Finding the coefficient of kinetic friction

rm_girl

1. The problem statement, all variables and given/known data
For our lab we had to find the coefficient of kinetic friction for a cart on a linear track. We pushed the cart on the track and it went through two photogates which measured the time it spent in the photogate.
So through the 1st photogate = 0.0040s
2nd photogate = 0.0062s
There was a flag on the cart which was 0.42cm.
So we found the instantaneous velocity through the first gate as v=0.0042m/0.0040s = 1.05m/s
The instantaneous velocity through the second gate was v=.0042m/.0062s = 0.677m/s

The mass of the cart is = 0.507 kg

2. Relevant equations
v_f = v_o + at

F=ma

F_f = u_kF_N

F_N = mg


3. The attempt at a solution
I was going to use v_f = v_o + at
find the acceleration as
a= v_f - v_o/t
but I don't know what the time is between the change instantaneous velocity.
I know if I get the acceleration I can plug into the F=ma, find the force and somehow get the frictional force from there.

haruspex

You will need one more piece of information. The distance between the gates will do. (But you didn't need the cart mass.)

rm_girl

Unfortunately we didn't measure the distance between the photogates either.
I only thought of getting the time/distance between the photogates AFTER the lab was done.
But I talked to my professor and apparently we can get the acceleration just from those two instantaneous velocity, unless he didn't understand our question when we asking him about the time issue.

haruspex

No chance. Suppose the distance between the gates was 1m. That would allow you to work out the acceleration, and would not contradict any of the information you provided. Now suppose it was 1km. This would still not contradict any known facts, but produce a rather different acceleration.

rm_girl

That's what I figured. Well, I can't go back and do the experiment again. So guess I'm screwed.
Thanks for the help though.

haruspex

You can't even estimate it from memory?
For the purposes of the lab exercise, there is merit in at least demonstrating that you could have worked it out if you'd had all the measurements.

SammyS

Do you have the time it took to go from one photogate to the other?

rm_girl

No I didn't get that time.

I didn't set up the track and photogate, my lab partner did. And I very much highly doubt he remembers either.
I think my professor will accept if I explain it in my lab report what variables I'm missing, then it should be fine.

rm_girl

Just to make sure, before I start typing up my report.

If were to find the acceleration from the equation
a = v_f-v_i/Δt
Then I plug that into the F=ma
since frictional force is F_f = u_kmg I would set
ma = u_kmg
and find u_k that way ????

haruspex

Yes, but would you really have known Δt? How would you have measured it accurately? I think it's more reasonable that you would have noted the distance between the gates

rm_girl

How would I find acceleration from the distance?

SammyS

There's a kinematic equation for that.

rm_girl

which would be?
the only equation I know that involves distance and acceleration is
d = v_ot + 1/2at²
which has two unknowns in the equation.

haruspex

You haven't met v_f² - v_o² = 2ad?
If not, you could have derived it from the above together with any other kinematic equation by eliminating t.

rm_girl

No, we never had to use that equation.
But I was just able to derive it using the equation I gave above. Thanks

haruspex

It's just force * distance = KE, with the masses cancelled out.