David slaying Goliath

Fig1 show clearly what happens. When the 1ball mass is eventually drawn close to the pivot it very rapidly wraps around it and arresting the vertical downward motion of the 100 ball mass. The question is why and how ?

Figs 2 to 5 shows more in detail the time history of some key parameters. Notice from Figs 1and 2 that the 1ball mass just barely manages to stop the 100ball mass before it reaches the pivot. Figs 3 and 4 show how the angular velocity and the centrifugal force very suddenly increase when this occurs. Fig 5 shows clearly how the big mass at the end rapidly surrenders all of its kinetic energy to the small mass.

So what is happening in laymen terms ?

Goliath confidently pulls on the cord, dragging David without any mercy towards the pivot. However, David, slowly but steadily, starts developing increasingly a larger centrifugal force but in addition starts using Goliath's force to his advantage. As Goliath reduces the swing radius of David, the centrifugal force of he latter increases. As a result Goliath has to do increasingly more work on David to pull him in, increasing his kinetic energy, resulting in more velocity and hence even more centrifugal force, resulting in more work done on David, resulting in more velocity, hence increasing the centrifugal force, etc., etc.. There is a positive feedback mechanism acting explosively till Goliath is depleted of all its kinetic energy. (in the math model the cycle than reverses). The resulting peak centrifugal force at the end becomes very large indeed as can be seen from Fig4.


mandrin