So far, you have performed a number of experiments with an emphasis on interpretation of data – both for the purposes of informing your experimental technique and for the evaluation of your final results. This is a key component of experimental science. Many of the most important experiments in science are ones which resulted in the measurement of something which – up to that point – was unknown and for which there was no theory or other means of determining whether or not the experimental results were correct.

So how do you know if your experiment was a “success” when there is no known “right” answer to compare your results to? The answer is that you evaluate your data throughout your experiment and use your data to refine your methods until you are confident that you fully understand each part of the experiment. When you understand each part, you can in turn trust the results and then allow only conclusions which are supported by the data. Other scientists will come along and build on the results of your experiment by developing theoretical models or performing additional experiments – maybe to verify what you found, to poke holes in the interpretation by finding conflicting information, or to use the model to make predications about new experimental results to look for – and over time, the community reaches a consensus.

The process of performing an experiment and reporting on the results of the experiment (as well as limitations on your results – i.e. experimental uncertainties) is of fundamental importance to the advancement of scientific knowledge.

In today's lab, you will perform an experiment to determine how much energy is required to rupture a piece of tissue paper. Since there is no “known value” for this process, you will have to operate under the same conditions as many research experiments.

You are given an apparatus which is suitable for making this measurement. It is up to you to use the physics you have been studying this quarter to determine what measurements need to be made, and how they will be used to accomplish the goal. Your goal is to report the amount of energy required to rupture a piece of tissue paper, along with an estimate of how well you know that value. In the process, you will need to look at your data to understand how well your experimental technique is performing and where you can make improvements to your experiment.

For this lab, you will use the apparatus setup as shown in figure 1. A steel ball bearing released from point (a) will travel down the tube gaining kinetic energy until it emerges at point (b) with some velocity, $v$. The ball bearing will then travel some distance, $d$, and fall a distance, $h$, before striking the floor at point (c).

If a piece of tissue paper is placed at point (b) and the ball bearing is again released from the same point (a), one would expect the distance travelled in this case will be less than in the case when there is no tissue paper. The difference in distance travelled will be related to the energy lost in punching through the piece of tissue paper.

Figure 1: The apparatus

Using what you have learned in lecture about kinematics and energy, it is up to you – with guidance from your TA – to decide what measurements to make and what calculations to perform. The energy lost to rupturing the tissue paper will be small, so you will need to make repeated measurements of the distances travelled to obtain averages with small enough uncertainties to produce a meaningful answer. You can use a magnet to ensure that you release the ball bearing from the same starting location (a) for each trial.

You will need to propagate your measured quantities and their associated uncertainties through some calculations in order to arrive at a final result with its uncertainty.

How do I give the height an uncertainty? Won't it be the same all the time?

When measuring some static quantity such as the height of the ramp or the mass of the ball, it doesn't make sense to measure quantities multiple times and use the standard deviation, because it is entirely possible that your measurements could be identical each time. In this case, the uncertainty in the measurement is determined by the resolution of the measurement device. For instance, see the photo below:

In this instance, we can probably agree that the stapler is at least 18.5 cm long. We might estimate that it is 18.51 or 18.52 cm even, but we can't make very good estimates here because we're trying to measure something smaller than our ruler's resolution (i.e., the 1mm scale.)

As a rule of thumb, we typically will use half the resolution of a measurement scale (0.5mm in this case) when estimating the uncertainty due to a measurement device.

For this lab, we encourage you to not try and use this for your distance measurements, $d$. This is because it will almost certainly be overshadowed by the statistical fluctuations (standard deviation) of the ball's travel distance.

A complete treatment of uncertainties takes into account both the limits due to statistical fluctuation and due to device resolution, but in these labs it is usually clear which will be more important.

TBD – copy from elsewhere