Final answer:
The maximum velocity of a roller coaster at the bottom of an 83 meters drop can be calculated using the conservation of mechanical energy, assuming no friction or air resistance, by equating potential and kinetic energy.
Step-by-step explanation:
To calculate the maximum velocity of a roller coaster with a mass of 3,320 kg when it reaches the bottom of an 83 meter drop, we apply the principles of conservation of energy. Specifically, we can use the conservation of mechanical energy, assuming no energy is lost to friction or air resistance.
Conservation of Mechanical Energy
At the top of the 83 meter drop, the roller coaster has potential energy given by PEtop = mgh, where m is the mass, g is the acceleration due to gravity (9.81 m/s2), and h is the height. When it reaches the bottom, all this potential energy will have converted into kinetic energy KEbottom = ½mv2, where v is the maximum velocity at bottom.
Equating potential and kinetic energy, we get mgh = ½mv2. By solving for v, we find that v = √(2gh). Substituting m = 3,320 kg, g = 9.81 m/s2, and h = 83 m, we can calculate the maximum velocity.
Keep in mind that actual roller coaster designs may incorporate factors that result in different velocities due to energy losses not accounted for in this simple theoretical model.