 2 sig. fig. Scientific Notation → 0.00010 J→1.0×10−4 J (2 sig. fig.) Mass, volume and Density

Density: Density of a body is obtained through equation:

ρ = m V where m is mass and V is volume of the object. Volume determination: To determine volume of an object, you need its dimensions (such as length, diameter, etc.) and plug them in correct equation. Dimension measurements: To measure dimensions of the objects, we use vernier calipers and micrometer. Mass measurements: To measure mass, we utilize the laboratory balance. Vernier Calipers Least count: The vernier calipers we use have least count of 0.01cm. Bottom prongs measure length or outer diameters. Top prongs measure inner diameters. Vernier Calipers: Taking Measurements Key Idea of taking reading: Total reading = Main scale reading + (Least count) X (smaller Marking # on vernier scale that line up or almost line up with some main scale marking) Offset Error In some instruments, the 0 of main scale do not match with the 0 of vernier scale even when the prongs are touching each other, causing error. This is offset error. Micrometer Least count: The vernier calipers we use have least count of 0.01mm. Micrometer: Taking Measurements Key Idea of taking reading: Total reading = Main scale reading + (Least count) X (Marking # on circular Scale that is just below central line on main scale) Percent error When average experimentally measured value for some quantity is̄x , and its true accepted standardized value is known to be A , either through literature or through theoretical considerations, then the percent error in the measurement done through the experiment is given by: % error = |x̄ − A| A × 100% End of Theory

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