Experiment 1: Measurement & Analysis Figure 1.1: Measurement Materials EQUIPMENT 1-Meter Stick Digital Balance 500 g, 1 kg, 2 kg Stamped Masses Metal Cylinder (2) Vernier Calipers (10) Cylinders (Plastic, Wood) String (Mass Cart) 5
6 Experiment 1: Measurement & Analysis Advance Reading Text: SI units for fundamental quantities, prefixes, significant figures, converting units, dimensional analysis. Objective Enhance measurement and graphing skills; introduce error analysis. Theory The fundamental quantities of mechanics are length, mass, and time. The SI units for these quantities are the meter (m), kilogram (kg), and second (s), respectively. All other mechanical quantities can be stated in terms of these quantities. For example, the unit of force in the SI system is the newton (N): 1N=1kg m/s 2. In terms of fundamental quantities, [mass] [length]/[time 2 ]. a newton is In this experiment, you will use a variety of instruments to measure the fundamental quantities of length, mass, and time (see Fig. 1.1). You will then use these measurements to calculate other quantities and perform error analysis (refer to Appendix A). All measurements have uncertainty; they can only be so precise. The precision of the measuring instrument used determines the uncertainty of a measurement. The size of the smallest scale division (the resolution) of an instrument determines the uncertainty of measurements obtained with that instrument. Uncertainty, (Greek letter delta), is either equal to the resolution or equal to 1 2 the resolution of the measuring instrument, depending on how the instrument is designed. Digital Instrument: Analog Instrument: = 1 2 = the resolution the resolution Analog instruments, such as rulers, are read by eye and can be estimated within ± half of a tick mark. Digital instruments can be as imprecise as a full digit in either direction. A digital reading of 5.2 g might be obtained for masses ranging between (5.100...1) g and (5.2999...) g, so their uncertainty is fully equal to the resolution of the instrument. Measurements of time and measurements made with a vernier caliper are considered digital, due to the manner in which they are read.
Prelab 1: Measurement & Instruments 7 Name: 1. What are the fundamental quantities of mechanics, their symbols, their respective units, and their symbols? (25 pts) 2. State the symbol and value for the following prefixes: (5 pts ea.) Prefix Symbol Value mega kilo centi milli micro 3. When comparing experimental values, what determines the correct equation to use? (Hint: Always read the Advance Reading material before you attempt the Prelab; this information is located in Appendix A.) (20 pts) 4. Convert the following: (10 pts ea.) 1.00 in. = 6.10 in. = cm cm 4cm 2 = m 2
8 Experiment 1: Measurement & Analysis PROCEDURE PART 1: Estimating Length 1. Close your eyes and hold your hands about 50 cm apart on the table. Have you partner measure the actual distance between your hands using a ruler. 2. Record this value in the table provided. What is the resolution of the ruler? Use this to determine the uncertainty in your measurement. 3. Repeat for 100 cm. 4. Have your lab partner estimate 50 cm and 100 cm in the same way. 5. Calculate your percent error for each estimate. How much did your measured value di er from what you expected? How large is that di erence compared to the length you expected? (50 cm, 100 cm) Percent error can be calculated as follows: % error = measured expected expected 100 15. Identify the metal in the cylinder using the density chart (Table 1.1, Page 9). Compare your value of density to the accepted value. What is your percent error? PART 4: Graphing 16. Measure diameter and circumference of the 10 plastic and/or wood cylinders provided. Use a piece of string for measuring circumference. 17. Graph Cvs.Don the computer. Open the Graphical Analysis software provided and enter your data in the columns on the left. 18. Fit the data with a linear regression line. Select from the drop-down menu bar: Analyze ) Linear Fit 19. Determine the slope of the best-fit line from the information box provided on-screen. PART 2: Estimating Mass 6. Pick up several of the stamped masses on the lab table to get a sense of their weight. 7. Close your eyes and have your partner hand you one of the stamped masses. Estimate its weight in grams and record it in the table provided. 8. Estimate again as your partner hands you a second mass. 9. Give your partner two di erent masses to estimate in the same way. PART 3: Measuring Density 10. Plug in the digital balance and zero it. 11. Measure the mass of the metal cylinder provided. What is the resolution of the balance? Use this to determine the measurement uncertainty. 12. Measure the height and diameter of the metal cylinder using the vernier caliper. 13. Calculate the volume of the cylinder. This is equal to the area of the base times the height. Show your work. 14. What is the density,, of the metal cylinder?
Experiment 1: Measurement & Analysis 9 Density Material (g/cm 3 ) Solids Metal: Aluminum 2.70 Stainless Steel 7.8 Brass 8.44-8.75 Bronze 8.74-8.89 Copper 8.96 Lead 11.3 Mercury 13.5336 Rock: Granite 2.64-2.76 Slate 2.6-3.3 Diamond 3.51 Garnet 3.15-4.3 Corundum 3.9-4.0 Wood: Pine (Yellow) 0.37-0.60 Oak 0.60-0.90 Ebony 1.11-1.33 Misc.: Ice 0.917 Bone 1.7-2.0 Chalk 1.9-2.8 Glass (Lead) 3-4 Fluids Atmosphere (STP) 0.001225 Water (20 C) 0.99821 Water (0 C) 0.99984 Mercury (20 C) 13.546 Table 1.1: Density of Selected Materials