Lab 19

Goal:
The goal of this lab is to create an inelastic collision and predict how the objects will move afterward within a small degree of error. Concepts that are applied include conservation of energy and angular momentum.

Summary:
In this lab we hang a meter stick from some pivot near the end of the stick, and lift the stick until it is parallel with the horizontal. We place a mass of clay directly under the stick so that they will impact when we release the stick. The two masses stick together and they rise some distance on the opposite side. We take appropriate measurements and calculate exactly how high the clay-stick mass will rise. We then carry out the experiment and compare our predicted height and actual height.

Procedure:
We start with measuring the masses of our instruments, namely the clay and meter stick.
Mass of clay: 0.0892 kg
Mass of meter stick: 0.0185 kg
 We follow by hanging the meter stick and aligning the clay blob such that they will collide when we release the stick. We had to add paperclips to the bottom of the clay blob so that it would collide more seamlessly with the stick. There was too much friction between the ground and clay otherwise. We mounted my phone 3 meters away to take slo-mo video. After video capture, we analyzed the motion of the stick in logger pro and obtained our actual maximum height of our stick-clay system.

We must also calculate our max height using our leet physics skillz. Illustrated below is this process.

Despite the pivot not being at the complete end of the meter stick, I chose to do my calculations as if it was. Our calculations represent a mathematical model of our experiment and in the interest of clarity and readability I put the pivot at the end. The real pivot is at 1 cm, of a 100 cm stick. The error introduced from this decision is minuscule, while making the cleanliness of my work twice as neat. 

Analysis:
Sources of error include friction at the pivot, energy lost due to clay deformation, assumption that the clay is a point mass and a slight (1 cm) approximation regarding pivot placement.

Conclusions:
Despite triple checking my measurements and calculations I was unable to reduce the error further, leaving our approximation significantly off without a clear reason why. My hunch is that the clay was acting similar to how a car's airbag functions, crumpling to dramatically reduce kinetic energy upon impact. Thus our actual height was lower because there was less energy leftover after the impact than expected.