Does this situation violate conservation of energy?

[geekmax]

I think this scenario violates the law of conservation of energy: A ball is rolling twards a fan, witch provides a constant force on the ball, with some amount of kinetic energy. As the ball gets closer to the fan, its kinetic energy is converted to "fan potential energy". Then, when the ball's kinetic energy is copletly converted to potential energy, the fan turns off. An instantanious force is then applied on the ball, and the ball rolls away from the fan. Now, the energy of the ball is smaller than the energy it had at first, because its kinetic energy is essentially zero and its fan potential energy is constantly decreasing. Where does the energy go?

oh, also, the surface the ball is on has no friction

 

[sophiecentaur]

The KE of the ball is not transferred to potential energy. It turns up just as thermal energy as the air turbulence around the ball gets more and more random.
There is no PE from the fan. It's all KE of the moving air. We're just talking friction effects.

 

[geekmax]

uh, yes there is potential energy because the force of the fan is a conservative force. Do things gain potential energy when they are lifted against the force of gravity? yes they do. Do they gain potential energy when they are pushed against the fan? same thing, yes they do

 

[lstellyl]

umm... you can think of the fan as providing a fictitious potential, but what is really going on is the electrical energy of the fan is moving the fan blades... which is then moving the air.

the air is pushing the ball and providing a force opposite the momentum of the ball.

this is a fictitious potential energy, but this analogy breaks down the second you turn off the fan.

the force on the ball from the fan is a frictional force. these forces are NOT conservative.

 

[geekmax]

its not ficticious. It provides a constant force, just like gravity, so the potential it gives is "real", just like gravitational potential. You could think of the situation as a physically possible situation of the ball going twards the earth, and then the Earth dissapearing. Or a charged particle moving twards an electric field, and then the electric field disappearing (a physically possible situation)

 

[lstellyl]

if i understand you correctly, what you are describing is not a physically possible situation... the Earth cannot just disappear... an electric charge cannot just go away... it takes energy to do so (allowing for conservation of energy when the potential energy goes away)

 

[russ_watters]

First istellyl is right that the fan energy is not conserved - this is obvious enough given that it expends energy whether the ball is there or not. Second, this "instantaneous force" adds another input. No violations here, just a problem you haven't diagrammed out. It would help you understand better if you wrote a mathematical conservation of energy statement.

 

[sophiecentaur]

The force due to the fan is there due to a constant input of energy. You could replace the ball by a turbine and get unlimited energy. If the ball is pushed against a spring or lifted, the force will not require any more energy to be expended. That is what is meant by conservative and it does not apply to your fan. Potential energy is Stored energy - not a constant supply of energy from some source. Don't confuse force with energy.

I agree that you can simulate a gravitational force using a fan but the total energy situation is totally different. If you were to do a total energy analysis then there would be no violation. Your supposed violation is there because you aren't including all the energy involved.

 

[geekmax]

Thanks a lot, I now understand conservative forces better. QUESTION OVER!

 

[Andy Resnick]

I think I should point out that the drag force (which is what the ball experiences from the fan) is not a conservative force. The energy associated with aerodynamic drag (or viscous effects in general) is dissipative. Energy is still conserved- the total energy is *always* conserved- but some of the energy is dissipated and not available to be converted back into work.