Since there is friction here, A is doing work even though the speed becomes constant after a while.
If B's contribution is only to turn a linear movement into a circular movement, B is not doing any work. The object is always moving perpendicular to the direction B is pushing. The angle between the object movement and B's pull force need to be different from 90* before any work is done. Changing direction is not the same as doing work - even though it makes a significant difference.
You wrote-: "If B's contribution is only to turn a linear movement into a circular movement, B is not doing any work. The object is always moving perpendicular to the direction B is pushing. The angle between the object movement and B's pull force need to be different from 90* before any work is done."
I think that you are wrong. The fact that the object is changing direction means that there is a force present that is causing that change of direction. If a force is present and causing a change in the direction of the object's path, then it is doing work by moving the object in another direction. Person A represents the tangential force that causes the object to overcome friction and move forward at a finite speed. Person B is providing another force that pushes the object in a constantly changing direction at every instantaneous moment in time, and causes the object to follow a circular path. Conceptually, person B is providing a push-force that constantly deflects the object in its straight line path, so that the object is forced to follow a circular path. In a Newtonian sense, that push-force must have energy and it must be working - if it has the capacity to constantly deflect the mass of the object to an ever-changing directional path (a circular path).
I think that your idea that person B cannot be doing push-work because he is standing at 90 degrees to the circular path is incorrect. He is only standing at 90 degrees to the circular path - as result of his successful work effort of constantly deflecting the object from person's A desired straight line push-action. If person B wasn't doing any work, the path would no longer be circular and it would become a straight line path again.
You wrote-: "The object is always moving perpendicular to the direction B is pushing." That is correct, but it is a reflection of person B's effective work effort. In fact, if person B increases his push-force by working even harder, he will still always be perpendicular to the circular path, but now the circular path will have a tighter (smaller) radius. If that doesn't represent the result of increased work effort, then I do not understand simple Newtonian physics.
"An object moving in circular motion is at all times moving tangent to the circle; the velocity vector for the object is directed tangentially. To make the circular motion, there must be a net or unbalanced force directed towards the center of the circle in order to deviate the object from its otherwise tangential path. This path is an inward force - a centripetal force."
That section states that at every instantaneous moment in time an object in circular motion is moving at a tangent to a circle and the velocity vector is directed tangentially. Tangentially means that it is directed at right angles to the radius of the circle at the point on the circumference where the object is presently located. That means that if there was no centripetal force operant, the vector force would cause the object to travel in a straight line direction - towards point B. What causes the orbiting object to remain on the circular path, and move to point C, is the presence of an unbalanced force directed towards the center of the circle - a centripetal force.
You asked for credible evidence that the clubhead arc is more rounded than the hand arc.
I posted a strobe photograph of Bobby Jones which demonstrated that the hand arc is less circular than the clubhead arc.
I also posted this composite photograph that shows the clubhead arc (in red) and also shows the hand position at different time points. An imaginary line joining the hand position points would be less circular and more U-shaped.
Of course, there is the problem of camera perspective distortion due to the fact that the camera is face-on, while the clubhead/hand arcs are on an inclined plane.
I therefore produced the following down-the-line views of the clubhead arc and hand arc.
Clubhead arc
Hand arc
Note that the hand arc is more vertical than the clubhead arc. Therefore there will be there less camera perspective distortion with respect to the hand arc, and there is every reason to believe that the hand arc is U-shaped rather than circular.
Do you have any problem with the quality of the "evidence" that I am presenting?
You asked for credible evidence that the clubhead arc is more rounded than the hand arc.
I posted a strobe photograph of Bobby Jones which demonstrated that the hand arc is less circular than the clubhead arc.
I also posted this composite photograph that shows the clubhead arc (in red) and also shows the hand position at different time points. An imaginary line joining the hand position points would be less circular and more U-shaped.
Of course, there is the problem of camera perspective distortion due to the fact that the camera is face-on, while the clubhead/hand arcs are on an inclined plane.
I therefore produced the following down-the-line views of the clubhead arc and hand arc.
Clubhead arc
Hand arc
Note that the hand arc is more vertical than the clubhead arc. Therefore there will be there less camera perspective distortion with respect to the hand arc, and there is every reason to believe that the hand arc is U-shaped rather than circular.
Do you have any problem with the quality of the "evidence" that I am presenting?
Jeff.
My only problem would be calling the path of this clubhead "more circular" that the path of the hands (#3 pressure point).
If the hand arc is really as circular as your drew it, and as circular as the clubhead arc, how does HK's endless belt analogy work? According to the analogy, the machine has a straight line belt section with a pulley at the end. The release phenomenon occurs when the hands pass around the small pulley. If the hand arc is circular, then the idea of the endless belt system (as described by HK) becomes inapplicable. So, how does a random/late release phenomenon occur in a golfer who has a perfectly circular hand arc path?
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.
If the hand arc is really as circular as your drew it, and as circular as the clubhead arc, how does HK's endless belt analogy work? According to the analogy, the machine has a straight line belt section with a pulley at the end. The release phenomenon occurs when the hands pass around the small pulley. If the hand arc is circular, then the idea of the endless belt system (as described by HK) becomes inapplicable. So, how does a random/late release phenomenon occur in a golfer who has a perfectly circular hand arc path?
Jeff.
They are not perfect circles, because there is movement in the center of the arc via shoulder turn and axis tilt.
How can the club path in the downswing be more circular when the left wrist is cocked for a large portion of the downswing (shrinking the radius from shoulder to clubhead) while the left arm remains straight (maintaining the radius from shoulder to hand)?
Notice that YodasLuke used #3 to mark the spline while you used the butt end of the club.
Last edited by Hennybogan : 12-28-2008 at 09:37 PM.
Bernt
The fact that the object is changing direction means that there is a force present that is causing that change of direction. If a force is present and causing a change in the direction of the object's path, then it is doing work by moving the object in another direction.
Jeff,
d Work/dt (work per time unit, power) = A * B * cos(ab),
A = centripetal force,
B = distance per time unit (speed),
ab = angle between force and speed = 90*
cos(ab) = Zero.
Work per time unit is zero at all times as far as the centripetal force is conserned. Therefore total work is zero.
Hybrid Mode
