Ballistic pendulum
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A ballistic pendulum is a device for measuring a bullet's momentum, from which it is possible to calculate the velocity and kinetic energy. Ballistic pendulums have been largely rendered obsolete by modern chronographs, which allow direct measurement of the projectile velocity.
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[edit] Construction
The device is similar to a clock's pendulum: a mass at the end of a pivot arm, with the arm and mass free to rotate. The pendulum usually strokes a marker that records the maximum height of the pendulum during the test. It is the height of the pendulum swing that indicates the quantity of kinetic energy absorbed during the collision.
[edit] Theory
In a perfectly inelastic collision, a bullet is fired into the stationary pendulum, which captures the bullet and absorbs its energy. The stationary pendulum now moves with a new velocity just after the collision. While not all of the energy from the bullet is transformed into kinetic energy for the pendulum (some is used as heat and deformation energy) the momentum of the system is conserved. By measuring the height if the pendulum's swing, the potential energy of the pendulum when it stops can be measured. This allows the pendulum's initial velocity to be calculated. Using the conservation of momentum, this allows the velocity of the bullet to be computed.
[edit] Mathematical derivation
Given g the force of gravity, and h the height of the pendulum, it is possible to calculate u the pendulum velocity:
We can then use momentum (p) conservation to get the speed of the bullet, v, as:
[edit] External links
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