1. The first version of the balloon floats at the end of two ropes, which are attached near the head’s ears. With that placement of the ropes, the head pivots easily and keeps tipping over. The hat makes the head top-heavy. Your teammates keep trying to put the hat above the head, but it only stays there for a few seconds before the head tips over again. Your whole team is quite demoralized. (A) Use concepts relating to equilibrium to explain briefly why the hat stays on top for a few seconds and then the head flips upside-down. (B) Use concepts relating to acceleration and potential energy to explain briefly why the balloon tends to flip upside-down.

2. To solve the flipping problem, your team initially adds a heavy weight to the bottom of the balloon. They hope to counterbalance the hat. Unfortunately, the weighted balloon doesn’t float at all. You propose an alternative solution: attach another rope to the bottom of the head. You’ll be able to use this extra rope to actively stabilize the head’s hat-on-top equilibrium. Your scheme works! Each time the head starts to turn over, a good downward pull on the new rope returns the hat to the top. Why does this technique work?

3. To test the canvas balloon for leaks, you fill it with ordinary air. Fortunately, it proves to be airtight. You then replace the air with helium at the same pressure and temperature. Compare the number of individual air particles the balloon contains when it is full of air to the number of individual helium atoms the balloon contains when it is full of helium.

4. The properly inflated helium balloon floats nicely in air. You realize as you watch it float that there are a number of different densities present in the situation: the density of the air, the density of the helium, the density of the canvas, and the average density of the entire balloon (both canvas and helium). Put those four densities in order, from lowest density to highest density.

5. The cartoon character’s trademark activity is squirting water out between its teeth. Your team decides to reproduce this effect by sending water up to the balloon through a clear tube and letting that water pour out of the balloon’s mouth. After a little construction, you are able to get a steady flow of water pouring down from the balloon—steady-state flow. You note that in this situation, the water’s total energy-per-liter doesn’t change as it travels up through the pipe, out through the mouth, and back down toward the ground. Identify the changes in form that the energy undergoes as it rises and falls in this situation, ignoring air resistance and frictional effects in the tube. Also, don't worry about what happens when the water finally hits the ground.

6. With the tube full of water, the balloon is having some trouble floating. Someone suggests doubling the amount of helium gas in the balloon--pumping in twice as many helium atoms while leaving the balloon's volume unchanged. Unfortunately, this scheme won’t make the balloon float better. (A) Why won't it help the balloon float? (B) Why might it cause the balloon to pop?

7. Another person suggests replacing all the helium gas in the balloon with hydrogen gas. An individual hydrogen molecule weighs approximately half as much as an individual helium atom. This person claims incorrectly that hydrogen gas can lift twice as much weight as helium gas. Explain briefly why a certain volume of hydrogen gas does not have twice the lifting capacity of an equal volume of helium gas.

8. You solve the floating problem by using a narrower tube for the water, so that it doesn’t weigh as much. However, this narrower tube doesn’t carry as much water per second as the wider tube did. To compensate, you raise the total energy of the water in the tube. That scheme works and your float is a great success. Give a simple explanation for why this rise in total energy per liter makes more water flow through the narrow tube.