Magician seeking help with deadly pendulum problem

[Rubin]

Hello Physics Forum!

My name is Adam Rubin. I am a magician and I write a monthly column called, Braindrops for Magic Magazine. I have a challenging physics problem on my hands that I thought you might find interesting. In 1926, a brilliant inventor named Stewart James published a trick called, "A Match for Gravity."

"The effect: A piece of string, about one meter 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 let's go of the match, the piece of string quickly winds around the pencil and suspends the watch in midair."

This is an incredible stunt and I encourage you to try it out for yourself. I have been experimenting with this principle for some time, using different lengths of string and varying objects on either end. Using only trial and error, I have discovered that two small keys on a key ring work quite well paired with heavier objects up to 200 g.

My goal is to discover a formula for this trick. Besides the weight of the two objects, other variables include; the length of the string, the angle of release, the circumference of the pencil, the material of the string, the number of times the string wraps around the pencil and perhaps some more that I don't even recognize.

I would love any guidance the Physics Forum can provide. If it would help, I can post a video of me performing the trick. There are many entertaining presentations possible for this simple stunt and if a solid formula was available, the trick could be done on a much larger more dangerous scale. The possibilities are very exciting. I hope I have piqued your interest and I look forward to your response.

Thank you in advance,
Adam

 

[benk99nenm312]

Mysterious... haha. But we are smart, we'll figure it out.

Does the watch stop running after you are done?

 

[Borek]

I think friction between string and the pencil is important - if there is no friction between them, watch would be wasted.

 

[flatmaster]

The wrapping occours because of conservation of angular momentum.

L = mvr
Where m is the mass of the object, v is it's velocity, and r is the leingth of string from the object to the pencil. We also have gravity, so this quantity isn't precisely conserved, but it illustrates the point. as the value of r decreases, the value of v increases, making the object wrap around the pencil. The classic example similar to this is a figureskater bringing their arms in close to their body to spin faster.

As for how the light object can suport the heave one after only a few wraps, there is an equation demonstrating this that I don't remember. However, I remember the ratio between the supported tention vs the "holding" tension is exponential, thus only a few wraps are required. it seems odd, but I remember the equation not depending on the coefficient of friction between the string and the rod. It's something like

T1 / T2 = e^(theta)

where theta is the total angle of wrapping. and t1 and t2 are the tensions on either side of the wire.

This was on one of the YouTube Walter Lewin lectures

 

[Creator]

This is an incredible stunt and I encourage you to try it out for yourself.

I'd be glad to give it a try, but this week I'll be performing my magic trick in India ; this week I'll be making the sun disappear on July 22nd...if you happen to be around the area, drop by and tell me what you think... it'll be visible to those in India, Nepal. and Bangeladesh.

Creator

( Warning: Kids under 15, don't try this one at home without parental supervision...very dangerous).

 

[negitron]

Meh, I've seen that one. He hides the Sun up his sleeve.