# Loop-the-loop question

#### faust9

Hello all.

I just stumbled across this site and as such would like to say thanks in advance for any insight to my little quandry...

Here's the deal: My team did a loop-the-loop lab for engineering physics and it went like this.

First we set a ramp at some height such that a car rolling down an incline would be able to negotiate a loop. We then measured the total distance traveled by the car and used that to compute the average friction coefficient.

With the average friction coefficient we could then calculate some height such that the car would just barely negotiate the loop (the normal force of the car at the apex to the loop would be as close to zero as possible).

Next we experimentally determined the height using the above criteria.

The quandry is that the H-calculated is 21% higher than the H-expected; however, our goal was a 5% variance.

My question is (before I actually go through and figure this out) do y'all think finding the actual coefficient of friction using the sum of the integrals of the friction down the incline, through the loop, and along the flat part of the track would change the answer appreciably?

Thanks for any insight.

David

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#### jamesrc

Gold Member
I think it would be worth the while considering that the normal force (and, consequently, the friction force) varies between ~0 to ~(mg + mv^2/R) over the course of the loop. The way you started is a good way, though. You know that no model will be perfect, so it's good to start out with a simple model (like a constant friction as you did) and see how good it is. If it's not good enough, then you refine it some.

#### faust9

Thanks for the resonse.

I did calculate the real μk as opposed to the average and the net result brought the difference to 19'ish%. I guess I'll have to simply explain the huge variance as the result of inelastic collisions between the car and the sides of the track.

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