# Experimental setup for 1 dimensional constrained frictionless motion

Physics textbooks are full of examples considering one dimensional constrained motion (in the gravitational field) with neglectible friction.

However I have never seen setups with curved paths where friction is really neglectible. There are non curved air tracks out there with neglectible friction and experiments with curved paths like this roller coaster model but with non neglectible friction. To make the question more concrete, consider the latter example:

I know this experiment and if you try to show conservation of energy (for example by measuring the top height and speed at the bottom) you have losses of more than 10 percent (depending on the track shape even much more).

So, what is the state of art to make such experiments with as low friction as possible with a curved track (like in the lower track of the image above)?

• Magnetic levitation on a superconducting rail should do the trick, look here, for instance, if you have the ressources. – denklo May 21 at 11:34
• @denklo Just asking, but don't you have to take into account the energy needed to produce the magnetic field? Doesn't all that do is make up for the losses that would occur due to contact and viscous (with air) friction? I think the OP is looking for ways to minimize viscous and dry friction losses. But by copy of this to the OP, I ask for clarification. – Bob D May 21 at 21:48
• @BobD If by "magnetic field" you mean the magnetic field of the rail, then i think it is not relevant for the experiment how much energy the environment of the moving body consumes, as long it is not transfered into its cinetic energy. If you refer the the magnetic field induced in the superconductor, then, if any energy is consumed there, it is not due to the current, as the resistance inside the sc is 0. – denklo May 23 at 7:28

Basically, you need to reduce the influence of friction.

1. from air. (It did matter if you rail was as large as shown in your picture, especially when it involved $$v^2$$ term. We did the lab in sophomore year, the $$v^2$$ term and $$v^3$$ term will start to show up with that kind of volocity) {answer: round ball}

2. from rail. (Avoid materials that's sticky.){answer: use soft oil to cover the rail.}

Another factor to take into account was the density, consider ping pong ball.

So A. a cheap way to do it was with a good size stainless steel ball.

However, there's yet another option if you got the budget and time B. use magnetic rail and superconductor. that way the only thing you need to worry about was air resistance.{and what's best, magnetic does no work}

I'm not an "expert" on reducing friction losses, but I think you need to consider viscous friction (due to contact of the vehicle with air, i.e., air drag) and dry friction (due to contact between the vehicle and the track, and the friction of the car axles).

As far as air drag is concerned, you could probably benefit from the designs of aircraft and motor vehicles. Although the scale is different, designers probably now what those factors are when they use wind tunnels to design the contours of the vehicle.

As far as dry friction is concerned, you need to look at the wheels of the vehicle and the type of surface of the track. Since gravity is the force propelling the vehicle (as opposed to wheel torque and static friction) I would think you would look for track surfaces that have the lowest coefficients of friction.

Then there are the materials and design of the wheel surfaces and the "axles". I remember working with my son on cub scout car racing and the benefit of using graphite on the wheel axles to reduce axle friction.

These are only some observations. They are not obviously mathematically rigorous, but perhaps they can help guide the analysis.

Regarding the use of magnetic levitation, as has been suggested, correct me if I'm wrong, but aren't you looking for ways to minimize lap time without the presence of forces other than that of gravity and friction?

I think air drag is a minor error in such experiments

You're probably right. You might consider a simple experiment to prove it. Configure a vehicle to try and deliberately introduce air drag without influencing other factors. Perhaps install a lightweight "sail" on a vehicle and see if it measurably slows it down.

One last major consideration. Are there any constraints on the design of the vehicles on the track. I mean, if there weren't any you could just use stainless steel balls as @user9976437 suggested. If this is a competition, then there must be some rules. And that goes for magnetic levitation as well.

So I guess the first question any of us should have asked you before answering your question is what are the rules of the competition, if any.

Hope this helps.

• I think air drag is a minor error in such experiments: aapt.scitation.org/doi/abs/10.1119/1.5025298 – Julia May 22 at 5:35
• You’re probably right. I was just trying to account for the possibility – Bob D May 22 at 7:25
• @Julia See my suggestion at the end of my answer – Bob D May 22 at 7:51