1. The Following instruments are available in your laboratory. What would be the absolute uncertainties in the measurements made with these instruments?
A. Ruler
B. Protractor
C. Watch
D. Scale
2. By using the instruments from the task 1, you have determined that it takes 3s for a toy car to travel through the distance of 162cm. What are the relative uncertainties of the distance and time measurements? Which measurements is the least uncertain?
3. Calculate the average speed of the toy car. Decide whether you can use the weakest link rule to determine the relative uncertainty in speed estimation. Determine the range of possible values for the actual speed of the car.
4. Why do we need to calculate relative uncertainty? Why isn't absolute uncertainty enough?
1. To determine the absolute uncertainties in the measurements made with the instruments, we need to look at the units and graduations of each instrument.
A. Ruler: The absolute uncertainty depends on the smallest graduation or division on the ruler. For example, if the smallest division is 1 mm, the absolute uncertainty would be ±0.5 mm since the measurement could be up to 0.5 mm above or below the actual value.
B. Protractor: The absolute uncertainty depends on the smallest division on the protractor scale. If the smallest division is 1 degree, the absolute uncertainty would be ±0.5 degrees.
C. Watch: The absolute uncertainty for time measurements using a watch depends on the precision of the watch. If it displays time to the nearest second, the absolute uncertainty would be ±0.5 seconds.
D. Scale: The absolute uncertainty on a scale can vary depending on the scale's precision. If the scale shows measurements to the nearest gram, the absolute uncertainty would be ±0.5 grams.
Note: These values are examples and hypothetical, the actual values depend on the specific instruments used.
2. To calculate the relative uncertainties of the distance and time measurements, we need to divide the absolute uncertainties by the measured values.
Distance relative uncertainty:
Relative uncertainty = (Absolute uncertainty in distance) / (Measured distance) * 100%
Time relative uncertainty:
Relative uncertainty = (Absolute uncertainty in time) / (Measured time) * 100%
To determine which measurement is the least uncertain, we compare the relative uncertainties. The measurement with the smaller relative uncertainty is considered to be the least uncertain.
3. To calculate the average speed of the toy car, we use the formula:
Average speed = Distance / Time
Using the previously measured values, the distance was found to be 162 cm and the time was found to be 3 s.
The relative uncertainties in distance and time can be used to estimate the relative uncertainty in speed using the weakest link rule. This rule states that the relative uncertainty in the result of a calculation is determined by the maximum relative uncertainty among the input quantities.
Therefore, the relative uncertainty in speed estimation would be the maximum of the relative uncertainties in distance and time.
To determine the range of possible values for the actual speed of the car, we can calculate the upper and lower limits. The upper limit is obtained by adding the relative uncertainty to the measured value, and the lower limit is obtained by subtracting the relative uncertainty.
4. We calculate relative uncertainty to understand the precision or reliability of our measurements. Absolute uncertainty alone may not provide sufficient information because it does not take into account the size or scale of the measured quantity.
Relative uncertainty gives us a percentage that allows us to compare the precision of different measurements. It is obtained by dividing the absolute uncertainty by the measured value and multiplying by 100%.
By calculating relative uncertainty, we can assess how reliable or accurate our measurements are, and also compare the reliability of different measurements. It helps us make informed decisions and evaluate the significance of our results.
In summary, while absolute uncertainty provides the magnitude of the uncertainty in a measurement, relative uncertainty gives us a standardized measure that can be compared across different measurements, enabling us to assess the quality and reliability of our results.