How Do You Calculate the Force and Time to Stop a Bullet Using Energy and Work?

[lilwigz]

Homework Statement

A 5.00g bullet moving at 600.0 m/s penetrates a tree trunk to a depth of 4.00 cm.

A) Use work and energy considerations to find the magnitude of the force that stops the bullet.

B) Assuming that the frictional force is constant, determine how much time elapses between the moment the bullet enters the tree and the moment the bullet stops moving.

Homework Equations

Ek= 1/2mv^2
W=fdcos(0)

The Attempt at a Solution

I tried to do Ek=1/2mv^2
Ek= 1/2 x ( .005kg) x (600m/s)^2 but i think that's wrong

 

[jegues]

Ek= 1/2 x ( .005kg) x (600m/s)^2 but i think that's wrong

This is how much energy the bullet intially has.

All this energy is transferred as the bullet travels through the tree a distance of 4cm.

So how can we solve for the magnitude of the force which stops the bullet?

HINT: Use kinetic energy-work theorem.

 

[lilwigz]

with the formula Fd(cos0)= (1/2 mvf^2)-(1/2mvi^2) i got -900J/.04m and i got the answer 22500N horizontally

 

[Matterwave]

looks good to me

 

[jegues]

i got the answer 22500N horizontally

They are asking for the magnitude of the force so you don't have to indicate a direction ("horizontally" in your case).

22500N is good enough! Now try part B!

 

[lilwigz]

since the frictional force is constant, the acceleration would be constant, so

v²=u²+2as
0=600²+2a(0.04)
a=-360000/0.08 = -4.5x10^6

a=(v-u)/t
t=(v-u)/a
=0-600/(-4.5x10^6)
=0.133 ms

 

[jegues]

v²=u²+2as
0=600²+2a(0.04)
a=-360000/0.08 = -4.5x10^6

a=(v-u)/t
t=(v-u)/a
=0-600/(-4.5x10^6)
=0.133 ms

Looks good to me!

 

[Matterwave]

You can find the acceleration a by Newton's law: F=ma

Iono how you're trying to find it there...answer looks right though.

 

[lilwigz]

thank you!

 

[jegues]

You can find the acceleration a by Newton's law: F=ma

How would you do that? You have no way of computing the frictional force.

 

[Matterwave]

You just did in part A
...

 

[jegues]

You just did in part A
...

Doh! Brainfart :)