Why is energy conserved in a frictionless roller coaster ride?

[pkc111]

Could some one please explain to me why energy is conserved in a roller coaster car on a frictionless roller coaster car ride when the conservation law says that energy will only be conserved when their are no outside forces applied. Isnt the force supplied by the rails to change the cars direction an outside force ?

Thanks very much.

 

[Doc Al]

Could some one please explain to me why energy is conserved in a roller coaster car on a frictionless roller coaster car ride when the conservation law says that energy will only be conserved when their are no outside forces applied.

The only force doing any work in this situation is gravity, which is a conservative force. (Perhaps you are thinking of conservation of momentum; the momentum of a system is conserved if there is no outside force.)

Isnt the force supplied by the rails to change the cars direction an outside force?

Sure (which is why the momentum of the car changes), but that force is always perpendicular to the car's direction of motion, thus it does no work.

 

[pkc111]

Thanks Doc Al that helps.

What about an elastic bouncing ball isn't the ground supplying an external force in the direction of motion ? The definition of the law of conservation of mechanical energy I have is:

"Conservation of mechanical energy applies to a mechanical process in which external force and non-conservative internal forces are absent"
http://cnx.org/content/m15102/latest/

It just implies that all external forces must be absent, not just ones in any particular direction.

Thanks

 

[Doc Al]

What about an elastic bouncing ball isn't the ground supplying an external force in the direction of motion ?

Absolutely, but strictly speaking, that force does no work on the ball. (The ground doesn't move.) During the collision, the kinetic energy of the ball will be transformed into elastic potential energy. If the collision is perfectly elastic, the ball will bounce back with the same kinetic energy.

In any case, the external force of the ground changes the momentum of the ball.

The definition of the law of conservation of mechanical energy I have is:

"Conservation of mechanical energy applies to a mechanical process in which external force and non-conservative internal forces are absent"
http://cnx.org/content/m15102/latest/

It just implies that all external forces must be absent, not just ones in any particular direction.

As long as the external forces do no work, they won't change the mechanical energy.

It also depends on how you define your system. In the roller coaster problem, consider the track as part of the system. So any forces between the car and track are internal forces.

 

[pkc111]

Thanks very much Doc Al that makes sense.