18-Nov-2014: Momentum with Inelastic Collision

Purpose:
The purpose of this lab is for students to use their knowledge in collision and momentum in order to find a certain variable, height after the collision.

Apparatus:
The ruler is set up so that it can swing most of its body below the pivot point. There will be a small piece of clay sitting right below the tip of the ruler so that when the ruler hits the piece of clay, the clay will stick to the ruler, causing an inelastic collision. Use Logger Pro to record the motion of the ruler to get the highest point the ruler reaches.

Explanation:

First we calculated the theoretical height using momentum, but we needed the angular velocity before the collision, so we used conservation of energy to find the angular velocity. With the angular velocity we came up with an equation of the angular velocity after the collision but right before the system lifts. We used the conservation of energy once again to find the height of the system. With the equation simplified, we ended up with the theoretical height of 0.6539m.

With Logger Pro set up, we recorded the motion of the ruler swinging into the small piece of clay, then swing up a certain height after the inelastic collision. The actual height was 0.6656m, which gives us a percent error of 1.7%.

Conclusion:

Before the collision, the moment of inertia was just the ruler, but after the collision, the moment of inertia was ruler and clay, which we used the parallel axis theorem. When the ruler collide with the clay, the collision was inelastic and this process slowed the angular velocity down. However, the clay was so light that the difference when the ruler swung by itself was not so different. The percent error is less than 5% so we can consider this lab experiment acceptable.