The Bullet-Block Mystery - ComPADRE

LivePhoto IVV Physics Activity 1

Name: __________________________ Date: ___________________________

1. Introduction

The Bullet-Block Mystery

Suppose a vertically mounted 22 Gauge rifle fires a bullet upwards into a block of wood (shown in Fig. 1a). If the bullet enters the block in line with the its center-of-mass (shown in Fig. 2a), it penetrates into the block which then rises up to a height of about 0.5 meters without spinning noticeably.1 If the vertical shot is repeated with the bullet hitting a block "off center" (shown in Figs. 1b and 2b), would the block also travel straight up or off to one side? Would it be spinning? Would it rise to the same height?

It turns out that the "off-center" bullet (Fig. 1b), causes an "identical" block to rise straight up to essentially the same height, as it spins counter-clockwise while rising and falling. This is puzzling. How can the bullet impart more kinetic energy to the block that's shot "off-center" and yet it rises to the about the same height in both situations? This doesn't seem to make sense!

Maybe the off-center bullet doesn't penetrate as far into the block, so that more of its initial energy is available to start the block spinning. However, x-rays of the two blocks shown in Fig. 3 show no difference in the penetration depth of the bullet in each block!

Fig.1: A rifle aimed at a 2"x4" block edges: [a] on center and [b] off center.

This is a mystery! Can this be explained? What if the energy lost as the bullet penetrates into the block is much greater than the kinetic energy the bullet imparts to the block? Then a tiny change in penetration distance could result in significant changes in a block's linear and rotational kinetic energy.

In this assignment, you can use manufacturer's data on a bullet's mass and muzzle velocity to calculate the kinetic energy a typical bullet has before entering the block and how much of it's energy is lost plowing into the wood. If you find that the energy the bullet loses changing shape and breaking chemical bonds in the wood is very large compared to the linear and rotational kinetic energy acquired by the block, the height difference between a spinning block and a non-spinning block might not be measureable!

Fig. 2: Edges of 5" lengths of 2x4 hit (top) on-center and (bottom) off center.

To complete this assignment, you'll need to consider conservation of linear momentum as the bullet penetrates the block. You'll also need to calculate linear and the rotational kinetic energy of the block just as it starts rising during "on center" and "off center" collisions between the bullet and block.

1 A video of this phenomenon can be seen on YouTube: or by completing the Bullet Block Interactive Video Vignette available at .

IVV Assignment: Bullet-Block

I. Preliminary Questions

Note: You will receive full credit for any thoughtful answers you provide for the preliminary questions whether or not they match the analyses you actually perform in the two sections on Activities and Reflection that follow. As part of the learning process it is important for you to think about how you can perform an analysis before starting. Do not change your answers to the questions that follow based on later analyses you perform.

1. Suppose a bullet is shot upward toward the center of mass of a block as shown in Figure 1(a) and penetrates into it. According to the laws of physics, what quantities of this bullet-block system should be the same immediately before the bullet hits the block and immediately after the bullet has penetrated into the block and the block starts rising? Circle your answer and explain why you picked it in each case.

Linear Momentum of the Block's CoM

T F

Angular Momentum T F of the Block about it's CoM

Kinetic Energy of the Block's CoM

T F

2. Suppose a bullet is shot upward to the right of the center of mass of a block i.e. "off center" as shown in Figure 1(b) and penetrates into it. According to the laws of physics, what quantities of this bullet-block system should be conserved immediately before the bullet hits the block and immediately after the bullet has penetrated into the block so that it has just started to rise? Circle your answer and explain why you picked it in each case.

NOTE:

Linear Momentum T F

Angular Momentum T F

Kinetic Energy of the Block's CoM

T F

11 - 2

Physics with Video Analysis

The x-ray images in Figure 3 show what happens to a bullet when it penetrates a wooden block on center and off-center. Each piece of wood and the speed each bullet as it enters a block is probably slightly different. However observations show that blocks rise to more or less that same height in different trials whether they are hit on-center or off-center.

Fig. 3: X-ray images of the right half of two 5" lengths of 2 by 4 pine boards shows the penetration when a bullet enters a block: (a) on-center (left image) or (b) off- center (right image). The small hole half-way up each block is where support nails were mounted at the center of each block's face.

What is conserved in the collision?

(a) When the bullet travels upward and hits the block in line with its center of mass and becomes embedded, the bullet transfers both momentum and kinetic energy to the block and bullet. What do the laws of conservation of momentum and energy predict will happen

(b)

(c) QuickTime movie entitled ................
................

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