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Home , Measuring instrument, Vernier scale

Pre AP Physics 1: Lab

Introduction: Proper measurement is the key to successful in the physics laboratory. The devices you will use most frequently for measuring length are the meter stick, the caliper, and the . The most common devices for measuring are the and the spring scale. In this exercise we will learn the correct way of using these devices and learn something about their . All physical are uncertain to some degree. The degree of depends upon both the and the person making the measurement. These are the result of several unavoidable factors: the limitations in the construction of the measuring instruments, the conditions under which the measurements are made, and the ability of the person using the instrument, to name a few. Repeated measurements can help to reduce uncertainty, but it can never be completely eliminated.

Objective: After completing this experiment, you should be able to make proper measurements with a meter stick, caliper, micrometer, triple beam balance, and spring scale. You should also understand that some uncertainty in measurements is unavoidable.

Apparatus: meter stick or metric vernier caliper micrometer wooden block triple beam balance spring scale ring stand clamp

Procedure: After each group has obtained the apparatus, your instructor will demonstrate the proper use of the caliper and micrometer and the reading of their scales. In making measurements with a meter stick, keep the following suggestions in mind. (a) Since the end of the meter stick may be worn, start the measurement at some intermediate mark like 10 cm. Of course, you must subtract this starting mark from the final reading. (b) Place the meter stick on edge when making measurements. This will avoid parallax errors, which are easily made when viewing the stick in the flat position. (c) Estimate the reading to the nearest 0.05 mm. In other words, the last digit of your measurement should be either 0 or 5. On a separate sheet of paper, construct a data table similar to the one below, to record your measurements. Since the block is small, use grams and centimeters for units. Using the meter stick, measure the longest of the block and record in the data table. Pass the block and meter stick to a lab partner and have them repeat the measurement. Do not influence their measurement by telling them what you measured. Repeat this process with one more team member. Record all three readings. Using the vernier caliper, measure and record the second longest dimension of the block. Using the , measure to the nearest .01 cm and estimate one more digit, either a 0 or a 5. Again pass the block and caliper to two other group members without influencing their measurements. Using the micrometer, measure the smallest dimension of the block. Read millimeters and half millimeters on the barrel of the micrometer and hundredths of millimeters on the thimble (the part you turn). Estimate the measurement to the nearest .005 mm. Again, repeat the measurement with two other group members. Be sure to convert to cm before recording in the data table. Using the triple beam balance, measure the mass of the block as accurately as possible and record. Then using the spring scale, measure the mass of the block as accurately as possible and record. Again, repeat the measurements with two other group members. Average each set of measurements and find the deviation for each measurement--the difference between the measurement and the average value. Report the largest deviation as the precision of Pre AP Physics 1: Measurement Lab

the measurement with a ± sign. The precision can also be estimated as one-half of the smallest scale division on the instrument. If your measurement deviations are smaller than this value, then use it instead. Calculate the relative uncertainty for each set of measurements by dividing the precision (the ± value) by the average value for the set of measurements. Multiply by 100 to convert to a percent and record in the data table. Calculate the of the block using the average of each of the three measured . Be sure to use proper number of significant figures for your answer based on your measurements. The precision of the volume measurement (after the ± sign) will be calculated below. Average each set of mass measurements and calculate the of the block for each average mass and record. Again, be sure to use proper significant digits for your results. (density = mass / volume) Sample Data Table: Device Trial 1 Trial 2 Trial 3 Average Precision Rel Unc % Meter stick cm cm cm cm ± Caliper cm cm cm cm ± Micrometer cm cm cm cm ± Balance g g g g ± Spring scale g g g g ±

Calculations Table Rel Unc % Calculated Average Value Volume ± Density (balance) ± Density (scale) ±

Error Analysis: Calculate the uncertainty for the calculated . Calculate the relative uncertainty of the volume by adding the uncertainty of each dimension. • Calculate the relative uncertainty of each density by adding the uncertainty of the volume to the uncertainty of the mass measurement used. • Calculate the precision of the volume and each density by converting the relative uncertainty percentage to a decimal and multiplying by the average value. • Discuss possible sources of error for each of the measuring devices used and any ways you can think of to minimize these errors.

Discussion questions: 1. Discuss how the accuracy of a measurement is affected by the choice of the measuring instrument and the person taking the measurement. Why is this important to consider when planning experiments or interpreting data? 2. Which two instruments have the greatest precision? 3. What advantage does the spring scale have over the triple beam balance that might make it preferable to use? 4. When does it make to use the micrometer, the caliper, or the meter stick? 5. If we wanted to extend this experiment, what other things could we have measured, and what devices could we have used?