1. The problem statement, all variables and given/known data The graph shows the net external force component F cos θ along the displacement as a function of the magnitude of the displacement s. The graph applies to a 65 kg ice skater. http://img9.imageshack.us/img9/3441/0671.gif [Broken] (a) How much work does the net force component do on the skater from 0 to 3.0 m? 93 Joules (Correct) (b) How much work does the net force component do on the skater from 3.0 m to 6.0 m? 0 Joules (Correct) (c) If the initial speed of the skater is 2.4 m/s when s = 0, what is the speed when s = 6.0 m? 2. Relevant equations W=F(Δx) KE=.5mv2 3. The attempt at a solution For part C. Here is my attempt. Firstly, I do not understand the reason that FCosΘ was used as a Force instead of simply F, due to the way the graph is drawn, I chose to simply represent it as F, which may have been my mistake, but I doubt that. I know the WorkTotal done on the skater was 93 Joules. So I thought that perhaps the change in Kinetic Energy would be equivalent to 93 Joules, allowing me to solve for Vf. So I tried that below. FCosΘ=31N W=FCosΘ(Δx) FCosΘ(Δx)=.5mvf2-.5mvi2 .5mvf2=FCosΘ(Δx)+5mvi2 vf2=(2(FCosΘ(Δx))/m) + vi2 which means to solve for vf I would use. vf=((2(FCosΘ(Δx))/m)0.5)+vi Yet that answer is wrong. I think my concept of this problem is wrong.. For Δx I used 3 instead of 6, since the force drops off to zero and the environment is frictionless, so it shouldn't make a difference.