HOW DOES A TIGHTROPE WALKER DO IT?
[picture from nytimes.com]
There are three answers. First, they manage their fear. second, they have good balance as the result of practicing for long hours. And third, they lower their center of gravity, or center of mass. In this activity, we build our own amazing tightrope walker.
CENTER OF MASS
[fromhttp://ruina.tam.cornell.edu/Book/] Many calculations in mechanics are greatly simpliﬁed by making use of a system’s Center of Mass. In particular, the whole complicated distribution of near-earth gravity forces on an object is equivalent to a single force at the object’s center of mass. An object can be moved in any direction by applying a force at the center of mass.
The center of mass of a body does not always coincide with its intuitive geometric center, and one can exploit this freedom. Engineers try to design a sport car center of gravity as low as possible to make the car handle better. The center of mass of a boat must be low enough for the boat to be stable. Any propulsive force on a spacecraft must be directed towards the center of mass in order to not induce rotations. Tracking the trajectory of the center of mass of an exploding plane can determine whether or not a massive object hit it. Any rotating piece of machinery must have its center of mass on the axis of rotation if it is not to cause much vibration.
The center of mass respects any symmetry in the mass distribution of a system. If the word ‘middle’ has unambiguous meaning in English then that is the location of the center of mass.
Locating the center of mass of an arbitrary 2D physical shape [from wikipedia.org]
INSTRUCTIONS FOR TIGHTROPE WALKER
1. Tie one end of the long string to a fixed surface such as a doorknob. Hold the other end of the string so that the string is taut. Try to balance the tightrope walker (roller J ). It should be impossible because the Center of Mass is so high that the slightest tilt from vertical enables gravity to slam the figure off balance.
2. Tie one end of long string to doorknob. Tie one end of short string to end hole of #14 cross beam. Put two #4 beams on top of the weight element. Run the short string through center holes of two #4 beams on the weight element and tie to other end of cross beam. Place tightrope walker on the long string and hold the other end of the string to keep it taut. It doesn't fall! Try inclining the string so that the walker rolls up and down the string. The weight lowers the Center of Mass and balances it under the walker. Now any slight tilt in the weight is constrained by the strings so that gravity actually helps to rebalance the walker.
3. Untie or cut off the short string attached to the weight element. In the Klutz book, a coat hanger is hung through the three center holes of the tightrope walker. Try it. The walker should still fall over because the Center of Mass is still too high. Gradually pull the hanger’s flat wire into a diamond shape, which lowers the Center of Mass. How much deformation is needed to lower the Center of Mass underneath the tightrope string?