# $\mu_k$ of surface from experimental vs theoretical acceleration [closed]

I have an air track at a slight angle with a glider. Final velocity is determined, and from that a is calculated, and from a, I have approximated g. I am trying to find $$\mu_{k}$$ between the track and the glider. The values that I am coming up with are about 1/100th of what I expect. What I have so far is:

$$g=\frac{a_{exp}}{\sin\theta}$$

$$a_{exp}=\frac{v_{f}^{2}}{2d}$$

$$g=\frac{\frac{v_{f}^{2}}{2d}}{\sin\theta}$$

$$v_{t_{f}}=\sqrt{g\left(2d\right)\sin\theta}$$

$$K_{exp}=\frac{1}{2}mv^{2}_{exp_{f}}$$

$$K_{t}=\frac{1}{2}mv^{2}_{t_{f}}$$

$$K_{loss}=K_{t}-K_{exp}$$

$$F_{fric}=\frac{K_{loss}}{d}$$

$$F_{n}=mg\cos\theta$$

$$\mu_{k}=\frac{F_{fric}}{F_{n}}$$

$$\mu_{k}=\frac{\frac{\frac{1}{2}m\sqrt{g\left(2d\right)}^{2}-\frac{1}{2}mv^{2}_{exp_{f}}}{d}}{mg\cos\theta}$$

Am i missing something obvious, or am I way off the mark?

## closed as off-topic by John Rennie, Aaron Stevens, Jon Custer, ZeroTheHero, tpg2114♦Aug 16 at 23:17

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• You need to give more information. All you have given is a derivation of an expression. What makes you think this expression is wrong? What did you measure? Where are you getting your expected value from? – Aaron Stevens Aug 14 at 10:40
• @AaronStevens the expected value for mu k was given by the professor to be in or around the second decimal place. I feel like my reasoning is correct, but I am getting values between 0.0018 and 0.0004 with a mean of 0.0008. I expect it to be negligible as it's and air track, just not this negligible. the measurements taken in the original experiment were of a glider along an inclined track across variable distances from an initial velocity of 0 through a photogate timer to get final velocity at end of run. from this g was calculated by dividing by the sine of the angle. – theoctagon Aug 14 at 16:18

## 1 Answer

It is not clear from your question how you you obtained a theoretical value for the kinetic frictional force which is so much larger than the kinetic frictional force measured by experiment.

I would expect the kinetic frictional force on an air track to be very small, as that is a key design feature, and possibly speed dependent.

If you incline the air track so that the glider travels down the track at constant speed you can get an estimate of the kinetic frictional force.
Also making the glider go down the track at different constant speeds, adjusting the inclination of the track as necessary, might enable you to find out if the kinetic frictional force is speed dependent.

• the theoretical value was given by professor as being close to or in the second decimal place. the experiment consisted of a single angle setup releasing the glider with initial velocity of 0, with constant acceleration from gravity (hence a/sin theta) across various distances, capturing the final velocity with a photogate to measure length of glider/time photogate obstructed. – theoctagon Aug 14 at 16:10