1. Your first new toy is a propeller-driven radio controlled airplane. You take it over to the store's internal airfield and begin to fly it around the cavernous building. Naturally, there is no wind. You soon find that you can make the airplane rise or fall simply by changing its speed. Even without changing the plane's tilt, you observe that speeding the plane up makes it begin to rise and slowing it down makes it begin to descend. Why does changing the plane's speed affect the forces on it and cause it to accelerate up or down?

Answer: The faster the plane moves, the more air it encounters each second and the faster that air move downward after being deflected downward. The plane must be pushing that increased amount of air downward harder, so the air pushes it upward harder.

Why: Doubling the plane's speed means that it encounters twice as much air each second and gives each kilogram of that air twice the donward momentum during their encounter. That's a total of four times as much momentum transfered each second. So the plane experiences four times the upward force from the air. Clearly, speeding up the plane leads to an increase in the upward force on the plane.

2. After flying straight for a while, it's time to turn. You dip the plane's left wing and raise its right wing, and the plane begins to accelerate (and turn) toward the left. What force is making the plane accelerate toward the left?

Answer: The lift force is pushing the plane toward the left.

Why: When the plane is tipped left-wing-low, the lift force it experiences is up and toward the left. The upward part more or less supports the plane against gravity (depending on how strong the lift force is) and the leftward part accelerates the plane toward the left.

3. The plane is once more flying straight and you decided to make it rise quickly. You tip its nose upward suddenly, hoping that it will begin to ascend. Instead, the plane practically stops in midair and falls. What happened to the airflow over the plane's wings and why did this cause the plane to decelerate so abruptly?

Answer: The airflow separated from the wings (created an air pocket behind the wings). The plane suddenly began to experience enormous pressure drag in the backward direction.

Why: The plane stalled. The airflow over each wing separated from that wing to form a huge air pocket behind the wing's top surface and producing pressure drag. The wing also lost most of its lift.

4. After tossing the pieces of your first plane into the recycling bin, you are soon flying your second plane. This time you're going for speed! You turn the throttle on full, but the plane will not go faster than about 100 mph. So you land it (successfully) and pick out an airplane that has a small jet engine. Once it's in the air, you put the throttle on full and the plane disappears from view before you have a chance to steer it. The store's air patrol finally catches up to it on the far side of the building, where it is flying straight-and-true at 300 mph. From the plane's perspective, the air passing it at a moderate distance is moving at 300 mph and has atmospheric pressure. Describe the speed and pressure of the air flowing into the inlet duct of the jet engine. (No need for exact values; just compare the two values with those in the normal airstream far from the plane.)

Answer: The air inside the inlet duct was moving slower than 300 mph and its pressure is above atmospheric pressure.

Why: The inlet duct of the jet is a diffuser and it allows the air to slow down and experience a rise in pressure.

5. You hop back on the bus and go over to the space port. You pick out a rocket which has a mass of 1 kg, of which 0.5 kg is fuel and 0.5 kg is the vehicle itself. The exhaust velocity—the speed at which the burning fuel emerges from the rocket's engine—is 3 kilometers-per-second. Neglecting air resistance and gravity, the rocket can end up traveling no faster than 3 kilometers-per-second in the direction opposite its exhaust. Explain briefly what sets this maximum speed.

Answer: If the rocket could eject all of its fuel at once and at the exhaust velocity, then one-half the original rocket' mass would be heading backward at 3 kilometers-per-second. To conserve momentum, the other half of the rocket (the vehicle itself) would have to be heading forward at 3 kilometers-per-second.

Why: The total momentum of the rocket was zero at launch and must be zero once its two halves were moving in opposite directions. If half the original rocket mass is heading one way at 3 kilometers-per-second, then the other half must be heading in the opposite direction at 3 kilometers-per-second. In reality, the rocket can't do this well because the fuel doesn't all travel at 3 kilometers-per-second backward.

6. In reality, the rocket starts to move before all of its exhaust is released. The fact that most of the backward-heading exhaust emerges from a forward-moving rocket reduces the rocket's maximum final speed. Why?

Answer: As the rocket picks up forward speed, its exhaust travels backward less quickly (according to spectators on the ground) and carries away less and less momentum per kilogram.

Why: Once the rocket is moving forward, the exhaust it sends backward comes from a forward-moving vehicle. Instead of moving backward at the full exhaust velocity, this fuel-from-a-moving-vehicle travels backward less quickly and is less effective at taking away backward momentum. Another way to look at this is that as the rocket picks up speed, the remaining fuel that it is carrying now has forward momentum invested in it. By throwing that fuel out the tail of the rocket, the rocket is wasting some of its precious forward momentum.

7. You launch two of these rockets simultaneously from nearly identical launch pads. The only difference is that one launch pad has a thick steel plate below the rocket before launch and the other has open space below the rocket before launch. At the moment of ignition, the plume of burning fuel from one rocket strikes the metal plate while the plume from the other rocket travels into open space. Despite this difference in launch pads, the two rockets rise to the same height in the same amount of time. Why did the steel plate make no difference? Wasn't that rocket pushing off the steel plate?

Answer: The rocket obtains thrust simply by pushing the fuel out of its tail. What that fuel does after leaving the rocket makes no difference.

Why: When the rocket pushes the fuel backward, the fuel pushes the rocket forward. What happens to the fuel after that isn't the rocket's problem.

8. Finally, you come to the liquid-fueled rockets and select one of the newest, highest-quality units. This rocket uses liquid oxygen and liquid hydrogen as its fuel, releases its exhaust at 5 kilometers-per-second, and is 90% fuel at the moment of launch—the vehicle has a mass of just 10 kilograms but carries 90 kilograms of fuel, for a total of 100 kilograms. When you launch it, the rocket ends up traveling much faster than 5 kilometers-per-second as it passes through the retractable roof of the building and heads off into space. Why isn't its maximum speed limited to its exhaust speed—5 kilometers-per-second?

Answer: Even though the fuel's average backward speed is less than the exhaust speed, it can carry away lots of backward momentum. If the remaining vehicle is only a small fraction of the rocket's original mass, then that vehicle will have to have an enormous forward speed to have enough momentum so that the sum momentum (vehicle plus fuel) is zero.

Why: When the vehicle is a small fraction of the rocket's original mass, its final speed must be very large for it to have as much forward momentum that the fuel has backward momentum.