# A bullet with a velocity of 575m/s Use work and energy considerations

1. Oct 20, 2009

### sarahjt1

1. The problem statement, all variables and given/known data

A 7.8g bullet moving at 575m/s penetrates a tree trunk to depth of 5.50cm. (a) Use work and energy considerations to find the average frictional force that stops the bullet. (b) Assuming that the frictional force is constant, determine hot much time elapses between the moment the bullet enters the tree and the moment it stops.

2. Relevant equations

I figure part (a) by:

KEi - Fk = KEf
KEi= kinestic energy initial, Fk=frictional force, and KEf= kinetic energy final

For part (b) I thought that the t=D/r would be sufficient but it's not?? I don't really understand what other equations to use in this scenario... HELP!

3. The attempt at a solution

For part (a)

1/2mV^2 - Fk*d = 1/2mVf^2
1/2(.0078)(575)^2 - .055Fk = 0
1289.44 - .055Fk = 0
-.005Fk = -1289.44
Fk = 2.34e4 N

For part (b)

t= .055/575
t= 9.5e-4 --> which is not correct, book shows 1.91e-4, huh?
1. The problem statement, all variables and given/known data

2. Oct 20, 2009

### Fightfish

What you are doing is assuming that the bullet travels at a constant velocity and suddenly stops after penetrating 5.50cm into the wood o.0, which definitely does not hold true especially when it is decelerating at a constant rate!
Think along the lines about the relation between impulse and force-time.

3. Oct 20, 2009

### sarahjt1

Ohhh... so this is a momentum question.

F delta t = mVi - mVf

so...

F delta t = (.0078)(575)- (.0078)(0)
2.34e4 (delta t)= 4.49
delta t = .000191 = 1.91e-4

Ah.. Thank you!!!!!! I would have never of seen that relationship... grrr.