# Calculation of Friction

• B
So Ive done a practical investigation.
Pretty much I used a elastic band to launch a puck on a horizontal floor. I have measured the extension and force for the elastic band, and the extension and stopping distance for the puck on two different surfaces.
How do I calculate the coefficient of friction?
thanks.

## Answers and Replies

BvU
Science Advisor
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2019 Award
How do I calculate the coefficient of friction?
Actually, there may be two of those: one as long as it's not moving and one if it is (the latter is usually smaller).
Did you calibrate your rubber band ? Is it a bit linear (like an ideal spring: extension = k ##\times## force) ?

Are you familiar with friction coefficient formulas like ##F_{\rm friction} = \mu F_{\rm normal} = \mu\, mg ## ?

Yeah, it's linear.

I have a force vs ext for the band, but dont have the force applied when I used it for the puck being launched.

You must calibrate the band for obtain k.

Then you need to suposse that all elastic energy of the band is transferred to the puck in the form of kinetic energy. Then: $$\frac 1 2 k·x^2= \frac 1 2 m·v_0^2$$

Then you can calculate the aceleration $$0=v_0^2+2·a·distance$$

During the mouvement there are only friction force, then: $$\mu·m·g=m·a$$
(mass cancel)
I don't know if there are some wrong in this procedure, please say me if this procedure is not correct. Sorry for my English.

Adem
Even in a moore compact way: Eband=Wfriction $$\frac 1 2 k·x^2=\mu·m·g·distance$$

sophiecentaur and Adem
Thanks guys!

sophiecentaur
Science Advisor
Gold Member
Static friction can be easily found with an inclined plane. (you can look this up) With a bit of care, you can also use an inclined plane to find the limiting slope that will keep the puck moving when nudged, which will give you the dynamic friction. (Good as a cross check if nothing else.)

The k of a rubber band can vary a lot over the full range of extensions. You tend to get a very S shaped curve so you need to operate over a range of expansions that doesn't involve the section where the band goes 'stiff' if you want an accurate value of the Kinetic Energy that it gives the puck. With a bit of care, you can also make sure that the band is not operating with low extension. (A restraining loop of thread, for instance).

Adem