Question

The passengers in a roller coaster feel 50% heavier than their true weight as the car goes through a dip with a 30 m radius of curvature. What is the car’s speed at the bottom of the dip?

Answer 1

F=mv²/r is the force experienced as a result of circular motion.

Total force on a passenger is mg+mv²/r because gravity is also acting on the passenger in the dip.

So this is 1.5mg and mv²/r=0.5mg so v²/r=0.5g. We are given r=30m. Take g=9.8m/s/s.

v²=0.5×9.8×30=147, so v=√147=12.12 m/s approx.