Understanding Energy Conservation and Momentum: Exploring Common Misconceptions

[oldspice1212]

For conservation of energy does the energy at the start always have to equal energy at the end, unless an force is acted upon? And is conservation of momentum the same?

I really get confused when it comes to these concepts of energy especially in the textbook.

 

[jedishrfu]

i like to think about pendulums. At the start of a swing it has a certain amount of potential energy, at the bottom of the swing the energy is converted into kinetic energy of motion and then it swings back up.

If the energy is conserved then each successive swing is the same height meaning the bob has the same potential energy (where it stops momentarily before reversing direction).

If there was friction in the swing mount or there was some air drag then each swing will be less and less meaning energy is being lost to heat ie the swing mount bearings are rubbing each other, the air is rubbing against the bob and its string and so they heat up a small amount and cause the pendulum to slow down.

If there was some mysterious pushing force like a magnet pushing the bob at the right moment in the right direction then energy would be added to the system and the pendulum swings would get higher and higher.

 

[oldspice1212]

So let me get this straight, at the start of any object there is potential energy "hence potential" and at the maximum end or point it converts to kinetic energy, or is also kinetic as it's moving, and if it lands back in the same position it is back at 0 potential energy but will have the same kinetic?

For conservation of momentum it's always the same, just in different areas?

 

[CWatters]

For conservation of energy does the energy at the start always have to equal energy at the end...

As long as it's a closed system total energy is allways conserved.

If you see a statement in a textbook that says "Inelastic collisions may not conserve kinetic energy" the important thing to notice is that it's only talking about kinetic energy. If you consider all other forms of energy as well the total will be conserved.

What matters is where you draw your system boundary and is it closed. Imagine a head on car crash where the cars end up stationary. Where did their Kinetic Energy (KE) go? It might appear that energy wasn't conserved because after the crash KE was zero. However that's not a correct interpretation. If you redefine your system to include heat you will realize that the KE went into deforming and heating up the metalwork of the cars. KE wasn't conserved but their total energy was conserved. The difference is due to the way you model the system. One isn't closed (heat escapes) the other is closed (heat remains within the system model).

Exam problems typically ask you to work out a velocity or KE after a collision. If you want to know if conservation of energy can be applied to solve the problem you need to decide if the system is closed and all the energy can be accounted for. Typically you can't use it to solve problems involving an inelastic collision because some energy is converted to heat which might be an unknown or unspecified quantity in the problem. But that's not allways the case...

Consider a bullet fired into a block of ice. How much water melts? The bullet has KE before the collision that is converted by friction into heat which melts the ice. If the block of ice is in an insulated box then you might well decide the system is closed and apply conservation of energy to work out how much water melts.

 

[CWatters]

Looking at the pendulum problem. If there is no friction or any other way for the system to loose energy then it can be considered closed. Total energy is conserved.

The pendulum swings back and forth converting PE to KE and back.

At the top of the swing the pendulum has:

PE = Max
KE = Min (zero as it's stationary briefly)

At the bottom of the swing the pendulum has:

PE = Min (zero if we define the pendulum as having zero height)
KE = Maximium

At all times including any point in between:

PE + KE = Constant

because the system is closed and energy conserved.

 

[oldspice1212]

Awesome! Thanks for taking time and explaining how it works, this was really helpful. Thank you so much!