Ralph wrote:
One exception to this rule, is a helicopter, It must produce energy and heat to hover, and while hovering it is considered not to be displaying measurable work.
First you say that it must produce energy to hover and then you say it does not display measurable work while hovering.
While the height of the hovering helicopter may not change, those rotor blades on it must push a lot of air out of the way to create the lifting force that allows the fuselage that they are attached to to hover. There is much aerodynamic drag on those moving blades and a
lot of energy must be
constantly expended by the heliocopter's engines to overcome that drag.
There seems to be some confusion here as to what happens, energywise, when a object is held at a fixed height by another object such as a support or a human arm.
Well, imagine a 100 lb block of lead that is held three feet off of the ground by a suitably shaped wooden pillar. The block does not move.
However, when the lead block was initially placed onto the pillar, something interesting took place on a submicroscopic scale inside the atoms of the lead block and the top of the wood when they came into contact with each other. As the lead was pulled down against the wood by the force of gravity, the negatively electrically charged electrons in the atoms coming into contact began to repel each other with a force that increased as the lead block came closer to the wooden pillar.
At some point, the increasing repulsive electrostatic force applied to the lead block by the wooden pillar equalled the attractive force that gravity applied to the lead block and, at that instant, the lead block stopped moving. Thus, any gravitational potential energy lost by the lead block after it made contact with the wood was immediately "stored" as an increase in the potential energy of the repulsive electric fields existing between the contacting electrons in the lead block and the wooden pillar.
From Einsteinian relativity we know that wherever we have mass we have energy and that wherever we have energy we have mass.
In the case of the lead block and wooden pillar considered above, there will be no net change in their rest masses as they come into contact and achieve an equilibrium position. Any rest mass lost by the lead block will result in an increase in the rest masses of the electrons that repel each other at their surface of contact.
ken
On 7/6/06, I found, in any overbalanced gravity wheel with rotation rate, ω, axle to CG distance d, and CG dip angle φ, the average vertical velocity of its drive weights is downward and given by:
Vaver = -2(√2)πdωcosφ