Designs for an electronic timer

[hy23]

I'm conducting an experiment to determine the brachistochrone. The setup is going to involve an inverted cycloid shaped track about 5 or 6 feet long. I need a way to measure the time it takes for a marble to roll down the track and I need a more accurate method than manually operating a stopwatch. Is there a way to somehow synchronize two stopwatches, having one placed at the start of the track and one at the finish line, or are there any better ways of doing this?

 

[vk6kro]

You probably need to start a stopwatch with one switch and stop it with another.

First you need to get at the contacts in the switches in the stopwatch so you can switch them electrically.

Then you need to make a switch that completes a contact (using a microswitch) but also releases the marble. You could have a piece of plastic just gently sitting on top of the marble with enough pressure to stop it rolling. Lift the plastic and start the timer with the same action.

Stopping the stopwatch is easier because the marble is moving and you can use this to push something which operates another microswitch to turn off the stop watch.

 

[Bob S]

You need to measure elapsed time to 0.001 seconds accuracy or better. Use a 10-kHz oscillator, use one phototransistor as a start gate, and another as a stop gate, to control a 4-decade BCD counter (like four 74190 decade counters) or four CD4026B CMOS decade counter with 7-segment driver. Or you can buy used pulse generators and gateable frequency (pulse) counters on eBay for under $100.00.

Remember that the moment of inertia of a rolling marble is (2/5)mr², so the marble does not accelerate at g·sin(θ) down the brachistochrone track. The "true" brachistochrone equation is for a frictionless sliding bead on a wire.

Bob S

 

[hy23]

I will definitely try to use something like gates and pulse generators...they are quite pricey though.

Regarding the brachistochrone, with rolling friction the solution will still be something close to the inverted cycloid right?

 

[vk6kro]

One problem is that your marble will take about a second to cover the first inch, if it is on a gentle slope.

So, measuring the finish time to ¹/₁₀₀₀th of a second is pointless unless you can measure the start time to the same accuracy.
And you can't do that with photo gates, because the width of the light beam is important for a slow moving marble.

So, although you could measure the start time with photo gates, the accuracy will be better if you use a mechanical switch to start the stop watch and release the marble at the same time.
Like this:
[PLAIN]http://dl.dropbox.com/u/4222062/start%20switch.PNG

Photo gates also require considerable shielding from other light sources and they need careful circuit adjustment to get optimum detection.

On the other hand, you can have a simple barrier, at the end of the track, that is hinged at one side and operating a microswitch at the other. Quite a small impact can operate the switch reliably for years.

 

[Bob S]

I will definitely try to use something like gates and pulse generators...they are quite pricey though.

Regarding the brachistochrone, with rolling friction the solution will still be something close to the inverted cycloid right?

For measuring a time interval measurement more accurately than a stopwatch, you will probably need a digital counter, at least 4 decades (x.xxx seconds). Although you could built one, my solution was to buy a used universal counter timer on eBay. I have had good luck with a used Global Specialties model 5001 universal counter timer I bought for about $50.00. In addition, you will need an oscillator (use a NE555 chip) and several NAND gates for gating the oscillator with the start and stop switches or photogates.

You can neglect friction for a rolling marble, but not the moment of inertia. For a frictionless block sliding down an incline, the velocity v is related to the vertical drop h by the relation

mgh = ½mv²

For a rolling marble with a moment of inertia I,

mgh = ½mv² + ½Iω² where I = (2/5)mr² and r = radius of marble.

Bob S

 

[hy23]

vk makes a good point though, I don't see anything going wrong with starting the clock mechanically, but for the impact that will operate the switch at the end of the track, I'm afraid that the marbles which are less that 1cm in diameter won't create enough impact, and even setting up additional apparatuses to multiply this impact might take slightly more time to turn the switch

 

[vk6kro]

You can make sensitive switches quite easily.

Something like this:

[PLAIN]http://dl.dropbox.com/u/4222062/switch.PNG

A metal tube is passed over a piece of wire and is supported by it.
A flat metal plate hangs from the tube.

The bottom of the metal plate is close to a metal contact.

The metal plate is pushed by the marble when it hits it and a contact is made between the wire at the top and the metal contact below.

This can be used to stop your stopwatch.

These switches would need some bounce protection on the output signal. These are simple circuits that stop retriggering if a second contact is made.

For this reason, it is probably necessary to use a proper counter with different terminals for start and stop, rather than a stopwatch that uses the same switch for start and stop.