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Conservation of Energy

The amount of energy in a closed system never changes.

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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 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

  • When there is a collision between two objects, the collision is either elastic or inelastic. In an elastic collision both the momentum and the kinetic energy of the system is conserved, while in an inelastic collision, the two objects in the collision stick together and only the momentum is conserved. In the case of the ballistic pendulum, the collision is inelastic because the bullet gets embedded in the block.
  • To determine the velocity of the bullet that is fired into the block, you would start from the conservation of momentum:

\begin{align*}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}}\end{align*}pinitialmbulletvbullet+bblockvblockvbullet=pfinal=(mbullet+mblock)vfinal=(mbullet+mblock)vfinalmbullet

  • Another method that would determine the initial velocity of the bullet, is the conservation of energy.
  • Watch a ballistic pendulum in action: 


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, 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

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