Maximum Distance of Package on Incline with Friction

[Shhtory]

A package is projected up a an incline of 21 degrees with respect to the horizontal, with an initial velocity of 9 m/s. The coefficient of friction between the package and the slope is 0.2. Determine the maximum distance the package will slide up the incline.

Sorry guys I'm just really stuck on this question so if anyone could help me out it would be great! Thanks guys in advance! :-) xx

 

[tiny-tim]

Welcome to PF!

Hi Shhtory! Welcome to PF!

Use the work energy theorem … change in (mechanical) energy = work done

 

[Shhtory]

Thanks Tiny-tim!

But since I don't have mass, height or force, how am I supposed to calculate work or mechanical energy? Is there too many unknowns or am I just not reading the question properly?

I know this make me look stupid but I just can't get my head around it! Thanks very much for your help though tiny-tim :p xxx

 

[gneill]

You should find that (eventually) the mass variable will cancel out. Try writing an energy conservation equation for the package in terms of the distance along the slope. Don't forget the work done by the frictional force.

 

[tiny-tim]

yup! … just call the mass "m" …

show us what you get ​

 

[Shhtory]

Thanks gneill! I think I got it now,

I used the formula (-cos21)(0.2)s=(Sin21)s-((9^2)/(2g)) = 7.573m

Hope its right, thanks 4 all ur help guy! xx

 

[gneill]

The result is okay. Your equation notation leaves something to be desired, however! I think that the last "= 7.573m" should be something more like "==> s = 7.573m". I only mention this because it would be a shame to lose marks on an exam or hand-in homework due to sloppy notation.