Every measurement has a measurement uncertainty. Discuss how precise and accurate measurement can be achieved in spite of the inherent measurement uncertainty. You could use either of the two options given below.
• Take a ruler and measure the height of the textbook three times. Record the three measurements, and discuss the uncertainty in your measurements. Remember to report the smallest markings on your ruler.
• Take an egg and a measure the weight of the egg three times. Record the three measurements, and discuss the uncertainty in your measurements. Remember to report the smallest markings or “resolution” on your scale.
Why don't you simply follow the instructions? The problem tells you what to do.
Take an egg and measure the weight of the egg three times. Record the three measurements. Explain the uncertainty in your measurements. Remember to report the smallest markings or "resolution" on your scale.
To achieve precise and accurate measurements despite the inherent measurement uncertainty, it is important to follow certain steps and guidelines. This can be illustrated through the two options provided:
Option 1: Measuring the height of a textbook using a ruler
1. Take a ruler with clearly marked units (e.g., centimeters or inches) and record the smallest markings or divisions on the ruler (e.g., 0.1 cm).
2. Position the textbook on a flat surface, ensuring it stands vertically.
3. Align the ruler against the edge of the textbook, ensuring the zero mark is at the base.
4. To obtain precise measurements, measure the height of the textbook three times, taking care to read the ruler carefully each time.
5. Record all three measurements, including the whole number and any decimal value indicated by the smallest markings on the ruler.
Uncertainty in the measurements:
1. To determine the uncertainty in each measurement, consider the smallest division on the ruler. For example, if the ruler has divisions of 0.1 cm, the uncertainty can be considered ±0.05 cm.
2. Since each measurement may vary slightly due to human error or limitations of the measuring instrument, the three recorded measurements may differ from one another.
3. Calculate the average of the three measurements to reduce the effect of random errors. This average value is a more accurate representation of the textbook's height.
4. The uncertainty in the averaged measurement can be estimated as the range within which the individual measurements fall (e.g., ±0.1 cm).
5. By using appropriate statistical analysis, such as calculating the standard deviation, one can obtain a more precise measure of the uncertainty associated with the measurements.
Option 2: Weighing an egg using a scale
1. Choose a scale with a resolution, or smallest markings, that allows for sufficiently precise measurements. Record the scale's smallest division (e.g., 0.01 grams).
2. Place the egg on the scale's weighing platform, ensuring it is stable and not moving.
3. Take three weight measurements of the egg, making sure to zero the scale before each measurement.
4. Record the three measurements, including the whole number and any decimal value indicated by the smallest markings or resolution of the scale.
Uncertainty in the measurements:
1. Similar to the ruler measurements, the uncertainty in each measurement can be estimated based on the smallest resolution of the scale. For example, if the scale has a resolution of 0.01 grams, the uncertainty can be considered ±0.005 grams.
2. Variations between the three recorded measurements may occur due to slight differences in how the egg is placed on the scale or due to the scale's internal precision.
3. Calculate the average of the three measurements to obtain a more accurate estimate of the egg's weight.
4. The uncertainty in the averaged measurement can be estimated as the range within which the individual measurements fall (e.g., ±0.02 grams).
5. Further calculations, like determining the standard deviation of the measurements, can provide a more precise measure of the uncertainty associated with the measurements.
In both cases, achieving precision and accuracy in the measurements entails using appropriate instruments, taking multiple measurements, calculating averages, and estimating the uncertainties based on the measuring instrument's resolution and the variations observed among the recorded measurements.