Solve for Length of Friction-Ridden Ice Patch | Work-Energy Theorem Hint

[kingsean]

I've been working on a problem and I'm stumped :| I'm usually pretty good at deriving the equations for problems and solving them once I find out what I need to be solved. But this one is a bit too ambiguous for me, and I'm looking for a few hints :) Anything is appreciated!

On an essentially friction-less, horizontal ice rink, a skater moving at 3.0m/s encounters a rough patch that reduces her speed by 45% due to a friction force that is 25% of her weight. Use the work-energy theorem to find the length of this rough patch.


I've tried a few methods but, alas, no answer. The back of the book says 1.5m if that is of any assistance.

Thanks again!

 

[dav2008]

Just solve the problem using "m" for the mass and it should cancel out in the end.

You know the initial energy will just be the kinetic energy ($$K$$) and that will equal the final kinetic energy plus work done by friction ( $$K$$+$$W_f$$ )

 

[kingsean]

Just solve the problem using "m" for the mass and it should cancel out in the end.

You know the initial energy will just be the kinetic energy ($$K$$) and that will equal the final kinetic energy plus work done by friction ( $$K$$+$$W_f$$ )

I've taken this into consideration, but my answers still end up being too high or too low :(

 

[dav2008]

I worked it out and got 1.46 meters as the answer.

I said that the final velocity was 3*.45 (although the wording would suggest that it should be 3-(3+.45) but that gives me 1.28)

Can you show how you're doing it and what answer you get?