(11/6/24)

You have seen problems in lecture which assume things like massless elephants and frictionless surfaces. This is done for the sake of simplifying the problem so that you can focus on a particular concept or to make the problem solvable in closed form.

Similar assumptions are made in experimental work. However it is often the case that non-idealities such as friction present in a system simply cannot be neglected, they must be investigated and accounted for. Part of doing experimental science is identifying these non-idealities and figuring out what to do about them. Sometimes you redesign an experiment in order to reduce their impact to an acceptable level. If you cannot reduce them you need to quantify their impact on your data so that you can properly take them into account.

The focus of this lab is on identifying, investigating and accounting for these sorts of non-idealities which cannot simply be swept under the rug.

The experimental task is to investigate the concept of conservation of energy in a system where you cannot neglect non-conservative energy losses. The setup is similar to one which you have likely encountered in lecture, two masses connected by a string with one hanging over the edge of a table while the other mass rests on the surface of the table as shown below.

The goal is to conduct an experiment to determine to what degree is energy conserved when the hanging mass is allowed to accelerate due to gravity. To first order the experiment requires measuring the potential and kinetic energies of the system before and after the mass is released. However there are at least two obvious sources of possible bias in due to non-conservative energy losses. In this lab you will need to perform additional measurements to assess these non-conservative energy losses so that you can account for them in your final result.

In this lab you will use a device called the iOLab. The iOLab is a device which contains a wide array of instruments and sensors which are useful for doing physics experiments. Including :

• 3-axis Magnetometers.
• 3-axis Accelerometers.
• 3-axis Gyroscopes.
• A Force sensor.
• Position encoders.
• Light and Sound sensors

Interestingly, most of the sensors in these devices are also found in your cell phone. The difference is that the sensors in the iOLab are designed to be used for scientific experimentation and can provide much more precise and accurate data than what your phone can achieve. You will use this device in a number of future labs in the PHYS140s sequence. The first part of this lab is an exercise to get you familiar with the device, what its capabilities are and how to use it. Work through the following tutorial.

You can never make a measurement too precisely. However you can reduce the size of your error bars to the point where new sources of systematic uncertainty become significant. This is where the real work of doing experimental science begins as you have to figure out what your experimental biases might be and what to do about them.

There are multiple ways to use the sensors in the iOLabs, but the position encoded wheels, force sensor and accelerometers should seem obviously useful.

To begin, design and conduct an experiment to determine to what degree is energy conserved when the hanging mass is allowed to accelerate under the influence of gravity considering only changes in kinetic and potential energy. Estimate the uncertainties in your measurements as well as you can. The goal is to perform the experiment as precisely as possible and to reduce your measurement uncertainties to the point where your results show a significant disagreement with the expectation that energy is conserved.

Connect the two iOLab devices by a piece of string, and then hang one of the devices over the edge of the lab bench. You can let the string slid over the corner of the lab bench, or if you prefer you could use one of the rods in the lab to keep the string more parallel to the surface of the desk. The other iOLab device should be placed wheel side down on the table top. Be sure to use a piece of foam on the floor to pad the fall of the hanging device.

It is up to you to decide which sensors in the two devices to use to measure the kinetic and potential energy of system at two points in the motion of the devices while the hanging device is falling under the influence of gravity.

Measure the total energy before and after the hanging mass has fallen through some distance as accurately as possible. Assess the uncertainties in your measured values and minimize the size of the error bars in your measurement. You should be able to show a significant deviation between the experimental results and the expectation that the total energy of the system is conserved.

At this point you should be able to identify two potentially significant sources of frictional energy loss. Figure out a way to measure these energy losses directly. Depending on how you performed the experiment the first time, you might have to change your setup and use different sensor combinations.

Determine quantitatively how much energy is lost due to these two sources of friction, including an accurate assessment of the uncertainties in these measurements. Yes, there are uncertainties and error analysis associated with your assessment of the impact of systematic errors in your experiment. There are always uncertainties associated with measured quantities.

Once you have accurately accounted for the non-conservative energy losses, factor them into your overall assessment of the degree to which you are able to establish that energy is conserved in this system.

Things which should make it into your group notebook include, but are not limited to:

• Diagrams and photos showing important details of your setup.
• Raw data, including measurements such as lengths and heights or values of masses used.
• Estimates on uncertainties in measured quantities.
• Screen shots of data recorded from the iOLab which illustrate how regions of interest were determined or which show interesting features in the data.
• Results of calculations, plots and fits of data.
• Enough verbal description of your process and procedures that you could come back into the lab a year from now and reproduce the experiment.