Yes- as long as the roller coaster car is not powered once it leaves the station and energy loss due to resistance can be ignored.
Energies of a system:
- Potential Energy
- Kinetic Energy
- The term "Mechanical Energy" refers to the sum of both types of energy.
A roller coaster car moving along a level track with an initial velocity has mechanical energy in the form of kinetic energy.
The car would slow down while gaining height as its kinetic energy converts to gravitational potential energy when moving upwards along the track. It would have no kinetic energy since all its mechanical energy are now in the form of gravitational potential energy in case it comes to a stop before reaching the top of the track.
Similarly, the car gains speed while losing height as some of its gravitational energy is converted to kinetic energy when it travels downwards.
The mechanical energy of this vehicle conserves since any of the movements, moving upslope, downslope, or level, would ensure that
<em>Loss in Potential Energy </em>=<em> Gain in Kinetic Energy</em>
and vice versa.
