An instrument for sensitive time interval measurements?

Question

I had the idea to do an experiment at home that would let me calculate the air resistance. $F_{net} = m.a = m.g - f_k$ (kinetic friction), in the case of free fall, so I thought I’d drop an object of known weight from a known height and calculate the acceleration using $Y?_f = 1/2 at^2$. Then I would know $F_{net}$, which in turn would give me $f_k$. The problem is that measuring the time with a stopwatch led me to wildly inaccurate results. This got me thinking about two things:

1- How do physicists measure small time intervals between two events (say the beginning and end of motion), especially in a lab environment? It seems to me that a mechanism must be developed that starts the clock on its own, without having to resort to human reaction times. Are there any instruments that utilize the speed of light or sound to measure the fall of an object? For instance, if an object is placed in front of a light beam, which is aimed at a camera or sensor, and the object falls, the light is revealed, detected by a computer, and the counting begins. The counting stops when the sound of the object hitting the ground or any surface is heard. Is there any such instrument that works this way? I've seen oscilloscopes in the context of measuring the speed of light, maybe that's similar.

2 - Is it possible to make a sensor at home for this purpose? A webcam-based program that senses motion, senses when motion comes to an end, and counts the time in between. I tried coding this in Python using OpenCV, but I need to brush up on my Python skills!

Answer 1

Are there any instruments that utilize the speed of light or sound to measure the fall of an object?

You could arrange for the object to trigger an electrical switch as it falls, and when it lands, and for these switches to produce pulses on an oscilloscope display. This method uses the speed of light in the sense that the signals are conveyed from the switches to the instrument itself at the speed of light.

You might also replace one or both of the switches with an opto-interrupter, if you are concerned that the mechanical action of the switch could disturb the motion of the object.

If timing more accurate than microseconds is required, you would want to carefully match the lengths of the cables connecting the two switches to the oscilloscope, and calibrate the scope trigger to make sure that the electronic delays within the scope are equal for the two channels (or any distance can be corrected for). With these precautions you should be able to achieve timing accuracy better than 100 ps fairly easily.

For instance, if an object is placed in front of a light beam, which is aimed at a camera or sensor, and the object falls, the light is revealed, detected by a computer, and the counting begins. The counting stops when the sound of the object hitting the ground or any surface is heard.

This is unlikely to be as accurate as the method I outlined above because:

1. The process by which a computer detects changes in the images collected by a camera is quite involved, taking many 1000's of processor cycles. Further, the number of cycles is uncertain --- it may take more or fewer cycles depending on details in the image that are irrelevant to the actual presence or absence of the object in the image.

2. The way that the computer "starts counting" also takes an uncertain number of processor cycles, at least if done on a computer with a multi-tasking operating system like Windows or Linux. This issue could be eliminated by using a microcontroller programmed on "bare metal" (i.e. without an operating system) as the computer.

3. The time taken for a sound wave to cross the room and reach the computer is very different than the time required for a light wave or electrical signal to cross the room. In principle this could be corrected for if we can run the test both ways, first with the optical event starting the counter and the acoustic event stopping it, and then with the roles of the events switched. But it is almost always better (more accurate) to minimize errors in the physical set-up first and only use corrections for measurement errors that are unavoidable.

Is it possible to make a sensor at home for this purpose?

Yes it should be possible to do this at home.