Hot wheels conservation of energy

The Hot Wheels variant of this laboratory is functionally more complex and takes much longer to set up. There are many moving pieces. And the results were surprisingly inconsistent.

The folding chairs approach was used to mount the ramps but with the chairs on the sinks instead of the table to gain more height.

The center table was set up with a 174 cm speed trap to measure velocity. Jaysleen opens the new box of Hot Wheels cars.

A timing start mark was made on the ramp where the height was effectively zero.

The track as viewed from the front. This was 8:50 AM and data recording had not yet begun. The track took that long to set up - from a start at 7:45. The track plus the board notes and the demonstration runs. 

The board notes as recorded after class.

DeAnne and Alisha gathering data. 

As more students arrived, they decided to set up a second dual track. Tikikos working on fixing the track riser to the chair.

Stacy, McGievens, Moira, and Tikikos working on the second track. 

McGievens doing a test run. 

The second track included an additional segment pair for a velocity speed trap distance of 181 cm.

In contrast, the first track had a 174 cm speed trap.

DeAnne, Alisha, Darla, and Jaysleen working with the center track. Jemira would wait until later to take data. 

DeAnne getting ready to time a car already released by Alisha. DeAnne and Alisha would obtain very linear data. 

McGievens about to time his car, Moira making measurements.

Mor-Jacinta timing while Eytriann observes.

Leona making measurements.

The board after class.

Desmos

DeAnne's data (in blue) was very linear. The other groups were either not far from linear or just barely a square root relationship. Something was occurring that pushed the system towards linearity. 

During the lunch break Emensio Eperiam showed me the data his group gathered and they also got a very linear relationship. So there is a systematic error (one caused by the experimental setup) that tends to lead to linear results. 

There are many possibilities. One possibility is a reaction time issue of some sort. Up at 483 cm/s the duration in the speed trap is down around 0.36 seconds on the 174 cm track. Reaction times are at least 0.1 seconds. At both the start and end of the 174 cm. This means that there is the potential for an error up around 0.2 seconds, or roughly 55% of the 0.36 seconds. That is a large amount of possible error relative to the measurement.

Another possibility is that perhaps there is something about the loss of velocity on the flat track that is a factor. Perhaps the amount of slowing is proportional to the amount of time on the flat track. More time, more slowing. This would cause the faster speeds, which spend less time on the flat stretch, to slow down less, which would lead to higher than predicted speeds for the higher heights. One sees this at heights below 8 cm where the cars often do not make it to the finishing gate. The cars lose 100% of their velocity. Perhaps a decreasing amount of loss is seen with increasing speed.

Next day thoughts

I am now of the opinion that the length of time on the horizontal track is at issue. The longer the time spent on the horizontal track, the more time for frictional forces to act, the greater the slowing of the car. At low speeds the loss in speed is large and the car underperforms a square root relationship. At high speeds there is less time for friction to act, so the car overperforms the square root relationship. My thinking was the system would produce a square root relationship, and some appear to have gotten hints of this, but the system may actually behave in a somewhat linear fashion. The wheels have a frictional force with their axles. Incarnations of this laboratory with marbles do not have these internal frictional forces.

The overall recommendation is to return to banana leaf marble ramps which perform in a more consistent and predictable manner.