Video Transcript
An experiment is made to measure the acceleration due to gravity on Earth. The results of the experiment are shown in the table. At least one of the following types of errors is indicated by the results. Select the appropriate error types. Possible error types are (A) systematic error, (B) random error, (C) zero error.
Looking at our table, we see a set of measurements made of the acceleration due to gravity on Earth. We can first notice that all five of these results are the same. And second, they’re all different from the known value of the acceleration due to gravity on Earth’s surface, 9.8 meters per second squared. So then, there does seem to be some type of error going on in these measurements.
Let’s recall now that while a systematic error is a problem in the measurement process that occurs for every measurement made, a random error is one that occurs unpredictably. And it typically has as its source unknown factors. Along with these types of errors, we can recall that a zero error occurs when the measurement of some quantity should be zero but the recorded value is not zero. For example, if we had a scale and nothing was on the scale and yet the scale was not returning a value of zero, that would be a zero error.
Because, as we saw, random errors occur unpredictably due to unknown causes and because all five of our measured values are exactly the same, it’s reasonable to say that there is no random error occurring here. If there were, we would expect to see at least one difference among these measured values. There is no such difference though. So we won’t say that any random error is occurring here.
What about then systematic or zero errors? Since all five of our measured values are different from the actual value of 𝑔 by the same amount, it does seem that there is something taking place that occurs for every measured value, some systematic error. This error type is indeed indicated by our results. Note that we are systematically underpredicting the value for 𝑔 by the same amount.
And then, what about zero errors? If we had a device for measuring acceleration called an accelerometer, we could measure the acceleration of an object, say, that wasn’t accelerating at all. That is, its true acceleration is zero meters per second squared. What if on making that measurement, our accelerometer returned a result of negative 0.5 meters per second squared. This would be an example of zero error. And in fact, this is exactly the kind of zero error that could take a true value of 9.8 meters per second squared and return a measured value of 9.3 meters per second squared.
Therefore, we can surmise that the systematic error that takes place in this measurement is a zero error. The errors could come down to a measurement device that is improperly calibrated. For our answer then, we choose (A) and (C). Area types indicated by these results include systematic errors and zero errors.
