Question #1:
You are driving to a birthday party with a friend. You have a helium balloon suspended between you two in the front seat, not quite touching the ceiling. The road takes a sharp turn to the left, causing you and your friend to feel you are being pushed toward the right. Does the balloon lean toward you, or toward your friend?
Question #2:
You have a toilet, whose water jets are directed straight down the sides of the bowl, so that when you flush, the jets do not impart any rotation to the water going down. When you look down at the water flushing, in which direction does the water spin when you are in Ohio? In Austrailia? If you were at the North Pole?
Question #3:
A 33 foot tall hallow pipe is capped on one end, turned upright, and filled completely with water. Two sensitive pressure guages indicate the pressure near each end. You note that the bottom pressure is almost 15 psi higher than at the top. I take you and the device up in a helicopter, and drop everything from 5000 ft altitude. While falling, you ponder if there has been any change in the pressure gauges. What do you think in this situation?
Bonus: For how many seconds do you think you can remain focused on this problem, starting from when I drop you?
Extra bonus for showing back up at the helipad after I've done my part!
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Answer #1
The balloon leans toward the inside of the car’s curve, the opposite of everything more dense. The air in the passenger compartments is heavier than the balloon, so it has stronger force throwing it to the outside. By buoyancy, the lighter helium balloon is pushed out of the way, and “floats” to the inside of the curve. Try it the next time there’s a helium balloon left over from a party. It’s counterintuitive.
Answer #2
The water flushes clockwise in the northern hemisphere and counter clockwise in the southern, due to the coriolis forces on it as the earth spins. However, to assist vortex formation, toilets are not designed to release water straight down, but rather at an angle. This rotation can be stronger than the coriolis force, making your geography less a factor. The downside is that if you talk about coriolis forces, and you spend your Rio vacation studying toilet bowl flushing, your girlfriend will have left you.
Answer #3
The pressure would be the same at the top as the bottom. While in free fall, the water does not have a pressure gradient with depth. Just like if I stand on your shoulders when we are stationary on earth, you feel my full weight, but if we jump from an airplane in such a configuration, you no longer feel my feet crushing your shoulders as we free fall.
Bonus Answer #3
Well, if you oversimplify the problem and ignore air friction as you fall, you will have about 18 seconds to do your pressure gauge observations. This answer is too low though, because air resistance will slow you down until you reach terminal velocity. At the other end of the approximation, if you did not assume a streamlined position, your terminal velocity would be about 120 mph, or about 176 ft/sec. If you fell at that speed you would have a full 28 seconds, so your pressure observation notes could be written more neatly. Truth be told, you won’t achieve terminal velocity immediately, so the real answer is less than 28. This at least tells us an upper and a lower bound, so you have twenty-something seconds.
Extra bonus answer
If you take a parachute, you can turn in your data in person, rather than making us walk all the way out to the impact site to retrieve your notes. Better still, you could arrange for an underclassmen to assist in the data collection.
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