# Speed of a Bullet Lab

 Materials: School Network and Macintosh Computer w/Interactive Physics Time Allotment: 3 Class Days

### Introduction:

The purpose of this lab is to analyze the momentum conservation of the firing of a bullet into a block of wood by means of a computer simulation. From knowing the mass of the bullet and the block and the velocity of the block after the collision, the veclocity of the bullet can be calculated. This method was actually used to measure muzzle velocities of firearms until more advanced methods were developed.

### Getting Ready:

This lab must be done on a Macintosh computer connected to the school network or upon a computer in the Science Computer Lab. To prepare for the lab, do the following steps.

1. Open the Physics Explorer application (Two Bodies model) by double-clicking on its icon; it is found in the directory /Local Drive/Physics/Physics Explorer.
2. Choose Open... from the File menu and navigate to the Physics 163/Unit 4 folder of the same directory.
3. Open the file titled Speed of a Bullet. A Physics Explorer simulation is opened. Check that the model window appears as shown below.

### Firing the Bullet:

Body2 (the patterned body on the right) at the end of the "tunnel" represents the block of wood resting on a frictionless surface. The bullet is fired from a position on the left.

a. Press the GO tool to run the simulation

• Describe the motion of the objects; comment on both before- and after-collision velocities. Be as precise as you can.

• In what ways does this simulation reflect the actual physical phenomena that you would expect to see when a bullet is fired into a block of wood?

• How is the simulation different?

b. The position-time graph below gives you a rough indication of the position of the block of wood in the tunnel, where 0 indicates its position prior to the collision. (On the x-axis, time 0 is the time when the bullet is fired and not the time of impact.)

Predict what you think the graph will record when you run the simulation (at time 0 the bullet is fired). Sketch a graph to illustrate your prediction.

Open the Control Panel window (using the Window menu). The Control Panel window provides the information you need to calculate the velocity of the bullet, including the masses of the bullet and the block of wood (which you can vary), the distance traveled by the block of wood, and a stop watch. The timer resets to zero when the bullet fires and is set to start timing when the bullet hits the block of wood.

c. Now run the simulation by pressing the "Fire!" button.

• Was your prediction about the graph accurate? ________ Explain any differences between your predicted sketch and the actual graph.

• Use the position-time graph to determine the approximate velocity of the block. Show your work in the space below.

### Applying the Conservation of Momentum

The simulation is designed to "fire" the bullet at a different speed each time you press "Fire!" (Imagine that different rifles are being used with different muzzle velocities.) Your task is to work out the velocity of the bullet (vbullet).

a. Use the variables mass of bullet mbullet, velocity of the bullet (vbullet), mass of block (mblock) and velocity of block (vblock) to answer the following questions.

• What expression gives the total momentum before the collision?

• What expression gives the total momentum after collision? (Note that the mass after collision is thebullet and block together and that each object moves with the same velocity after the collision.)

• How are the answers of the two points above related? Write this as an equation.

• Which quantities in your last answer do you know before running the simulation?

b. Run the simulation and calculate the velocity of the block (vblock) by using the distance traveled and timer boxes in the Control Panel window.

• vblock=

Finally, use the equation you wrote in part A. to find the speed of the bullet. Substitute values into the equation and solve for vbullet.

• vbullet=

Click on the "Bullet Speed" button to check your answer. Are the two numbers the same? (Note that the time and distance data you use have been rounded off to one decimal place, which may result in differences of 1-2%.)

c. Repeat the simulations and calculations for four trials, using different masses for the bullet. Use your own values in your calculations.

### Extension:

Apply your understanding of this lab to solve the following two problems.

1. A 0.050-kg bullet moving with a velocity of 800 m/s embeds in a 2.5-kg block of wood. Determine the post-collision velocity of the wood and embedded bullet. PSYW

2. A 0.35-kg bullet embeds into a 12.0-kg block of wood and slides across a block of ice with a speed of 16.1 m/s. If the block was initially at rest, determine the speed of the bullet before the collision with the block of wood. PSYW

### Conclusion:

Write a pargraph to summarize what you have learned about momentum conservation as the result of this lab. Do a bang-up job!

This page created by Tom Henderson and last updated on 11/26/97.

Special thanks to lab assitant Dan Reid for assistance with the typing.