Ballistic Pendulum

The objective of this lab was to observe an inelastic collision and determine how high the two masses that collided would travel.  Below is the ballistic pendulum that was used in the demonstration.  In the picture, you can see a "cannon", a wire suspended block, a ball below the block, and a wire which will come into contact with the block and ball and will stay at the position of highest swing reached.  The wire is used to measure an angle from the vertical the block and ball travel.

Here is a closer view of the block and ball for visual aid.

The ball was placed into the cannon and fired into the block which rose a height from its original position and made an angle with the vertical at its peak swing.

Weighing the ball determined its mass to be 0.00763kg and the block came out to 0.0809kg.  Next, the length the block hung down was measured and was determined to be 0.21 meters.  After firing the ball, the block/ball combo created a 16 degree angle with the vertical.

We are asked to determine how fast the ball was traveling before it hit the block.  The problem was divided into two parts; before the ball hit and after.

Here we see the ball after it was fired and when it gets stuck in the block.  This is a momentum problem with momentum being conserved as the outside forces cancel out.  Initial momentum has the ball with it's initial velocity.  Final momentum has the ball and block moving as one with their new speed.  Solving for the final speed gives me an expression.

In the second part of the problem, the ball and block are moving together as one and have kinetic energy that will be transformed into potential energy as it swings an angle with the vertical and reaches a height above it's initial position.  Since the angle the combo created is known, the height it reached can be solved for.  Setting the initial and final kinetic energy and potential energy equal to each other gives an equation that reads that the initial kinetic energy is equal to the final potential energy.  Substituting in the expression for the velocity of the combo allows for the initial velocity to be solved for after inputting values.