In your formula, the work output is zero because of the way the formula is structured. That's why I sometimes distrust the input of physicists (like nmgolfer) who are capable of deep mathematical expositions based on mathematical formulas. The "real" issue is not the accuracy of the formula, the "real" issue is it's relevance. The most important question is what's the best perspective to look at a problem, and then one has to decide which formula to use in that situation.
In the situation of centripetal force, if the force doesn't provide the tangential force needed to move a mass at a certain speed a certain distance, then one shouldn't be using a formula that 'a priori' uses those requirements (speed and distance) to calculate work output. Secondly, the idea of a centripetal force always being at 90 degrees to the mass is only a mental concept, and it obviously results in zero work output according to that formula.
Consider the example I gave of person B applying a force to deflect the mass (that was being pushed in a straight line direction by person A). Presume that he doesn't apply a force at right angles to the moving mass, but presume that he stands at an angle to the mass - as described in this next example - and pushes in the direction of the arrow.
If you look at the angle that he is pushing, one can imagine that the object will not travel in a straight line path and that it will be deflected slightly leftwards. The amount that it will be deflected leftwards depends on the magnitude of person B's push-force relative to the magnitude of person A's push-force. If person B's push-force far exceeds person A's push-force, then the degree of leftwards deflection will increase. Note that person B's push-force will make the object travel faster, because a component of the push-force is working in the same direction as person's A's push-force. In other words, from a conceptual perspective, one can describe person B's push-force as having two directional components - a vector component that works in the same direction as person A's push-force and helps increase the speed of movement of the mass in person A's straight line direction, and a vector component that works at 90 degrees to person's A's straight line path, and that causes the mass to be deflected slightly leftwards. Both vector components are doing work.
Now consider another example.
Note the direction of person B's push force. It is directed somewhat backwards. If one dissects person B's push-force into two directional components - one vector component will work in direct opposition (180 degree angle) to person A's push-force and that will slow the speed of movement of the mass. The other vector component will conceptually work at right angles to person's A direction of push-force and that will cause the object to be deflected leftwards. Both vector components are producing a work output. The amount that the object is deflected leftward depends on the magnitude of person B's push force relative to the magnitude of person A's push force.
Hopefully, you will understand what points I am trying to make.
1) The first point is that the force (exerted by person B) that deflects the object leftwards is a "real" force that requires energy, and one has to rationally conclude that the force is doing work by deflecting the object.
2) After the object has been deflected, one can look back at the circular path that was transcribed on the ice rink and one can 'a posteriori' theorize as to what "force" resulted in the path being circular rather than straight line (towards destination D). One can simply conceive/theorize that a deflection force was present that caused the path to become circular-shaped. One can conceive that the "force" has centripetally accelerated (deflected) the object - defined simply as a "force" that causes an object (that already has enough energy to move in a straight line direction) to follow a circular path rather than a straight line path. In one's mental conception, one can conceive that the "force" is directed towards the center of a hypothetical circle, which means that the "force" is operating at 90 degrees to the circular path transcribed on the ice rink. However, this "force" and its 90 degree directional angle relative to the final arced path transcribed on the ice rink is merely a mental construct. In reality, there was only one force exerted by person B and it was in the direction of the red arrow, and the red arrow is not perpendicular to the circular path's arc.
For a starter, a real force can exist without any energy spending. For instance, when you stand on the ground, you are subject to a gravity force. It is as real as any other force, but while you'r standing, it doesn't do any work.
Regarding your curve pattern. You could put up a fence that forces the object to turn. The forces from this fence will not use any energy and they will not work. Still they will do the same "work" as the centripetal components in your examples.
In the world of golf swings & Newton, work is related to energy pretty much in the same way as acceleration is related to speed. Whenever you do work you change the mass-speed of the club or any other moving mass. (or you generate kinetic energy somewhere). When you don't do work, the energy remains constant - or is reduced due to resistance.
If you learn to see the difference between forces that work and forces that doesn't, you will get a clearer image of what swing speed is made of.
Bernt - If you prefer to see certain forces as existing without performing work, then you are free to perceive the world functioning in that manner. I think that if a force exists and it is operant, then it is performing work - even if the object remains stationary. So, in your example of a person standing stationary, you do not see any "work" because the object is stationary. I see "work" - because muscles forces are required to keep the person stationary and erect in the presence of gravity. If body muscles weren't actively working to oppose the force of gravity, then the person would fall to the ground.
Consider this ice rink example.
In this example, person B is applying a push-force at a 180 degree angle to person A's push-force. If the push-forces are equal, then the object will remain stationary and not move in a straight line direction towards destination D or along a circular path towards position C.
If the object remains stationary, you may "feel" that person A and person B are not working. However, in my mental universe, both person A and person B are working just as hard as before (as in those previous examples) because they are supplying the same amount of push-force (energy) as before - the only difference is that their push-forces are working in perfect opposition thereby eliminating any possibility of there being any net force available to move the object on the ice rink.
According to Newtonian physics - forces can be in a state of balance that results in an object being stationary.
Note that it states the following with respect to Newton's first law of motion = An object at rest tends to stay at rest and an object in motion tends to stay in motion with the same speed and in the same direction unless acted upon by an unbalanced force.
In other words, it takes an unbalanced force to disturb a an object from its position of rest. If the forces are in balance, then the object will remain at rest - even though the forces are working.
You wrote-: "Regarding your curve pattern. You could put up a fence that forces the object to turn. The forces from this fence will not use any energy and they will not work. Still they will do the same "work" as the centripetal components in your examples."
The fence is working in a Newtonian sense - by providing an unbalanced force that deflects the object.
It states with respect to a person riding in a car.
"Have you ever experienced inertia (resisting changes in your state of motion) in an automobile while it is braking to a stop? The force of the road on the locked wheels provides the unbalanced force to change the car's state of motion, yet there is no unbalanced force to change your own state of motion. Thus, you continue in motion, sliding along the seat in forward motion. A person in motion tends to stay in motion with the same speed and in the same direction ... unless acted upon by the unbalanced force of a seat belt. Yes! Seat belts are used to provide safety for passengers whose motion is governed by Newton's laws. The seat belt provides the unbalanced force which brings you from a state of motion to a state of rest."
In this example the book on the table is at rest - because the table top is providing a force to balance the force of gravity.
Therefore, inanimate objects can provide an unbalanced force that changes a state of motion to a state of rest. An unbalanced force can also cause a change of direction - as in the examples I have previously supplied (where person B supplied the unbalanced force that deflected the object) or in the presence of a fence which provides the unbalanced force that deflects the object.
Feel free to redefine basics physics all you want. But IMO you should really study the concept of work in the Newtonian sense before you throw it in the trash bin. So far Newton mechanics has been more than adequate for all my purposes related to mechanics.
Should I ever face a problem where Newton's doesn't deliver I will most likely turn to Einsteins theory of relativity. And perhaps also have a close look at quantum mechanics.
If I still haven't found what I'm looking for, maybe I will ask you for assistance
I wasn't redefining Newtonian physics. I was attempting to clarify it for your educational benefit. I apologize for not being successful in my multiple attempts, but I did make a serious effort (which involved a considerable amount of "work").
"Work" that is not successful in moving a person's mind is still work!
Hybrid Mode
