Ballistic Pendulum

A gun shoots a bullet of mass into a wooden sphere of mass . The sphere hangs from a fixed point; the bullet makes the sphere swing up to a height , here taken as 0.1 meters. The bullet has an initial kinetic energy ; when it hits the sphere their kinetic energies are combined. As they swing up together, the kinetic energy is converted into potential energy. In order to make the sphere go up to 0.1 m, the velocity of the bullet must vary. Its velocity can be deduced using the conservation of energy. Vary the mass of the sphere and see how the velocity of the bullet must change in order to maintain the same velocity of the pendulum.



  • [Snapshot]
  • [Snapshot]
  • [Snapshot]


The velocity of the sphere and the bullet is and the initial velocity of the bullet is , where is the acceleration due to gravity, is the maximum height of the sphere and and are the masses of the bullet and the wood sphere, respectively. You can derive these expressions as an exercise.
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.

Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Step-by-Step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Powered by Wolfram Mathematica © 2018 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+