Calculating Coefficient of Kinetic Friction for a Slide Loving Pig

[HobieDude16]

slide loving pig force...

ok, here's a problem that is supposed to be easy, and i thought i knew how to do it, but obviously not, cause i can't get the right answer...


In figure 6-21, a slide loving pig slides down a certain 24° slide in twice the time it would take to slide down a frictionless 24° slide. What is the coefficient of kinetic friction between the pig and the slide?

what i did:
i set 2 times the force without friction (mgsin24) equal to the force without friction minus friction (mgsin24-MUkmgcos24) and tried to solve for MUk... but that didnt work, and i have no idea what happened. here's what the equation i used looked like:
2(mgsin24)=mgsin24-MUkmgcos24... so that is the same as
2sin24=sin24-MUkcos24
then sin24=-MUkcos24
so tan24=-MUk
buuuut that didnt work, so what do i do wrong?

 

[vsage]

Two times the time doesn't translate to two times the force IIRC

 

[HobieDude16]

whats a way to relate the force to time? i can't find a formula to do that?

 

[HobieDude16]

this problem is supposed to be a 1 of 3 dot problem (How hard it is, 3 is hardest) so why is it so hard for me?

 

[vsage]

This doesn't really follow up with what I just said though but the resultant force of the slide with friction is less than the no-friction slide (and wouldn't go UP by any factor > 1) To figure the factor by which the resultant force is different from the no-friction force consider the units of force and how time plays into it.

 

[HobieDude16]

uhhhh in lamen's terms? i can't figure out what you're saying

 

[vsage]

Here's what your equation above said to me when you said 2 * mgsin(24) = mgsin(24)-mg(cos(24))*u or whatever:

Twice the force of mgsin(24) is created by applying friction to the same force which of course doesn't make sense.

F = kg*m/s^2 right? What effect does making s 2s have?

 

[HobieDude16]

so your saying make it 1/2 mgsin(24) yadda yadda yadda?

 

[vsage]

not quite.. Take a close look at the relationship of force to time given its units above.

 

[HobieDude16]

ohhhhh 1/4? that seems to make sense, so if i made it 1/4 (instead of 2), then did the rest the same way i did it, it shoudl work?

 

[vsage]

I'm fairly sure it would. You won't know for certain until you try it out I guess. I'm not exactly a physics expert just happened to see something possibly wrong.

 

[HobieDude16]

heck yeah man, that worked... thanks a lot! now how bout my other thread, any ideas there?