# Finding uncertainty of a measurement

• cmkluza
In summary, the conversation discusses finding the average reaction time and uncertainty using an equation and measurements. The equation used is t=\sqrt{\frac{2(\frac{D}{100})}{9.81}}, with D measured in cm and acceleration due to gravity at 9.81. The uncertainty of D is \pm0.05cm and the average time and distance are 15.48cm and 0.17s. The attempt at a solution involves converting the absolute uncertainty to a relative uncertainty and simplifying it to a square root with a relative uncertainty. However, the correct answer takes into account the absolute value of D when calculating the uncertainty of t.
cmkluza

## Homework Statement

What is your average reaction time? What is the uncertainty?

## Homework Equations

To find time I used the following equation:
$$t=\sqrt{\frac{2(\frac{D}{100})}{9.81}}$$
D is measured in cm, hence the division by 100 (to get meters).
9.81 is acceleration due to gravity (this comes from $x = \frac{1}{2}at^2$)
While measuring D, I used a measuring stick with smallest unit 1cm. Therefor, uncertainty of D is $\pm$0.05cm.
My average time and distance are 15.48cm and 0.17s.

## The Attempt at a Solution

I'm not certain what the best way to go about this is. So, the first thing I do is convert the absolute uncertainty to a relative uncertainty: $\pm 0.05cm \longrightarrow \frac{0.05}{15.48} \times 100 = \pm 0.32$%.

With a relative uncertainty, multiplication and division by a constant no longer matter, so far as my understanding goes. So, this simplifies down to a square root with a relative uncertainty. Therefore I just multiply my uncertainty by 0.5: $\frac{1}{2} \times 0.32 = \pm 0.16$%.

Is this the correct answer? Something about this whole process just didn't seem right to me, but I've never been good at uncertainties and whatnot.

That's not correct. Even though you are using relative uncertainties, the uncertainty on t depends on the absolute value of D. Have a look at http://www.rit.edu/~w-uphysi/uncertainties/Uncertaintiespart2.html

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## 1. What is the definition of uncertainty in a measurement?

Uncertainty in a measurement refers to the degree of doubt or error associated with a numerical value obtained from a measuring instrument. It is a reflection of the limitations and imperfections of the measurement process.

## 2. Why is it important to determine the uncertainty of a measurement?

Determining the uncertainty of a measurement is important because it allows scientists to understand the reliability and accuracy of their data. It also helps in comparing and evaluating different measurements and their associated uncertainties.

## 3. How is uncertainty calculated in a measurement?

Uncertainty is calculated by considering various sources of error, such as instrument limitations, human error, and environmental factors, and determining their contributions to the final measurement. This is often done using statistical methods and formulas.

## 4. Can uncertainty be eliminated from a measurement?

No, uncertainty cannot be completely eliminated from a measurement. However, it can be reduced by using more precise instruments and following proper measurement techniques. It is important to report the uncertainty associated with a measurement to accurately represent the data.

## 5. What factors can affect the uncertainty of a measurement?

There are several factors that can affect the uncertainty of a measurement, including the precision and accuracy of the measuring instrument, the skill and technique of the person performing the measurement, and the environment in which the measurement is taken. Other sources of uncertainty can include the calibration of the instrument, the stability of the measurement, and the presence of systematic errors.

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