10 Feb, 2013
In a cup
PRESENTATION: In a circular movement the variation of the speed of an object implies the presence of acceleration, accounting for the change of modulus and direction of the speed.
- Shapes of bubbles and drops in motion, James O’Connell, Phys. Teach. 38, 232 (2000)
INTRODUCTION: A glass containing a ball inside is agitated by turning it with the correct frequency, the ball will spin faster as the turning speed increases. This situation serves to illustrate the phenomenon of resonance and the synchrotron principle, a type of elementary particles accelerator where an applied alternating voltage of increasing frequency accelerates the particles while keeping their orbital radius constant.
OBJECTIVE: To make the ball go out of the glass counterbalancing the force of gravity by spinning the glass.
MATERIALS: a glass of transparent plastic, a small ball.
SETUP: Introduce the ball in the glass, and place it on an even surface. Make the ball rotate inside the glass by spinning it with a circular movement on the surface, whose frequency is increased continuously. If the rotating speed is high enough the ball climbs the glass walls until it jumps out of it.
EXPLANATION: The ball may escape the glass because its forms an angle a with the vertical. If the rotation angular speed of the ball w exceeds the value w0=[(g/r)tana]1/2, then than ball is able to climb the wall as the normal component of the force is directed upwards and exceeds the force of gravity, pointing downwards. So, in order to make the ball escape the glass it must be spinned with a frequency higher that the threshold value f=w0/2π. In the former equation, r represents the difference between the upper radius of the glass and the ball radius, and g stands for gravitational acceleration.
CONCEPTS: angular speed and acceleration, centrifugal and centripetal forces, gravity force, synchrotron, cyclotron, frequency, resonance.
- Tipler P.A. Física. Barcelona: Reverté, 2010.
- De Juana J.M., Física General, Pearson, 2009.
- Serway R.A y J.W.Jewett. Física. Madrid: Thomson-Paraninfo, 2010.
- R. Ehrlich, Turning the World Inside Out and 174 Other Simple Physics Demonstrations, Princeton University Press, 1997.
STUDENTS 2011-2012: Eloy Barcia, Jaime Castineira, Cristian Chapela, Marta Fernández
LINK pdf STUDENTS (in Spanish):