Invite students to predict how changing the ball’s starting velocity (in magnitude or direction) will affect its path. This is a good opportunity for one or more student volunteers to participate.

Background

The surface of this “potential well" is shaped so as to model an inverse square gravitational force. When a ball enters the well enters the well, it is attracted to the center; if it has no initial velocity, it will fall directly to the center. But if it enters with some velocity tangential to the center, it will fall into an elliptical orbit that gradually decays to the center as the ball rolls around the well.

When you roll the ball across the surface, you use some initial force to start it moving. Once it is rolling on its own, though, the only forces acting on it are the force of gravity, pulling downwards, and the normal force and frictional force of the surface holding it up. So the ball accelerates as it rolls down the surface, exchanging potential energy for kinetic energy, until it falls into the hole.

Invite students to make predictions about the relationship between depth and pressure, and perhaps even sketch what they expect the graph of this relationship to look like. Then take a few data points and see what happens.

This set of conjoined glass tubes is filled with green-dyed water. The water level in the four different tubes is the same even though the volumes and shapes of the tubes are very different.

Engagement Suggestion

Background

This illustrates that the pressure in an open container of liquid is dependent only on the depth, not the shape or area.

Air enters the aspirator bottle, initially almost filled with water, through a tube inserted through a sealed stopper into the water bath, while the water leaves through a nipple near the bottom of the bottle. This arrangement provides a constant water pressure head, which is equal to the height of the water column between the nipple and the bottom end of the tube. Thus the water jet will have the same range as the water level in the bottle falls from its initial level to the level of the bottom of the tube.

The idea of this gizmo to provide water at a constant pressure, was first proposed by Edme Mariotte, a 17th century French scientist. A device called the Mariotte siphon, making use of this concept, is used in agriculture to provide irrigation at a constant flow rate and as a research tool in determining the properties of soil. His work is also cited in the Catholic Encyclopedia.

Q: When you remove the clamp, what will happen?: (a) the small balloon will get smaller and the large one larger, (b) the two balloons will become equal, or (c) they will stay the way they are.

A: The small balloon will blow up the larger one, and get smaller, due to surface tension effects. The rubber is thicker in a smaller balloon, and thus produces greater surface tension.