A roller coaster car rises 50 m. If the next rise, after 120 m of travel it is 40 m. What is the maximum allowable friction force for a 500 kg cart ?.

Question

A roller coaster car rises 50 m. If the next rise, after 120 m of travel it is 40 m. What is the maximum allowable friction force for a 500 kg cart ?.

Answer 1

The difference of potential energy between the two points at height difference $\Delta h$ is $$ \Delta E_{\text{pot}}=mg\Delta h.$$ The work of a force $F$ along a way of length $s$ (and always parallel to the trajectory) is $$ W=Fs.$$ If we assume that the coaster has no additioal energy (e.g., starts with no kinetic energy at the 60 m point), we must have $$ W\le E_{\text{pot}}.$$ As $m,g,\Delta h, s$ are known, you can obtain an upper bound for $F$ from this.