**Analyzing the Relationship between a Train’s Center of Mass and its Tipping Point**

The purpose of this experiment was to determine if there was a direct (linear) relationship between a train’s center of mass and its tipping point. It was predicted that as the center of mass gets higher above the track, the more unstable the train will become, making it easier to tip (especially at higher velocities). This was measured using a model train set. The velocity was set to several different values, and then mass was gradually added to the engine until it tipped over. The amount of mass added to the engine when it tipped off the tracks while traveling around a curve was recorded as the tipping point. This process was then repeated, and the values were averaged for each of the different velocities By determining the relationship between the center of mass on a train’s tipping point, data could easily be extrapolated to the real world. Given the train’s center of mass, the maximum speed the train could safely travel at without tipping could be easily calculated. This is relevant because train crashes can be deadly. Anything that can be done to minimize crashes without significantly deceasing the speed of the train has a lasting impact in the community. To analyze the data, a linear regression t test was used. The data was graphed and a line of best fit regression was added to the graph. The results were that the relationship between a train’s velocity and tipping point was indeed linear. As the velocity of the train increased, the amount of mass required to tip the train decreased. This was proven due to the low p-value as well as the high r and r2 values from the statistical analysis.

### Research Conducted By:

Trent Szczepaniak

*Center Line High School*