Final answer:
The velocity of the roller coaster 16 m above the ground is calculated by using conservation of energy. As the roller coaster moves to level ground with friction, the kinetic energy is transformed into thermal energy, which causes the roller coaster to stop.
Step-by-step explanation:
A roller coaster that starts at the top of a hill 42 m above ground with a velocity of 5.0 m/s will have a different velocity when it reaches a point 16 m above ground. Assuming no energy is lost to friction, we can use the conservation of energy principle to find this new velocity.
Conservation of mechanical energy states that the total mechanical energy (potential energy + kinetic energy) remains constant in an absence of external forces like friction. The roller coaster at the top has both potential energy due to its height and kinetic energy due to its speed.
When the roller coaster descends to the height of 16 m, its potential energy decreases, but its kinetic energy increases by the same amount, again assuming no energy losses to friction. Using the equation for conservation of energy, we can equate the initial mechanical energy at 42 m to the final mechanical energy at 16 m, and solve for the final velocity.
For the roller coaster to come to a complete stop on a level track with friction present, we would use the work-energy principle. The work done by the force of friction must equal the kinetic energy the roller coaster had at the start of the level track to bring it to a stop. This work is calculated as the force of friction times the distance needed to stop.
Throughout the trip, the roller coaster experiences transfers between potential energy and kinetic energy. Starting from the top with high potential energy, it converts this to kinetic energy as it descends. When it moves on a horizontal track with friction, the kinetic energy is converted into thermal energy due to the work done by friction, eventually bringing the coaster to a stop.