[SOLVED] Work-Energy Principle 1. The problem... On an essentially frictionless horizontal ice-skating rink, a skater moving at 3.00 m/s encounters a rough patch that reduces her speed by 45.0 % to a friction force that is 25.0 % of her weight. Use the work-energy principle to find the length of the rough patch. 2. The relevant equation... KEi + PEi + W(by friction) = KEf + PEf where i = initial and f = final 3. My attempt... Since Work by friction = -Fd, then you can substitute F for (.25 x mg), correct? that is because the Force of friction (F) is 25% of her weight (mg). Ultimately, this is going to allow m to cancel out. With that, I have the equation: .5mv^2 + mgh + (-.25mg)d = .5mv^2 + mgh Factoring out the m so it can cancel out I now have: m (.5v^2 + gh + (-.25g)d) = m (.5v^2 + gh) Since this is all happening on a level surface, then h = 0. Now I am left with: .5v^2 + (-.25g)d = .5vf^2 Now, plug in our known values... .5(3^2) + (-.25 x 9.8)d = .5(.45 x 3)^2 Note: v final = 3 x 45% as stated in the problem Solving for d, I get 1.46 meters. But this is wrong... I've also tried this same exact setup using a final speed of 0, getting a distance of 1.84 meters. That, too, is wrong.