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Chapter 6: Q. 46 (page 156)

A rifle with a barrel length of 60cm fires a 10g bullet with a horizontal speed of 400m/s. The bullet strikes a block of wood and penetrates to a depth of 12cm.

a. What resistive force (assumed to be constant) does the wood exert on the bullet?

b. How long does it take the bullet to come to rest?

Short Answer

Expert verified

a). F=6700N=6.7kNpointing out of the wood

b).t=0.0006s=600μstake the bullet to come to rest

Step by step solution

01

Step 1. Given Information

We have, rifle with barrel length l=60cm

Weight m=10g

The horizontal speed of v=400m/s

Depth d=12cm

02

Step 1. Part a).  Find the resistive force

Rearranging the following well-known equation of kinematics we get

vf2=v02+2ad⇒v02=-2adsincevf=0

From Newton's second law we have a=Fm, which we can substitute in the previous equation find

v02=-2Fdm⇒F=mv022d

Substitute our values, we get

localid="1649521147287" F=-0.01×40022×0.12≈-6.7kN

03

Step 1. Part b).  Find the time

Knowing the definition of acceleration, we can find time taken for the bullet to come to rest.

a=vf-v0t⇒t=-v0a⇒t=-mv0F⇒t=-0.01×400-6700=0.0006s⇒t=600μs Sincevf=0

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