




The information below is intended to provide a description of the demonstration,
an explanation for elementary students, and further explanation for
high school students.
Please keep in mind that not all demonstrations are presented
at each show.




SWINGING TRAY






Figure I.


Figure II.


Figure III.




Equipment:

Metal pizza tray, attached on the edge at three places with a string.
The strings all come together at a point above the tray and are wound together.
Plastic cup

Step 1:

The plastic cup is filled with water and placed on the tray. (See Figure I.  Food coloring has been added to show the water.)
The demonstrator asks if it is possible to get the cup upside down without spilling the water.

Step 2:

The demonstrator carefully begins swinging the tray in a circular fashion. (See Figure II. and Figure III.)
Remarkably, the water is not spilled!
As an aside, it is actually quite easy to swing the tray without spilling the water, the difficulty arises when the demonstrator tries to stop swinging the tray.




Basic Ideas:

At the Earth's surface, all objects experience a downward force due to gravity. This force depends on the object's mass:
the greater the mass, the greater the force.
An object traveling in a circle behaves as if it is experiencing an outward force.
This force, known as the centrifugal force, depends on the mass of the object, the speed of rotation, and the distance from the center.
The more massive the object, the greater the force; the greater the speed of the object, the greater the force; and the less distance from the center, the greater the force.

Step 1:

During this step, the water in the cup is experiencing a force downward due to gravity.
The cup does not fall, however, because it is being supported by the tray.

Step 2:

When the demonstrator swings the tray in a circle, there is still a force downward due to gravity.
But this time, when the tray is upside down, the cup is no longer being supported by the tray.
The water does not fall, however, because it is experiencing an upward force due to its circular motion.
This force is great enough to cancel out the force due to gravity.




Basic Ideas:

At the Earth's surface, F_{g} = mg, where F_{g} = force due to gravity, m = mass, and g = gravitational acceleration.
F_{c} = mv^{2}/r, where F_{c} = centrifugal force, m = mass, v = speed, and r = radius.
To perform the calculations we have estimated that the water in the cup has mass of 0.40 kg, the radius of the circle is 31.5 inches, which is 0.80 meters, and the rotational speed is 5.0 meters per second.

Step 1:

During this step, the water in the cup is experiencing a force downward due to gravity.
We calculate this force (see calculation below) to be 3.92 Newtons.
The cup does not fall, however, because it is being supported by the tray.
F_{g} = 0.40 (kg) * 9.8 (m/s^{2}) = 3.92 (N)

Step 2:

When the demonstrator swings the tray in a circle, there is still a force downward due to gravity.
We calculated this force is Step 1 to be 3.92 Newtons.
During this step, when the tray is upside down, the cup is no longer being supported by the tray.
The water does not fall, however, because it is experiencing an upward force due to its circular motion.
The centrifugal force is calculated (see calculation below) to be 12.5 Newtons.
This force is more than great enough to cancel out the force due to gravity.
The fact that the centrifugal force is much greater than the force due to gravity is not surprising.
This additional force creates tension on the string which is felt by the demonstrator and allows him to control the swinging motion.
F_{c} = {0.40 (kg) * {5.0 (m/s)}^{2}}/ 0.8 (m) = 12.5 (N)



The following physics topics are discussed during this demonstration:



Sponsored by the Physics Department and the Center for Science, Mathematics, and Engineering Education  University of Virginia
