Work Problem/Graph Given/Find final velocity.

[myxomatosii]

Homework Statement

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 (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?

Homework Equations

W=F(Δx)
KE=.5mv²

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 Work_Total 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 V_f.

So I tried that below.

FCosΘ=31N

W=FCosΘ(Δx)

FCosΘ(Δx)=.5mv_f²-.5mv_i²

.5mv_f²=FCosΘ(Δx)+5mv_i²

v_f²=(2(FCosΘ(Δx))/m) + v_i²

which means to solve for v_f I would use.

v_f=((2(FCosΘ(Δx))/m)^0.5)+v_i

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.

 

[rl.bhat]

Your last step is wrong.
Check it.

 

[LowlyPion]

Seems a little complicated.

W = ΔKE

What is the initial KE?

Just add the Joules from a) and then solve for velocity?