# How Can CSI Measure the Muzzle Velocity? The Ballistic Pendulum.

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### The Idea

You can tell how fast an object, such as a bullet, is moving by how it affects the momentum of another object.

### What You Need

• projectile and launcher:
• golf ball and a ramp
• precision projectile launcher
• hand-thrown hardball or golf ball
• balance to measure mass
• box
• tape
• string
• ring stand or improvised support
• protractor
• meterstick

### Method

1. Build (or buy) a receiver box that meets the following conditions:
• The moving projectile should be caught and retained in the box. Lining the interior with double-sided duct tape or foam rubber can serve to capture the projectile.
• The box is suspended from the ring stand.
2. Suspend the box from the ring stand using the string.
3. Determine the mass of the projectile.
4. Determine the mass of the catcher box and include any of its contents.
5. Direct the projectile toward the catcher box and allow the box with the projectile caught inside to swing upward.
6. Measure the maximum height above the initial starting position that the catcher box and the projectile reach. (Alternatively, the angle and radius of the pendulum formed by the supported catcher box can be recorded.)

The basic design of the apparatus is shown in Figure 56-1.

The velocity of the projectile can be determined from the following equation:

where m is the mass of the projectile, M is the mass of the "catcher box," g is the gravitational constant = 9.8 m/s2, and h is the height that the catcher box is lifted by the momentum of the projectile.

### Expected Results

The more momentum the projectile has, the greater the angle the pendulum swings through. For a given mass, a greater velocity causes a greater projectile.

### Why It Works

The momentum of the projectile ("bullet") is transferred to the box. The greater the momentum of the projectile, the higher the box is driven.

### Other Things to Try

A semiqualitative version of this consists of placing a cardboard box filled with tissue paper on the floor and comparing the distance it moves with balls rolled or thrown into it at different speeds. This can be refined by measuring the coefficient of kinetic friction between the box and the floor and the distance the box slides along the floor. Use of the equations of motion can be solved to determine the initial velocity of the box.

Various ballistic pendulum designs are also available from science supply companies.

### The Point

The velocity of a moving object can be determined by measuring its effect after colliding with another object of known mass. The ballistic pendulum is based on conservation of momentum applied to a pendulum. The larger the velocity of the incoming object, the higher the pendulum swings.