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Ballistic Pendulum - An Inelastic Collision

Ballistic Pendulum - An Inelastic Collision

Credit: makeemlighter
Source: http://commons.wikimedia.org/wiki/File:Ballistic_pendulum.svg
License: CC BY-NC 3.0

Something as simple as a wooden block can be used to measure the muzzle velocity of a bullet. Known as ballistic pendulums, these devices have been used for decades in labs and classrooms to help investigate the conservation of energy and momentum.

Amazing But True

Credit: David Lenker
Source: http://www.flickr.com/photos/7325282@N02/3817643083
License: CC BY-NC 3.0

Pool balls hitting each other is an example of elastic collision [Figure2]

  • A collision between two objects must either be elastic or inelastic. In an elastic collision, both the momentum and the kinetic energy of the system are conserved. On the other hand, in an inelastic collision, momentum is conserved and the two objects stick together after the collision. In the case of the ballistic pendulum, the collision is inelastic because the bullet is embedded in the block.
  • To determine the velocity of the bullet that is fired into the block, start with the conservation of momentum:

p_{initial} &= p_{final} \\m_{bullet}v_{bullet} + b_{block}v_{block} &= \left(m_{bullet} + m_{block}\right)v_{final} \\v_{bullet} &=\left(m_{bullet} + m_{block}\right) \frac{v_{final}}{m_{bullet}}

  • Watch a ballistic pendulum in action: 

http://www.youtube.com/watch?v=cVjxn4KjOb4

What Do You Think?

Using the information provided above, answer the following questions.

  1. Why is the collision inelastic and not elastic?
  2. When a bullet is fired into a ballistic pendulum, where is the kinetic energy lost?
  3. If the bullet that is fired at the ballistic pendulum exits the block, is the collision elastic or inelastic? Would you still be able to determine the initial velocity of the bullet?

Image Attributions

  1. [1]^ Credit: makeemlighter; Source: http://commons.wikimedia.org/wiki/File:Ballistic_pendulum.svg; License: CC BY-NC 3.0
  2. [2]^ Credit: David Lenker; Source: http://www.flickr.com/photos/7325282@N02/3817643083; License: CC BY-NC 3.0

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