# Work Problem/Graph Given/Find final velocity.

1. Apr 6, 2009

### myxomatosii

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.

Last edited by a moderator: May 4, 2017
2. Apr 6, 2009

### rl.bhat

Your last step is wrong.
Check it.

3. Apr 6, 2009

### LowlyPion

Seems a little complicated.

W = ΔKE

What is the initial KE?

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

Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook