Chapter 6: Q. 46 (page 156)

A rifle with a barrel length of $60$ cm fires a $10$ g bullet with a horizontal speed of $400$ m/s. The bullet strikes a block of wood and penetrates to a depth of $12$ cm.
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). $F = 6700 N = 6.7 k N$ pointing out of the wood

b). $t = 0.0006 s = 600 μ s$ take the bullet to come to rest

Step by step solution

Step 1. Given Information

We have, rifle with barrel length $l = 60$ cm

Weight $m = 10$ g

The horizontal speed of $v = 400$ m/s

Depth $d = 12$ cm

Step 1. Part a). Find the resistive force

Rearranging the following well-known equation of kinematics we get

${v_{f}}^{2} = {v_{0}}^{2} + 2 a d \Rightarrow {v_{0}}^{2} = - 2 a d$ since $v_{f} = 0$

From Newton's second law we have $a = \frac{F}{m}$ , which we can substitute in the previous equation find

${v_{0}}^{2} = - \frac{2 F d}{m} \Rightarrow F = \frac{m {v_{0}}^{2}}{2 d}$

Substitute our values, we get

localid="1649521147287" $F = - (\frac{0.01 \times 400^{2}}{2 \times 0.12}) \approx - 6.7 k N$

Step 1. Part b). Find the time

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

$a = \frac{v_{f} - v_{0}}{t} \Rightarrow t = - \frac{v_{0}}{a} \Rightarrow t = - \frac{m v_{0}}{F} \Rightarrow t = (- (\frac{0.01 \times 400}{- 6700})) = 0.0006 s \Rightarrow t = (600) μ s$ Since $v_{f} = 0$

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Short Answer

Step by step solution

Step 1. Given Information

Step 1. Part a). Find the resistive force

Step 1. Part b). Find the time

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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

Step by step solution

Step 1. Given Information

Step 1. Part a). Find the resistive force

Step 1. Part b). Find the time

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Oscillations

Medical Physics

Measurements

Thermodynamics

Turning Points in Physics

Electrostatics

Study anywhere. Anytime. Across all devices.