In a research paper, any sentence that presents an idea, information, or a direct quote from a specific source requires a citation. Based on the sentences you provided, if they are taken from a specific script or source, they would all require citations. However, to be certain, it depends on whether the content is common knowledge or not.
Typically, the sentences that provide specific facts, analysis, or a unique formulation of ideas (such as technical explanations) would necessitate a citation.
In this case, the following would likely need citation if they are not common knowledge:
- “Engineers meticulously calculate G-forces and design the tracks…”
- “Friction from the wheels and track, combined with magnetic or friction brakes, safely bring the ride to a stop.”
- “Gravity pulls the coaster down, while centripetal force keeps it moving in a circular path…”
The first and second sentences convey specific engineering concepts that might be detailed in a source, while the last sentence combines principles of physics that, while foundational, may still need a citation for specific context or application.
However, the lines “Welcome to ‘The Physics Behind Roller Coasters’…” and “As the coaster slowly climbs, it’s gaining height.” seem more introductory or descriptive and might not require citation if they don't provide unique insights or data from a specific source.
Ultimately, if in doubt, it’s safer to provide a citation when using specific phrases or concepts that originate from a particular source.