045 Kinetics

The kinetics demonstration attempts to tie together the concepts of the past two weeks in physical science by putting six dynamics equations on the board.

a = constant, d=½at²,  v=at, p=mv, KE=½mv², GPE=mgh

Although the original idea was that the velocity at the bottom of the slope can be predicted from the energy equations and then a measured slope can be obtained in a method similar to the banana leaf marble ramp laboratory, the following spring I became intrigued by the ability to obtain a predicted height from actual measurements of the height. This was in part because the height was considered to be one of the larger sources of uncertainty in the calculations.

The spreadsheet in spring 2024 set the gravitational potential energy to be equal to the kinetic energy by definition. But given the conservation of energy laboratory just done the day before, rather than use the data to find a predicted height, the more appropriate goal is to see if the kinetic energy at the slope bottom equals the measured gravitational potential energy using the accelerations that the students measured in the laboratory three the week before. 

In laboratory three, measurement of the acceleration of gravity, I opted to go full discovery mode and did not introduce the known value of gee. The laboratory remained true to the position that what the students can measure in the laboratory becomes the established fact. The systems in place in laboratory three now produce far more accurate measurements of gee than were obtained in the past. The average across the laboratory three groups was within five percent of the published value.

This term the board layout was more logical and more careful than spring 2023 - the first term I had stayed with six dynamics equations. The focus was on predicted versus measured slope bottom velocities and confirmation of the conservation of energy. Equations were color coded and subscripted to match the spreadsheet.

A morning 75 meter statistics run had premarket the sidewalk. We were outside by 12:19.

The main run was left at 21 meters in length, which just past a post. This put the leveling line in the air and gave a drop height of 0.7 meters. I then ran the speed trap from 21 meters to 24 meters. This worked and kept things on a three meter rhythm.

Two timers handled the slope time, two timers the speed trap. The average time was used for both.

The focus was on predicting the velocity and comparing the energy values.

I then tried to wrap up by stepping back from the weeds and explained that even if one was lost in the math, the core point was that these six equations are connected a set of equations. And much of physics works this way. Maxwell's four equations of electromagnetism. Einstein's ten equations of general relativity. We cannot work those equations in this class. But we can come to see sets of equations essentially as families of interrelated equations. And that is how physics works. Not as single equations which exist in isolation, but as a set of interconnected mathematical relationships.