Pig on a slide Friction Problem

by Kharmon7814
Tags: friction, slide
Kharmon7814 is offline
Nov16-03, 09:29 PM
P: 7
A slide loving pig slides down a certin 35 degree slide in twice the time it would take to slide down a frictionless 35 degree slide. What is the coefficient of kinetic friction between the pig and the slide? Here is what I have so far....
[sum]Fx=ma=mgsin [the] -[mu]mgcos[the] I canceled out the mass on both sides and get
[sum]Fx=a=gsin [the] -[mu]gcos[the]

For the y forces I have

As far as the difference in the time with or with out friction I have x=mgsin[the]=(1/2)a[tex]t^2[/tex] for the slide with no friction and I have x=mgsin[the]=2a[tex]t^2[/tex]for the slide with friction
This is all the info I have been able to come up with...I can't figure out how to put it all together. Thanks for helping. I've been working on this one for awhile. [g)]
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jamesrc is offline
Nov17-03, 12:07 AM
Sci Advisor
PF Gold
P: 478
Be careful about mixing up forces, accelerations and positions. For example, your second equation has forces equalling accelerations (not good). I'm assuming the 'x' direction is along the ramp and that the pig starts at the top of the ramp from rest (I'm told pigs like to rest). So lets call the distance down the ramp (same for friction/no friction) Δx. In either case,

[latex] \Delta x = \frac{at^2}{2} [/latex]

which is where (it seemed like) you were heading.

The acceleration is different in each case and the time is different in each case. Let's call the time down the frictionless slide T, and the time down the slide with friction 2T. From your force balance, you found the acceleration with friction already, let's call it af:

[latex] a_f = g\sin \theta - \mu g\cos \theta [/latex]

without friction (anf) is simply:

[latex] a_{nf} = g\sin\theta [/latex]

To put it all together, equate Δxf with Δxnf:

[latex] \frac{a_f(2T)^2}{2} = \frac{a_{nf}T^2}{2} [/latex]

substitute in your expressions for af and anf and solve for μ

[latex] 4\left(g\sin \theta - \mu g\cos \theta\right) = g\sin\theta [/latex]

[latex] \vdots [/latex]

[latex] \mu = 3\tan\theta [/latex]

(I suggest you verify my algebra for yourself in case I made a careless error or two.)

(Last line corrected for algebra)

[latex] \mu = \frac{3\tan\theta}{4} [/latex]
Kharmon7814 is offline
Nov17-03, 12:29 AM
P: 7
Funny how it seems so obvious when someone explains it. Thanks for your help.

Kharmon7814 is offline
Nov17-03, 12:46 PM
P: 7

Pig on a slide Friction Problem

It turns out to be (3/4)Tan[the] I got the final answer to be [mu]=.53 Ahhhh, now I can sleep at night[zz)]
jamesrc is offline
Nov17-03, 01:47 PM
Sci Advisor
PF Gold
P: 478
Good job. Glad I put in that disclaimor; maybe I should just add it to my signature. I guess I was so wrapped up in using the new [latex] \LaTeX [/latex] functionality that I forgot to distribute the 4.

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