045 Kinetics

Building on the demonstration of last term, I took the acceleration through to the predicted velocity and predicted drop height. The organizing concept was that across the top of the board would be six expressions or equations:

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

and the demonstration would put all of these together. I did not go with integrating the acceleration to get v=at and d=½at². I decided this just added another layer of obscurity for the students. I did mention t

that v₀ = 0 and d₀ = 0 without really explaining why I needed those two statements.

This replicated the demonstration of fall 2023 but with the additional step of predicting the vertical drop height. This added to the needed equipment. I needed surveying line, two tape measures, a level, chalk, timers, a RipStik.

If the acceleration a is constant, then the acceleration can be obtained from 2d÷t². That acceleration can be used to predict the velocity from v=a×t. In turn, that velocity can be used to calculate the momentum and kinetic energy. 

From conservation of energy, the drop height can be calculated. Measuring the final velocity and slope height provide actual values for comparison.

Two runs were made

A prebuilt spreadsheet can rapidly calculate values from measurements.

Start was at the upper "double pole." 

The string crosses the intersecting sidewalk near the top and is a potential tripping hazard.

Hedweag and Daniel work on the drop height measurement

There are a lot of moving pieces. The line has to be leveled with a level. Chalk, string, 30m tape measure, 8m tape measure (for the 3m speed trap), scissors, timers, RipStik. The actual vertical drop height was measured to be 0.4 meters or 40 centimeters. I would use the older RipStik as the newer one actually has more friction in the bearings. Strange but true.

Jazzlyn and Darx observe

This went well with friction bringing the actual speed in at just under the theoretically predicted value.