# Quick question about uncertainty in using a stopwatch

• NicolaiTheDane
In summary, the conversation discusses the use of a stopwatch to measure the time of a falling object along a ruler and the potential error caused by human reaction time. The suggestion is made to use video and frame-by-frame analysis for more accurate results. The concept of systematic and random error is also mentioned, as well as the potential influence of expectation on reaction time. The spread of reaction time for humans is unknown, but it is believed to be less significant than individual reaction times. It is also noted that human precision is better than reaction time alone.

## Homework Statement

Watching an object fall, along a ruler, using a stopwatch to take the time from when the object flies passed the upper part of the ruler, and again when it hits the floor (bottom of the ruler)

## The Attempt at a Solution

My friend is doing introductory mechanics and says that since using a stopwatch requires someone to react to something visually, there'll have to be an uncertainty of about 0.2 seconds, both at the beginning and at the end, for a total of 0.4 seconds. From my experience this is correct, hence why they shouldn't have done it this way, as the fall takes about 1 sec, so the fractional error is enormous. But I'd be happy to have it confirmed before I agree with him. Is this correct?

(People in his group argue for 0.05 seconds in total, which given how they performed the experiment, sounds unreasonable to me)

There are several things going on here. The visual reaction time is only one thing, but is somewhat countered by the person actually expecting the fall. Unless you have a very long ruler, the best thing would be to capture the process on video and then go frame by frame to determine the times more precisely.

One thing about reaction times is that both of the reaction times will be delayed. If you had exactly the same reaction times to both measurement points, then this effect would cancel out in the difference. Of course, that is not going to be the case, but there is an overall systematic error (mean reaction time - which is the same for both times) and a random error (spread of reaction times - which is different from both points but I would expect it to be smaller than the systematic error) at play here.

Orodruin said:
There are several things going on here. The visual reaction time is only one thing, but is somewhat countered by the person actually expecting the fall. Unless you have a very long ruler, the best thing would be to capture the process on video and then go frame by frame to determine the times more precisely.

One thing about reaction times is that both of the reaction times will be delayed. If you had exactly the same reaction times to both measurement points, then this effect would cancel out in the difference. Of course, that is not going to be the case, but there is an overall systematic error (mean reaction time - which is the same for both times) and a random error (spread of reaction times - which is different from both points but I would expect it to be smaller than the systematic error) at play here.

If I had done the experiment, and had the same tools, I would have used a phone camera and loggerpro. But they choose this way, so better methods wont' change much at this point.

But you're saying that because the person is expecting it, the reaction time is similar at both ends and is thus reduced? Doesn't expecting it, and viewing it from a distance make reacting too quickly just as likely?

Expecting it is likely to reduce the bias from reaction time alone. The random part (spread in reaction times) which is actually the only one that enters into the measurement will probably remain.

Orodruin said:
Expecting it is likely to reduce the bias from reaction time alone. The random part (spread in reaction times) which is actually the only one that enters into the measurement will probably remain.

Excuse my ignorance, but what is the spread of reaction time on average for a human?

NicolaiTheDane said:
Excuse my ignorance, but what is the spread of reaction time on average for a human?
@Orodruin is not professing to know that, and certainly I do not, but it would be safe to assume it is much less than the individual reaction times.
If the experiment was repeated several times with the same parameters then you could find the spread from the data.

haruspex said:
@Orodruin is not professing to know that, and certainly I do not, but it would be safe to assume it is much less than the individual reaction times.
If the experiment was repeated several times with the same parameters then you could find the spread from the data.
I believe it is also something that cannot be stated precisely as it probably depends on many things, such as if the person taking the measurements had a good night's sleep or not.

Human precision in this is much better than reaction time. Based on reaction time alone we would never be able to catch or bat a ball. The ball does not instantly appear at the start point or the end point. We observe the trajectory over time and anticipate when the ball will be at a certain point. We are remarkably good at this particularly with some practice.