Tim Pennings: Physics in the sauna
Tim Pennings explores fascinating physics puzzles and their surprising solutions. He breaks down why throwing an anchor lowers a lake's water level, why a helium balloon moves forward in an accelerating car, and why wet sand is firm, offering a fun look at everyday science.
A while back, I wrote a column, “Mathematics in the Sauna.” (Find it and all previous columns at timothypennings.blogspot.com.) Since physics is equally interesting with its own collection of surprises, here is its counterpart.
Try this: You are in a rowboat on a lake. When you throw the anchor out of the boat into the water, will the level of the lake go up, go down, or stay at the same level?
Of course, practically speaking, any difference would be negligible. But a physicist wants the pure answer — no matter how insignificant.
So, what’s the answer? Think about it — and commit yourself, before continuing.
As with many puzzles, we can visualize the solution by considering an extreme case. It also helps to think about this one in reverse. Suppose you have a dishpan containing a heavy rock and filled with water, and a Styrofoam bowl floating on the water’s surface. What happens to the level of the water if you take the rock out of the water and place it in the bowl? The weight of the rock will cause the bowl to sink further into the water, causing the water level to rise. This is because, while in the water, the rock only displaces its volume, but when placed in the bowl, it displaces its weight.
Conversely, taking the rock/anchor out of the bowl/boat and dropping it into the dishpan/lake will cause the water level to go down. Did you get it right?
If not, this one is similar — a second chance: You are sitting in a stationary car, windows closed, and holding a helium balloon on a string in front of you. What happens to the balloon as you accelerate the car forward? Will the balloon bend towards you, bend away from you, or continue floating straight up?
To answer, first consider what would happen to a ball in the car hanging from a string? We’d see it bend backwards because its mass (inertia) tends to keep it still as the car moves forward. Would the balloon do the same? Nope! It does the opposite, since it is lighter than the air around it. Compared to the lighter-than-air balloon, the air molecules (like the ball) move backwards, causing the balloon (like a bubble in shampoo) to move forward. Give it a try sometime — it’s very noticeable.
Another? The Earth revolves around the Sun rather than the Moon, so the force of gravity from the Sun must be greater than from the Moon. Given that, why does the moon have a greater effect on tides?
Answer: The tides are caused by the difference in gravity’s pull on the closer ocean water versus on the solid Earth beneath it. And the difference in gravity is more noticeable from the moon because the moon is closer to the earth.
Coming down to earth a bit, here is a puzzle that Einstein asked a friend when they were walking together on a beach. When we walk on completely dry sand, or sand underwater, our feet will sink into the sand. But when we walk on damp sand at the water’s edge, the sand forms a firm surface on which we can walk without sinking. Why?
Einstein’s answer: As we learn in high school chemistry, water molecules on the water’s surface form sideways bonds with other surface water molecules, and there are no competing bonds with water molecules above them. All of those sideways bonds give rise to surface tension — which is why spiders can run across the surface of the water. (You can also very carefully lay a needle on the surface of water.)
Turnabout is fair play. Someone once asked Einstein a puzzle: Why (as was determined by the Milliken Oil Drop Experiment) does each electron have the same charge as every other? Good question! Einstein’s answer: I don’t know – why are all rabbit pellets the same size?
Finally, a question I heard on NPR’s "Car Talk" years ago. Which is worse? To crash head-on into an identical car going the same speed in the opposite direction, or to crash into an immovable wall. These two MIT grads initially claimed the crash into another car was worse, but I knew they would change their minds. Sure enough, the next week they corrected themselves. In both cases, the front atom of the car comes to an instant halt, and the rest of the car collapses into it. Same result. Don’t try this one.
— Tim Pennings is a resident of Holland and can be contacted at timothy.pennings@gmail.com. Previous columns can be found at timothypennings.blogspot.com.
