Final answer:
The questions entail calculating the acceleration and time elapsed for a roller coaster car on an inclined track, understanding kinetic and potential energy changes on a cosine-shaped track, and analyzing the forces experienced by passengers in a roller coaster loop.
Step-by-step explanation:
The question relates to the physics of motion, specifically how it applies to roller coasters. While details like the floor of the service elevator do not relate to the problem, the given scenarios involve gravitational force, acceleration, and forces experienced by passengers.
41. Roller Coaster Acceleration and Time Elapsed:
(a) To find the acceleration of the roller coaster car, one could use the formula a = g sin(θ), where g is the acceleration due to gravity (9.81 m/s2) and θ is the angle of incline. Since the angle is 20 degrees, the acceleration a would be g sin(20°).
(b) To calculate the time elapsed before the roller coaster reaches the bottom, the kinematic equation s = ut + 1/2 at2 can be used, solving for t when u (initial velocity) is 0, a is the acceleration found in part (a), and s is the track length (30.0 m).
Roller Coaster Kinetic Energy with a Cosine Track:
For question 7, as the roller coaster follows a cosine track, its kinetic energy would vary according to its position. At the top of the cosine curve, the car's velocity — and thus kinetic energy — would be at its lowest, as it has the most potential energy. As it moves down the curve, the potential energy is converted into kinetic energy, which peaks at the bottom of the curve.
Roller Coaster Forces:
Concerning the forces experienced by a child in a roller coaster car in a loop, the force exerted by the car seat on the child at different points in the track would depend on the speed of the roller coaster and the radius of the loop. The centripetal force required to keep the child in the seat can be calculated using F = mv2/r.