Question

Considering the conservation of mechanical energy when designing a roller coaster,

which statement below is true?
(A) No other hill on the roller coaster track can be higher than the first hill and
the hills following the first hill must randomly vary in height-short, tall, tall,
short, etc.-in order to conserve the mechanical energy of the system.
(B) Only one other hill can be higher than the first hill and there must be a hill
placed on the track between the first hill and this higher hill such that its slope
is twice as steep as the slope of the higher hill.
(C) No other hill on the roller coaster track can be higher than the first hill
because the energy required to climb such a hill would be greater than the
total mechanical energy of the system.
(D) The only way to conserve the total mechanical energy of the system is to
conserve the roller coaster's gravitational potential energy by making sure that
the last vertical drop is the same as the first.

Answer 1

Option C is true: No other hill on the roller coaster track can be higher than the first hill because the energy required to climb such a hill would be greater than the total mechanical energy of the system. This is because roller coasters rely on their initial potential energy (at the top of the first hill) to provide the energy needed to make it through the rest of the track. If subsequent hills are higher than the first hill, the roller coaster would not have enough potential energy to make it up the hill and would slow down or stop. Therefore, roller coasters are designed with successive hills that gradually decrease in height, allowing the roller coaster to conserve its mechanical energy and maintain its speed throughout the ride.