Troubleshooting Lab Errors with a Ballistics Pendulum

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Errors in lab experiments, such as those involving a ballistics pendulum, can stem from various factors, including equipment malfunction or measurement inaccuracies. A rod that fails to pull back or shoot correctly can indeed indicate an error, potentially affecting the results. Measurement errors can also arise from the limitations of the measuring device, where the smallest unit may not reflect the true error due to reaction times or other variables. Statistical methods, like calculating the range or standard deviation from repeated measurements, can help quantify these errors. Understanding and estimating errors is crucial for accurately interpreting experimental results and validating theories like F = ma within the context of experimental error.
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Hey guys, I was just wondering what is an error during a lab? I always get these parts wrong on my lab, mainly because I don't know of any errors that are occurring in a lab.

For my lab I was using a ballistics pendulum and sometimes the rod wouldn't pull back right or shoot right. Would that be an error?
Or would it be something like the rod damaged the wood and could have caused the wood to travel farther?

Thanks for your help.
 
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I see "error" as a technical term meaning the accuracy of a measurement.
For example, if you measure something with a ruler whose smallest calibration is a tenth of a centimeter, you automatically round it to the nearest tenth of a centimeter, as in 2.5 cm, when it is anywhere in the range 2.45 to 2.549 cm. The easiest way to say this is 2.5 ± 0.05 cm.
The ±.05 is the error in the 2.5.

Sometimes the smallest unit of the measuring device is not the real error. For example, when measuring time whether you have a clock with a second hand or a stopwatch calibrated in hundreds of a second, you will find that you are out by a reaction time. The error in this kind of measurement can often be found by repeated the same measurement a few times and using some statistical measure such the range or standard deviation of the values measured.

Sometimes a measurement is really a minimum or a maximum so the error estimate is a + or a - rather than a ±.

The error estimate is very useful in labs. Say you have an experiment to measure acceleration and force on something. It will never be perfectly accurate so you can't conclude that F = ma, but you may be able to show that the data fits the formula F = ma "to within experimental error". Error bars on a graph are often a good way to do this. Can you draw the F = ma line on the graph to within the range of the error bars?
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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