In this section we talk about two problems that are particularly good problems for stimulating discussion about mathematics and modeling. Actually the two problems are mathematically the same. We are looking at one mathematical problem in two different settings.
The two pictures below show two cylindrical tanks. The picture on the left shows the start of an experiment. The tank on the right is almost filled with water and the tank on the left is empty. The two tanks are connected by a pipe at the bottom and the tank on the right has an open spigot at bottom. Water will flow from the tank on the right onto the floor and into the tank on the left. The picture on the right shows the situation after a short time. There is a puddle on the floor and some water in the tank on the left.
We are interested in the following question --
Will the water level in the tank on the left always be lower than the water level in the tank on the right?
The picture below shows a electrical circuit with two capacitors and two resistors. At the beginning of the experiment there is a charge in the capacitor on the right and the capacitor on the left has no charge at all. After a short time some of the charge in the capacitor on the right will have flowed into the ground and some will have flowed in the capacitor on the left.
We are interested in the following question --
Will the charge in the capacitor on the left always be lower than the charge in the capacitor on the right?
Before going on spend some time thinking about this question. You have two tasks.
