Arrow embeds in wooden block, how far does it slide

[stonecoldgen]

Homework Statement

a 120g arrow moving at 75m/s strikes and sticks in a 3.63kg wooden block, initially at rest. If the coefficient of friction between the block and the table it sists on is 0.409, how far does the block slide before stopping?

Homework Equations

m1v1+v1+m2v2=m1v1'+m2v2'

fr=mu(coefficient of friction)mg=sigmaF+fr

maybe:
v'=v+2ad

The Attempt at a Solution

I substituted values for the conservation of momentum equation

m1v1+v1+m2v2=m1v1'+m2v2'
(.12)(75)+(3.63)(0)=(.12)v1'+(3.63)v2'
9=3.75v' (v1' and v2' are the same as they are now ''the same piece'')
v'=9/3.75
=2.4m/s

so i figured out how fast the arrow stuck on the block would go

now, i would calculate the friction force i guess (.409)(3.63)(9.8)=14.5N

but i have no time, therefore no acceleration and don't know what to do

 

[Delphi51]

Welcome to PF, Stonecoldgen!
Not that it matters much, but add the mass of the arrow in that friction force calc.

I wonder if you could get the last step via an energy calculation?
Kinetic energy converted to work against the friction force.