I built an apparatus for a physics experiment. It's an aluminum channel ramp with a Vernier photogate, a chrome steel ball, and a grove electromagnet. The Arduino MC has the Sparkfun Vernier shield. Everything works great. The electromagnet releases the ball. The measurements on the photogate are consistent to within a millisecond. I've measured the angle of the track using a digital protractor, and I measure the length of travel to the photogate with a laser. I'm confident my measurements are valid to at least three significant digits.
Thus, I should be able to calculate the acceleration due to gravity (and yes, I'm accounting for the rotational energy) by conservation of energy.
However, the values are consistently off. They vary by angle. Shallower angles have more error, sometimes as high as 10%. Please note the results are very consistent across trials. So my precision is high, but accuracy is low.
Also of note, I have the line in the code that save my micros() right next to the digitalWrite() that turns off the electromagnet. Those events have to be within a microsecond or two of each other. Right?
I'm left searching for sources of error. First, I was wondering if my steel ball had become magnetized, and I was getting some Lenz effect with the aluminum channel. But nothing "sticks" to the steel ball. So I don't think it's accidentally magnetized.
How much latency should I expect in the electromagnet? The force has to decay over a small increment of time--it can't be instantaneous. I don't know how to test for this or how to calculate the effect (if it's even real). That's the last possible error I can think of.
If I remember the drill correctly, you need to time the ball right AFTER it leaves the magnet. So you need a sensor to monitor this, not the time of the release of the ball. The acceleration of the ball will be a constant for it's entire path.
I wonder how you are powering the magnet and how you are turning it off. Any capacitance storing a charge will delay the release.
Paul,
I think you're right. That's one way to avoid the issue. I have a second photogate that I can align just ever so slightly in front of the ball. That should make any initial velocity negligible.
Thanks,
Jeff
It is not clear from your description whether friction between the ball and channel could be dissipating energy, and the loss would be more important at shallower angles.
The concept of "rolling without slipping" is idealized and not accurate for most real life situations.
jwells:
How much latency should I expect in the electromagnet? The force has to decay over a small increment of time--it can't be instantaneous. I don't know how to test for this or how to calculate the effect (if it's even real). That's the last possible error I can think of.
Yes, the magnetic field takes time to dissipate inversely proportional to the back EMF from the coil
at switch off.
Typically an electromagnet is driven using a free-wheel diode across the coil to protect the transistor
doing the switching. This makes the switch off about the slowest it can possibly be though.
Using a resistor or TVS diode allows a higher back EMF voltage at turn off to speed up the turn off.
The higher the voltage the quicker the turn off, but without some limit the electromagnet will generate
extremely large voltages and just fry the transistor.
Ideally you'd use a high voltage transistor and TVS diode (or MOV as voltage limiter) for snubbing
at high voltage. This gives the quickest turn off of the magnetic field.
There is another effect though, which may be relevant, which is remanence in the magnetic
core of the magnet - this might take a while to decay even if the current in the coil falls to zero
very rapidly. It depends on the nature of the core. If its silicon steel laminations it is likely to
decay rapidly, if a lump of soft iron I'm not sure. Also there will be eddy current effects with a
lump of solid metal.
I do think that even though aluminum is not magnetic, when a magnet moves next to aluminum, there is interaction because of the movement. I see you mentioned the Lenz effect, the aluminum ramp will certainly slow down the steel ball, in my opinion (possibly)
An example is, take a magnet and a strip of aluminum, the magnet doesn’t react to the aluminum. Now, hold the aluminum strip at a slight angle and release the magnet resting on the strip. You will see the magnet sticking to the strip and sliding down slowly.
I know we are talking about a steel ball and not a magnet. Maybe switch out the ball for a glass marble as a quick check
There will be a small braking effect if the steel ball retains significant magnetization after release,
a plastic ramp would be better if that's the case, but apparently no magnetization is detected for
these chrome steel balls.
Mechanical friction is going to dominate at shallow angles, which is why air-cushion rails are preferred for
this sort of experiment. Smoothness of the rails and balls will help, as surface roughness or dirt worsen the
situation. Some judge of this can be made by measuring the shallowest angle at which a ball stays
put. Anodized aluminium surfaces are far more likely to stay smooth as being a ceramic coating very
much less wear will happen. Larger balls will be less sensitive to small scale fluctuations in the surface height.
At steeper angles and longer runs viscous friction from the air will become more important, but
large heavy steel balls are going to be close to ideal unless very high speeds are attained I think.