What is the maximum force exerted on a bullet lodged in a block?

[kminkel]

Homework Statement

A 10.0-g bullet traveling at 200 m/s strikes a fixed wooden block. The bullet comes to rest 22 cm inside the block. The magnitude of the force exerted on the bullet by the block over its 22-cm travel is shown in graph. Find the value of Fmax.

http://www.scribd.com/doc/135229669/Physics

Homework Equations

W=Fd
W=KE=.5mv^2

The Attempt at a Solution

I tried to treat is as a work problem and set Fd=.5mv^2.
I got an answer, but it wasn't one available to me.
I don't know what I am missing

 

[tiny-tim]

welcome to pf!

hi kminkel! welcome to pf!

W=Fd

use the more general work done = integral of force "dot" distance

(W = ∫ F.ds)

show us what you get ​

 

[Ampere]

Your idea is a good one, except the equation is only Fd for constant F. The graph shows F varies with distance, so what you're really doing is integral of F*dx.

Find the area under the curve (triangular + rectangular regions) and try setting that equal to the KE.

Edit: Looks like I was beaten to it!

 

[kminkel]

With using the W=.5mv^2, I got the W=200 J.
But with the integral what would I use as the bounds? Would it be from 0 to .11 m or 0 to .22 m? Then how would you get rid of the integral symbol to solve for F. I'm sort of really confused.

 

[Ampere]

You are integrating over the whole distance that the force is being applied (0 to 0.22m). If integrals are unfamiliar to you, just think of it like area.

Set the area under the curve from 0 to 0.22m equal to KE.

 

[kminkel]

If I set the areas equal to .5mv^2...
.11x+.5(.22)x=.5(.01)(200)^2
.11x+.11x= 200
.22x=200
x=909.09
That isn't an option /:

 

[tiny-tim]

But with the integral what would I use as the bounds?

uhh? don't make it so complicated!

the integral of a curve is the area under it

(and yes, sometimes physics questions really are that simple! )

 

[kminkel]

If I set the areas equal to .5mv^2...
.11x+.5(.22)x=.5(.01)(200)^2
.11x+.11x= 200
.22x=200
x=909.09
That isn't an option /:

I see my error. I have the wrong base for the triangle. I fixed it and got 1212.12 which is an option! Thank you Both so much!