The magic of science     

“A Match For Gravity”  1926

In the September issue of The Linking Ring in 1926, “A Match For Gravity” became the first Stewart James trick to officially see print.
        
Effect:  A piece of string, about one metre long, is tied to a kitchen match. The other end of the string is fastened to a watch borrowed from a spectator. The performer holds an ordinary lead pencil horizontal to the ground in one hand while holding the wooden match in the other hand. After the end of the string with the attached watch is draped over the pencil, and the end with the match is pulled taut, the spectator’s watch is left dangling five or so feet above the ground. The magician then asks the audience what will happen if the match is released. The obvious answer is that the watch will hit the floor and break. But when the performer dramatically lets go of the match,the piece of string quickly winds around the pencil and suspends the watch in midair.
    
    
“A Match For Gravity” is an interesting illustration of centrifugal force but more particularly, and rather dramatically, of the shortening of the swing radius. Since both are of interest for serious golf  aficionados, I have translated this magicians trick into mathematics.  Instead of matches and watches, I have, more appropriately used golf balls. The ensemble is shown in Fig1.  
    
  

Anyone can do this experiment.  One golf ball attached at the end of a 1 to 1.5 m long cord and three others at the other end.  Drill perhaps a small hole through them to be able to pass a cord, or just tape them together at the end of the rope. Put a nail into the wall holding perhaps a little grooved wheel acting as a low friction support pivot for the cord.  Maybe inserting a small fish tension scale for the more serious experimenter. That is all that is required.
    
Before someone is going to insist that this is not golf swing I will be quick to congratulate him in advance with his extreme perspicacity.  Indeed it is not a golf swing. It is meant to be an illustration of a magician's tricks which might be of interest to the curious golfer genuinely interested in the physics principles present in a golf swing.
    
It is quite surprising but there are still many who simply discard centrifugal force from the outset as some form of fictitious force - considering it to be some form of magician's tricks somehow required to balance things in science. However in our experiment it obviously exists and moreover is also readily measured. Just insert a small fish tension scale just above the '3ball mass'. As shown below in Fig4 the force exerted on the 3ball mass is primarily due to the centrifugal force exerted on the cord by the rotating 1ball mass.

So what happens when we release the 1ball mass? This is shown graphically in Fig 2. Initially both masses fall almost freely downwards. However as soon as the 1ball mass starts developing some angular velocity it starts exerting a centrifugal force, transmitted along the cord,  which rapidly becomes much larger than its inherent gravitational force mg. Indeed a centrifugal force so large that it also exceeds rapidly several times the weight of the 3ball mass = 3mg, hence effectively decelerating and subsequently lifting it against gravity.   For comparison Fig 3 shows what happens when mass the 1ball mass is hanging down. At release the heavier 3ball weight then immediately starts falling down being heavier than the 1ball weight.

To get a better feel for what happens I have shown in Fig4 the magnitude of the centrifugal force vs time. The dashed orange line represents the gravitational force, mg, due to the weight of the 1ball mass. When the 1ball mass obtains its maximum velocity, passing the vertical, it is generating maximum centrifugal force. At that moment, for this particular configuration, the centrifugal force is, rather dramatically, about 19 times the gravitational force mg, due to its mass, primarily due to the shortening of the swing radius for the 1ball mass around the pivot.

Fig5 shows another view more clearly illustrating the shortening of the swing radius for the 1ball mass.



mandrin