4-27-15: Bullistic Pendulum

Purpose:
To find the velocity of the metal ball out of the spring-loaded gun using the conservation of momentum and conservation of energy.

In this lab, we studied an inelastic collision using a ballistic pendulum. The colliding bodies are a small metal ball, fired from a spring-loaded gun, and a metal catcher. The catcher is also the bob of a pendulum that is initially at rest. When the gun fires the ball collides with the pendulum, it is trapped in its catcher which then starts to swing. A light metal rod is pushed up with the pendulum and records the angle that the bob of the pendulum travels.

Set up:

Ballistic Pendulum

The ball is placed inside the spring-loaded gun:

Metal Ball Placed Inside Gun

The gun is then fired so that the pendulum pushed up the metal rod, recording the angle the pendulum traveled:

Theta: 17.2 degrees

We knew we were going to need to use the angle to find the height the pendulum and metal ball reached together. Therefore, according the derived equation, height was L-Lcos(theta) so we then found the length (L) of the pendulum string.

Length: 21.7 cm

With given masses of the pendulum and metal ball and the data above, we now had enough data to find the initial velocity of the metal ball fired out of the gun. 

Using conservation of energy we set the potential energy equal to the kinetic energy of the metal ball and pendulum bob to find the final velocity of the metal ball and pendulum bob combined after their collision (or just before rising). We then used conservation of momentum, using this final velocity, to find the initial velocity of just the metal ball. 

Velocity Equation Derived

Initial Velocity of Metal Ball

Due to varying factors, such as human error in taking data and the accuracy of our tools, we calculated the uncertainty of this calculated value of the initial velocity. 

The initial velocity of the metal ball from the spring-loaded gun turned out to be 5.06 +/- 0.502 m/s. 

Conclusion:

Using the conservation of energy and momentum we were able to calculate the speed of the spring-loaded gun on the metal ball. Despite the minimal calculated uncertainty, and other possible factors such as force of the metal rod and friction of the metal ball inside the gun, we found a speed that made sense and found reasonable method of calculating a gun's speed of its bullets.