Final answer:
The questions are based on the principles of physics, focusing on circular motion and mechanics, dealing with the forces and acceleration involved in amusement park rides like pendulum swings and roller coaster loops.
Step-by-step explanation:
The amusement park ride questions you've asked pertain to the physics of circular motion and mechanics. Specifically, they are about topics such as rigid pendulum motion, centripetal acceleration, and the forces at play during vertical loops on roller coasters. For instance, when considering a Viking ship amusement ride that operates like a pendulum, riders experience a moment of weightlessness when the ship is at the top of its arc before gravity pulls it down, leading it to accelerate until it reaches the bottom. The speed increase toward the bottom of the swing is due to the conversion of potential energy into kinetic energy.
Similarly, for modern roller coasters with vertical loops, the radius of curvature influences the centripetal force required to keep passengers safely in their seats. When calculating the speed of a coaster at the top of a loop with a specified radius of curvature and an acceleration greater than gravity, you are essentially applying the principles of circular motion to determine the necessary velocity to achieve that acceleration.