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Finding the coefficient of kinetic friction 
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#1
Nov2912, 01:49 PM

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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_{k}F_{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. 


#2
Nov2912, 03:46 PM

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



#3
Nov2912, 08:15 PM

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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. 


#4
Nov2912, 08:59 PM

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Finding the coefficient of kinetic friction



#5
Nov2912, 09:08 PM

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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. 


#6
Nov2912, 10:43 PM

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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. 


#7
Nov3012, 12:02 AM

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



#8
Nov3012, 01:28 PM

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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. 


#9
Dec212, 04:36 PM

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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_{k}mg I would set ma = u_{k}mg and find u_{k} that way ???? 


#10
Dec212, 04:52 PM

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#11
Dec212, 06:24 PM

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#12
Dec212, 07:01 PM

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#13
Dec312, 01:38 PM

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which would be?
the only equation I know that involves distance and acceleration is d = v_{o}t + 1/2at^{2} which has two unknowns in the equation. 


#14
Dec312, 03:40 PM

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If not, you could have derived it from the above together with any other kinematic equation by eliminating t. 


#15
Dec312, 04:22 PM

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


#16
Dec312, 10:13 PM

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