How far away are the Stars?
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Answer:
The two types of energy possessed by the roller coaster are:
- Potential energy: it is the energy possessed by the roller coaster due to its position. It is calculated as
where
m is the mass of the roller coaster
g is the acceleration due to gravity
h is the height of the roller coaster relative to the ground
- KInetic energy: it is the energy possessed by the roller coaster due to its motion. It is calculated as
where
v is the speed of the roller coaster
Moreover, according to the law of conservation of energy, the total mechanical energy of the roller coaster (the sum of potential+kinetic energy) is constant during the motion:
This implies that:
- When PE increases (because h increases), KE decreases (because v decreases)
- When PE decreases (because h decreases), KE increases (because v increases)
Now we can apply these conclusions to the motion of the roller coaster:
- When it moves from A to B, potential energy is converted into kinetic energy, so PE decreases and KE increases
- When it moves from B to C, kinetic energy is converted into potential energy, so PE increases and KE decreases
- When it moves from C to D, potential energy is converted into kinetic energy, so PE decreases and KE increases
- When it moves from D to E, kinetic energy is converted into potential energy, so PE increases and KE decreases