PHYS 200 Introductory Physics I Lab 1 Significant Figures & Uncertainty Measurements 2026 NEW UPDTE

PHYS 200 Introductory Physics I | Lab 1: Significant Figures & Uncertainty Measurements 2026 NEW UPDTE Athabasca University

Lab 1: Significant Figures & Uncertainty Measurements

INTRODUCTION The purpose of any standard experiment is to determine how two (2) physical quantities are related to each other. With quantitative measurements, there is always some degree of uncertainty in measuring the values. For experimental research to be meaningful, it is essential to understand the likelihood of sources of error, and the limitations of the scientific instruments used through concepts such as significant figures, and measurement uncertainty.

Significant figures are an important concept in physics because they help show the precision of measurements, and provide a standardization of values for completing calculations and performing experiments. In addition, significant figures also prevents giving false values of precision (overstatement of accuracy); help verify values provided in experiments and solutions, across different areas of disciplines are consistent; avoids mathematical errors; and helps ensure measurements and designs for real-life experiments are rational, consistent, and safe. Measurement uncertainty is another important concept in physics because it helps quantify the value of error in experimental results and measurements. This also helps clarify the reliability (and accuracy) of experimental results and as such, improves experimental designs and enhances scientific communication.

The experiment for Lab 1 is to understand the importance and rules of significant figures and measurement uncertainty by studying the distance travelled by a vehicle over a fixed interval of time.

PROCEDURE The purpose of this scientific experiment is to calculate the average and instantaneous speeds of a vehicle using significant figures and the uncertainty in the calculated values.

Data provided included the distance travelled at 10-minute intervals and the uncertainty in the measurement of distance (δd = ±0.1 kilometre) and time (δtm = ±0.2 minutes).

Table L1.2 from Lab 1: Procedure section provided the distance travelled by the car

versus time every 10 minutes, starting from 0 minutes to 170 minutes. The speed had to be calculated in km/hour, and as such, the time given in minutes was converted to hours by dividing the time by 60. The data was graphed and the average speed and instantaneous speed were calculated to four (4) significant figures together with the associated uncertainty as described in the following sections.

DATA The detailed sample calculations for the new column Time In Hours (δth = hours) calculated in Table L1.2, is included in Appendix A: Calculations of Solutions to Time in Hours and Uncertainty in Time (Hours). The final values for th = (hours) column are listed in Table L1.2 below. The uncertainty in the measurement of time in hours was calculated to be δth = ±0.003 hours. In addition, the distance travelled was plotted against the time in hours on a graph paper, and a best-fit line was drawn to estimate the average speed in km/hour. The graph “Distance Travelled vs. Time” is attached in Appendix B. The time in hours (hr) was the independent variable plotted on the x-axis, and the dependent variable, the distance travelled in kilometers (km) was plotted on the y-axis.

Table L1.2: Distance travelled by car versus time Time in Minutes δtm = ±0.2 (min) 0 10.0 20.0 30.0 40.0 50.0 60.0 70.0 80.0 90.0 100.0 110.0 120.0

Time in Hours δth = ±0.003 (hours) 0 0.167 0.333 0.500 0.667 0.833 1.000 1.167 1.333 1.500 1.667 1.833 2.000

Distance δd = ±0.1 (km) 0 17.5 34.5 52.5 76.1 87.0 105.0 122.3 144.0 152.3 177.0 191.1 209.0

130.0 140.0 150.0

2.167 2.333 2.500

227.4 241.0 263.7

160.0 170.0

2.667 2.833

285.2 292.1

ANALYSIS AND DISCUSSION As shown on the graph attached in Appendix B – Distance Travelled vs. Time, a best- fit line was drawn between the data points on the graph. This line gives the average speed of the vehicle over the 170 minutes of travel time or 2.833 hours. The instantaneous speed within a 10-minute (0.167 hours) was also calculated for a specific time. The uncertainty measurements were also calculated for the average and instantaneous speeds.

The slope (y = mx + b) provides the average speed of the trip. The straight line that passes (on the average) through the data points shows the best linear fit to the data presented. The slope calculated for this experiment was 104 kilometers per hour (km/hour) and the y-intercept (b) was 0.0 km. The instantaneous speed at 75 minutes was calculated by dividing the distance travelled between 70 and 80 minutes by the time (0.167 hours).

CONCLUSION The average speed of the trip from Calgary was calculated to be 104.0 km/hour. At any point in time, the instantaneous speed can be more or less (or faster or slower) in comparison to the average speed of the trip. For the equation y = mx + b, the y-intercept (b) = 0.0 km. The instantaneous speed at 75 minutes was 130.2 km/hr, significantly higher than the average speed over the 2.83 hours. The uncertainty for the average speed was too small to be accurately plotted on the graph, because the graph paper’s grid boxes were very small compared to the scale of the y-axis (0.1 km uncertainty compared to 10 km per square). In addition, the scale on the graph paper was too small

to show the error bars.

In general, using a larger size graph paper to accurately depict the error bars and the uncertainty value for the average speed would help improve the accuracy of measurements for this experiment.

QUESTIONS See answers to the Lab 1 Questions, provided in Appendix C – Detailed Solutions to Lab 1 Questions.

REFERENCES 1. OpenStax. (2022). College physics 2e. OpenStax. https://openstax.org/books/college-physics-2e/pages/1-introduction-toscience- and-the-realm-of-physics-physical-quantities-and-units.

2. Athabasca University (n.d). PHYS 200: Introductory to Physics I, Physics Lab 1 Instructions – Graphical Analysis, Introduction, Procedure, Analysis. Athabasca University (Online format). https://learning.athabascau.ca/d2l/le/content/18346/Home? itemIdentifier=D2L.LE.Content.ContentObject.ModuleCO-550992