Swinging Tray

__Difficulty: 4 out of 10__

**Materials:**

· Pizza tray

· Plastic cups filled with water

**Procedure/ observation:**

1. Fill the cups with water and place them evenly on the tray

2. carefully begin to swing the tray in a circular fashion. (Sway it left and right first and then while gaining speed make a full circle) 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.

3. BE VERY CAREFUL WHEN STOPPING THE SPINING

**Explanation:**

**F**=

_{c}**mv**/

^{2}**r**, where

**F**= centrifugal force,

_{c}**m**= mass,

**v**= speed, and

**r**= radius.

ESIMATE:

cup has mass of 0.35 kg,

radius of the circle is 0.35 meters

rotational speed is 6 meters per second

radius of the circle is 0.35 meters

rotational speed is 6 meters per second

During this step, the water in the cup is experiencing a force downward due to gravity.

Fg= ma

Fg= ma

**F**= 0.35 (kg) * 9.8 (m/s_{g}^{2}) = 3.43 (N)When the demonstrator swings the tray in a circle, there is still a force downward due to gravity. We calculated this force is 3.43 Newton’s. 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 6 Newton’s. 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**= {0.35 (kg) * {6.0 (m/s)}_{c}^{2}}/ 0.35 (m) = 6 (N)
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