Calculating the Sliding Distance of a Block After Being Pierced by a Bullet

This article provides a detailed step-by-step guide on how to calculate the sliding distance of a block that has been pierced by a bullet. We will need the initial velocity of the bullet, the coefficient of kinetic friction, and the mass of the bullet and block to perform the necessary calculations.

Introduction

The sliding distance of a block after being pierced by a bullet is a fundamental problem in physics. Understanding this phenomenon can provide insights into the mechanics of bullet penetration and the effects of friction. This guide will walk you through the process using a specific example.

Given Information

Consider the following scenario:

A bullet with a mass of A-kg is fired with an initial velocity of 154 m/s toward a 5.44-kg stationary solid block resting on a surface with a coefficient of friction of 0.215. The bullet emerges from the block with a reduced velocity of 20.2 m/s after passing through the block.

Step-by-Step Calculation

Calculate the Kinetic Energy Lost by the Bullet

The kinetic energy (KE) is given by the equation:

[ KE frac{1}{2}mv^2 ]

First, calculate the initial kinetic energy (KEinitial) of the bullet:

[ KE_{initial} frac{1}{2}A(154)^2 ]

Next, calculate the final kinetic energy (KEfinal) of the bullet after it emerges from the block:

[ KE_{final} frac{1}{2}A(20.2)^2 ]

The kinetic energy lost by the bullet (ΔKE) is the difference between the initial and final kinetic energies:

[ Delta KE KE_{initial} - KE_{final} ]

Plugging in the values:

[ Delta KE frac{1}{2}A(154^2) - frac{1}{2}A(20.2^2) ]

Calculate the Frictional Force Acting on the Block

The frictional force (Ff) is given by the equation:

[ F_f mu mg ]

Where:

μ is the coefficient of kinetic friction (0.215). m is the mass of the block (5.44 kg). g is the acceleration due to gravity (9.81 m/s2).

Plugging in the values:

[ F_f 0.215 times 5.44 times 9.81 ]

Calculate the Displacement of the Block

The displacement (d) is given by the equation:

[ d frac{Delta KE}{F_f} ]

Plugging in the values for ΔKE and Ff calculated above, you can find the displacement of the block.

Conclusion

By following these steps, you can accurately calculate the sliding distance of the block after being pierced by the bullet. Understanding these calculations is crucial for various applications, including the design of protective materials and the study of bullet penetration mechanics.

For more in-depth analysis and further resources, you can refer to advanced physics textbooks and engineering publications.

Keywords

sliding distance, bullet penetration, friction coefficient