Impulse: Finding the average force

[impstudies]

Homework Statement

The 2kg head of an axe is moving at 60m/sec when it strikes a log. If the blade of an axe penetrates a 20mm into the log, find the average force it exerts.

m= 2kg
V= 60m/sec
d= 20mm or 0.02m

Homework Equations

F= pFINAL - pINITIAL / time
t= d/v

The Attempt at a Solution

m1v1 = axe
m2v2 = log

t = 0.02/60
= 3.33sec
F = [m1v1 + m2v2] - [m1v1 + m2v2] / time
= [(2kg)(60m/sec)+(m2)(0)] - [(2kg)(m2)(0)] / time
= (120 kg.m/sec + m2) / time ?

^ considering the log has 0 velocity? but has no mass given?

I solved for the time then used the impulse formula pFINAL-pINITIAL/time but since there is no mass of the log given I'm baffled because I feel like I'm using the wrong equations. I was lost if I should find the momentum or impulse since the axe makes contact with the log. I'm really bad at physics, your help is so appreciated :(

 

[Doc Al]

t = 0.02/60
= 3.33sec

Don't assume the speed is constant. The axe comes to rest. (What's the average speed of the axe?)

F = [m1v1 + m2v2] - [m1v1 + m2v2] / time
= [(2kg)(60m/sec)+(m2)(0)] - [(2kg)(m2)(0)] / time
= (120 kg.m/sec + m2) / time ?

^ considering the log has 0 velocity? but has no mass given?

Forget about the log. Just analyze the change in momentum of the axe.

 

[impstudies]

i assume the speed here is the velocity?
the axe comes to rest so its Vf = 0, with Vi = 60 m/sec

= vf-vi
= 0-60
= -60m/sec

is that right?

 

[Doc Al]

i assume the speed here is the velocity?
the axe comes to rest so its Vf = 0, with Vi = 60 m/sec

= vf-vi
= 0-60
= -60m/sec

is that right?

You found the change in speed. If you want to calculate the time for the axe to come to rest, you need the average speed.