Conservation of energy as a demonstration laboratory

This term a holiday took out the week four banana leaf marble ramp laboratory day. With the first five weeks deeply interconnected and building from day-to-day, losing lab four was particularly problematic. Momentum was moved to Monday and laboratory four was done as a demonstration on Wednesday.

Laboratory four attempts to demonstrate that gravitational potential energy becomes kinetic energy. Height above the table is graphed against velocity at the bottom of the ramp.

Set-up took 40 minutes, tape, scissors, and the Hot Wheels sets. 

The original cars were long gone, a new car was purchased and unpackaged only in class. 

The top of the rig was affixed to the overhead track using copious amounts of tape. The finishing gate was also taped down after being pulled to provide a small amount of tension on the track.

Timing for velocity calculations was done on the last 180 cm of track. Timer start was at the 180 cm mark.

The flat sections of track are not exactly flat. While the car could have free rolled on the bare table, the tracks kept the car in a straight into the finishing gate which popped a flag when the car entered the gate. This actually helped with the timing.

A chair was used to sort of catch the car, but in practice a student caught the car.

The left board shows the set-up, variables, calculations, and resulting data table. Zero cm above the table was shown to produce a velocity of zero.

An initial attempt at 5 cm above the table never reached the gate.

A second run at 8 cm high reached the gate. Two more runs were done from 8 cm, the third displaying that a wide variation in time was possible from 8 cm. A glance at the clock suggested there would not be time to make multiple measurements from each height. 

Desiring a doubled height, the next height was 16 cm. One student offered the estimate that the speed would double. Two runs were done from 16 cm. After 16 cm high, all runs were single shot except the final run at 104 cm. A form of the Fibonacci algorithm was used above 16 cm. This helped move the lab forward more quickly. At 104 cm there was still vertical height available on the track, but speed trap times were down to 0.4795 seconds - reaction times were becoming a limiting factor. Whether the 377 cm/s measurement was a reasonably accurate measurement was unknown.

Once graphed in Desmos, the result was surprisingly well modeled by a square root relationship.

A correlation coefficient r of 0.993 was as strong as anything produced by the banana leaf marble ramp. And although the car has spinning wheels, there is less impact of rotational kinetic energy on this system. Perhaps this version could be deployed for laboratory four, perhaps with modifications given that a height of 100 meters produces times under half a second. A chair, perhaps on the sink, using the back to secure the track top, could be explored in future iterations. Each rig provides two tracks. Might even need only a single rig, and multiple cars. Students could go back to working in pairs. Track could potentially be pre-marked. 

Desmos was set up on a cell phone. The Smartboard was not logged into. The Desmos graph was echoed onto the Smartboard. Time was tight and in retrospect there wasn't the time to make multiple timings from each height. Despite this potential limitation, the data well supported a square root relationship.