Maths
Physics
The speed of an air gun bullet
Author
Victor Strandell; Bromangymnasiet Hudiksvall
Target Group
13-15 years old students
Brief Description
To use and make the laws of physics visible by calculating the velocity of a bullet.

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## 1 - Teacher's guide

### The speed of an air gun bullet

How to calculate the speed of the bullet from an air gun using data from a classroom experiment.

#### Equipment

A wooden block is hanging from approximately 2 m height (as long as possible) in four thin strings making a pendulum. We use a frame of aluminium where the strings are fixed in the upper end. We put the frame between a table and the ceiling.

An airgun with “feather bullets” minimizes the risk for ricochets.

The length of the strings, the masses of the bullet and the block are needed for further calculations.

#### Method

This method needs only a few and simple measurements and use of momentum/energy conservation. It takes at least 1h. It takes longer if all students are to write an individual lab report based on their own calculations.

A student fires the gun roughly 1 dm from the block. Be careful.

The block with bullet moves round 5-10 cm in the bullet’s direction. If you put an L-shaped paper at the front end of the block, the paper will stay in the uttermost position after the shot.

#### Calculations

Using the distance s - which you measured with the movement of the L-shaped paper - and the string length, you can calculate the elevation of the block using Pythagora’s theorem. The potential energy is equal to the kinetic energy and gives you the speed of the block.

In the figure the height difference of the block is exaggerated.

The momentum of the bullet is equal to the momentum of the block; the speed of the bullet is settled.

#### Final comment

This demonstration is well-designed to help make the laws of physics visible.

What can we say about the result? We can always compare the speed we found with data from the Internet, but a discussion dealing with accuracy is necessary. Many things in this experiment can go wrong and they really do!

Remember to look at the example student report where the calculations are more precisely presented. See the student’s report below. The discussion part from the calculation by a student as shown below is not complete.

## 2 - Calculation by a student

### Calculation of a bullet's velocity

#### Method

Look at the figure.

y = 1.960 m

m1 = 0.492 kg

m2 = 0.0009 kg

s = 0.065 m

By shooting the bullet (m2) into the block of wood (m1) strapped to the pendulum, we could measure ‘s’.
This can later be used to measure the difference in height for m1.

#### Calculation

We begin by calculating ‘x’ by using the reverse Pythagorean theorem.

x = √1.960² - 0.065² = 1.95892

Now, that we have ‘x’ we can calculate the difference in height for m1 by subtracting y to x.

1.960 - 1.95892 = 0.00108 m

With the difference in height, we can calculate the velocity m1 had at the moment of impact. We do this by setting the formula for calculating potential energy and kinetic energy equal to each other.

mgh = (mv²)/2

gh = v²/2

9.82 * 0.00108 = v²/2

2 * 9.82 * 0.00108 = v²

√(2 * 9.82 * 0.00108) = v = 0.145 m/s

We can now finally calculate the velocity of the bullet by setting the momentum before impact which, as it turns out, equals the momentum after impact.

0.0009 * v1 = 0.492 * 0.145

v1 = (0.492 * 0.145)/0.0009 = 79.2 m/s