27 Apr, 2012
In a seesaw
PRESENTATION: Most unstable systems present some risks that make them unsuitable or not recommended for a laboratory, although their study is of great interest. One solution to solve this paradox is the system constituted by a motorized seesaw and a ball. This a classical system used to explain control engineering, and it is well known because despite its simplicity it serves as an example of many models in this area. In this case, we will not use an engine, but an oscillatory movement.
- Hanging-Picture Instability, Bruce Denardo and Richard Raspet, Phys. Teach. 43, 298 (2005)
INTRODUCTION: The operation of this project, relying on the dynamical equilibrium of a ball on a seesaw, is based on the periodic movement created by the mass distribution of the system. The forces acting on the ball placed in the uneven seesaw are its weight and the normal force, if the friction is ideally considered negligible. The weight, which can be divided in normal and tangential components, causes the displacement along the seesaw, and makes it turn at the same time. As the angle of the seesaw with the horizontal changes, the resulting force acting on the ball changes as well, producing a harmonic oscillatory movement that would go on indefinitely in an ideal case and whose projection on a plane would be a simple harmonic movement. Nevertheless, the friction makes it impossible for the system to complete more than three oscillations.
OBJECTIVE: To obtain at least two oscillations of the ball in the described system.
MATERIALS: two tubes of hard plastic for the seesaw, two elbow joints, wood cubes of different sizes, two balls, screws, adhesive tape, glue.
SETUP: Use the larger cube of wood as a base, and place the smaller cube on it. Construct the seesaw with the elbow joints, the screws and the two plastic tubes. The ball will move over the rail formed between the two tubes.
EXPLANATION: The experiment tries to obtain a dynamic equilibrium in the ball-seesaw system, and in optimal conditions it can produce three oscillations. Form a theoretical point of view, if the equilibrium is attained, the movement should go on indefinitely, but getting this in real conditions is impossible. The searched equilibrium may be obtained only if the ball starts the movement at a certain distance x from the center of the seesaw according to the equation:
x=0,189 A L (M/m)1/2
where A is the angle in radians between the seesaw and the horizontal, L is the seesaw length, M its mass and m that of the ball.
CONCEPTS: equilibrium, simple harmonic equilibrium, equilibrium bar.
- F. Beer, J.J. Johnston, Mecánica vectorial para ingenieros, Mc Graw-Hill, 2005.
- S.M. Lea, J.R. Burke, Física. La naturaleza de las cosas, Thomson, 1999.
- W.F. Riley, L.D. Sturges, Ingeniería mecánica, Reverté, 1999.
- R. Ehrlich, Turning the World Inside Out and 174 Other Simple Physics Demonstrations, Princeton University Press, 1997.
STUDENTS 2011-2012: César García, Iván Garrido, Andrés Gilsanz.
LINK pdf STUDENTS (in Spanish):