Quote:
Originally Posted by savydan  Awesome. One question in general:
You chose a 49 inch shaft.
If the shaft was 39 inches or shorter, then the propagation time would be less than 4 ten-thousands of a second.
So, on that basis, would the heavy mass come into play? Is it as simple as "all or nothing" depending on the length of the shaft?
In other words, if we cut that shaft inch by inch after each hit, would we reach a point where the heavy mass has a major effect? |
savydan,
When you want to keep it simple there will invariably be someone asking some very pertinent question concerning the more difficult aspects of the problem.
I will try however to give some plausible image how to view the behavior of the shaft as it behaves when impacted.
Look at the animation - a slender piece of material is approximated as consisting of small masses connected by springs. Imagine the heavy mass m1 and the clubhead mass m2 to be attached respectively at each end. Furthermore m3 is being impacted by the ensemble of m1, spring, and m2.
When impact occurs there will be a disturbance starting to travel through the spring. On a slower time scale the springs will start to compress longitudinally till eventually they form a compact solid mass and only then a full force can be transmitted along the shaft.
Hence you can see that for very small time intervals the shaft decouples both end but on a larger timescale it behaves as a truly solid mass being able to fully transmit a force applied at either end. In between we are dealing with complex dynamic transient effects quite difficult to analyze.
When I slowly sink into a swimming pool there is no resistance whatsoever. If I miss a dive however it starts hurting and water seems to less user friendly. If some one has the funny idea to dump me from a helicopter into a swimming pool the water behaves rather more like a solid. Hence the world around us depends strongly on the timescale used.
It is exactly for this reason that I used - ‘temporal dimension’ - as title for my post.
I might be tempted just for fun to analyze it further mathematically using the mechanical model as shown in the animation.
