Potential energy/velocity

Question

roller coaster 1: Potential energy: 1,617,000J, mass 5,500kg

Rollercoaster 2: potential energy: 2,205,000J, mass: 5,000kg

gravitational constant: 9.8

1. roller coaster 1 has no kinetic energy, and at the bottom of it's first fall, it has no gravitational potential energy. Using conservation of energy, how fast is rollercoaster 1 moving at the bottom of its drop.
2. Assume the same thing for roller coaster 2, how fast is it moving at the bottom of its drop

Answer 1

Assuming we neglect any frictional forces, in that case, we have conservation of mechanical energy.

Δ( KE + PE ) = 0

Since both rollercoaster start at the top of the fall without any kinetic energy and at the bottom they have no gravitational potential energy, means its gravitational potential energy at the top will be converted entirely to its kinetic energy at the bottom (again only if we neglect any frictional forces, otherwise some of its energy will be converted into heat, sound, deformation,...).

In symbols:

E_{total, top} = KE_top + PE_top = PE_top

E_{total, bottom} = KE_bottom + PE_bottom = KE_bottom

E_{total, top} = E_{total, bottom}

PE_top = KE_bottom

Now you know the amount of kinetic energy the rollercoasters have at the bottom and you know their masses. With this information, you can derive their speeds.

KE = mv²/2

v = √(2*PE_top / m)