You are a passenger in a car that is driving down the highway at 100 km/h (60 mph). You are sitting in the right-rear seat and all the windows are closed tightly. The air flowing around the car makes a sharp inward bend as it travels around the windshield and past the right-front window (the front window on the passenger-side of the car). By the time this air flows past your window, it has straightened out and is traveling almost directly backward toward the rear of the car.
1. When your friend in the front passenger seat opens his window a little, your ears pop due to a drop in the car's air pressure. However, when you then open your window a little, the pressure in the car rises back toward normal atmospheric pressure. Explain why (a) opening the front passenger-side window caused a sudden decrease in the car's internal air pressure, and (b) why opening your window caused that pressure to increase back toward atmospheric pressure.
2. With both windows slightly opened, in what way is air circulating through the car? Use this result to explain why it is that when you friend throws his gum wrapper out the front-right window, it comes back inside through the back-right window and hits you in the face. (Good thing it was just the wrapper!)
3. You now open your window completely and stick your right hand out into the passing stream of air. With your palm facing directly forward, into the onrushing wind, you feel a tremendous force pushing your hand toward the rear of the car. What is this force, and why does it occur?
4. You now tilt your hand so that your palm is facing forward and somewhat downward. You feel a new force that makes your hand feel lighter and it almost floats upward of its own accord. What is this force you feel, and what causes it?
Traveling to mars is a challenge, in part because getting there takes so long. If we could speed up the space ship, travel time would be less of a problem. One possibility is the VASIMR engine, an engine that uses radio waves to heat its exhaust so hot that the exhaust leaves the engine at 300 km/s (about 700,000 mph). A normal rocket exhaust speed is only 4 km/s, so the VASIMR engine exhaust travels about 75 times as fast as normal engine exhaust.
5. Explain why each kilogram of exhaust ejected at 300 km/s provides 75 times as much thrust as each kilogram of exhaust ejected at 4 km/s. (We are assuming a specific amount of fuel use each second.)
6. Calculating exactly how fast a rocket will travel after ejecting all of its fuel as exhaust is complicated by the fact that the rocket's speed changes while its engine operates. For simplicity, suppose that a rocket could eject all of its fuel at once, while the rocket is still at rest. Now suppose that the total mass of the rocket consists of 1 part spaceship and 10 parts of fuel. Explain why the spaceship portion of the VASIMR rocket would reach a final speed of 3,000 km/s.
7. The VASIMR-powered rocket must be careful not to eject its fuel too quickly because that would injure the astronauts on board. Why would sending out too much fuel each second at the 300 km/s exhaust speed of the VASIMR engine injure the astronauts? (Note that this question has nothing to do with radiation sickness problems or anything like that.)
8. Getting to mars is one thing; stopping for a visit and then returning to earth is another. If the rocket needed to be 10 parts fuel to 1 part rocket in order to move quickly enough to travel past mars in a short amount of time, what would it have to be (in terms of parts fuel to parts rocket) to reach mars in a short amount of time, stop for a visit, and then return to the earth in a similar short amount of time, and stop here?