PHYSICS 161 Measurement Uncertainties Lab Introduction In the part I of this lab you perform a &quot;warm up&quot; experiment where you will measure the mass and dimensions of a steel sphere. You don't need to turn in a lab report for this experiment. From your measurements, you will calculate the density of the sphere. Assume that the scales are accurate to 1%. You will have to take multiple measurements of the diameter of the sphere in order to calculate the uncertainty in diameter and the corresponding uncertainty in volume. Reference Measurement Uncertainties handout. Young and Freedman, University Physics, 12th Edition: Chapter 1, sections 1.5-1.6 Theory PART I: The density (symbolized the by the Greek letter, ) of an object is defined as the mass divided by the volume: m v The volume of a sphere is dependent on its radius, r, or its diameter, d: = V = 4 3 3 r = d 3 6 Procedure Measurement of a steel sphere's density 1. Determine the value of and the uncertainty in diameter, d, of the steel sphere by measuring it at least 10 times with a meter stick. The meter stick is used in order to have a larger uncertainty. 2. Calculate the average diameter and standard deviation. To use Excel for the calculation, enter the diameter values in cells A2 to A11. In cell A12 enter &quot;=average(A2:A11)&quot; and in cell A13 enter &quot;=stdev(A2:A11)&quot;. 3. Calculate the volume and the uncertainty in volume. 4. Calculate the density of steel and its uncertainty. Within how many standard deviations does your result agree with the accepted density of steel (7.80 x 103 kg/m3 ) Figure 1: Vernier Calipers 5. The vernier caliper can be read to an accuracy of 0.05 mm. To measure the sphere with the vernier caliper, close the jaws of the caliper lightly on the sphere as shown in figure 1. Do your best to make sure that you are measuring the widest cross-section of the sphere. 6. Notice that there are two blades to the caliper: one is fixed, in figure 1 it is the lefthand blade of the caliper and it is connected to the fixed measuring scale. The other blade slides and has 10 <a href="/keyword/tick-marks/" >tick marks</a> on its base; it is on the right in figure 1. There are also two different units: on the upper edge are inches, on the lower edge centimeters. Use the lower scale. Figure 2 7. To read centimeters and millimeters, use the leftmost tick mark (as shown in figure 1). This gives an approximation because if you look closely, the leftmost tick mark will NOT be perfectly aligned with the fixed measuring scale. Note whether the tick mark is to the left or right of the millimeter mark you estimated on the fixed scale. This indicates whether your approximation is actually lower or higher than the true value. If the leftmost tick is to the left of your millimeter estimate, then the actual value is lower. If it lies right of your millimeter estimate, the actual value is higher. 8. Try to estimate the answer to 0.1 of a millimeter. Although this is clearly impossible, start with this estimate, and in step 9 you will use the vernier scale in a slightly different way to get an accurate reading. As an example, for figure 2, a rough estimate would be 1.88 cm. 9. To use the vernier scale, look at the <a href="/keyword/tick-marks/" >tick marks</a> on the sliding portion of th...