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The task of the ball with helium in the car

 

 

Imagine that you are in a car where a balloon filled with helium is tied to the floor. The windows are closed. You push the gas pedal. What happens to the ball: will it move forward, backwards or will it remain in the same position?

 

What happens to the ball?

 

  • Move back against the movement;

  • Move forward in motion;

  • Will remain in place.

 

car

Intuition suggests that when accelerating, the balloon will be thrown back. However, we are wrong in this situation. Your task is to determine how the ball actually moves and explain it to the interviewer with the help of deductive argument.

 

A pretty nice solution is to suggest an analogy with the spirit level. Despite the fact that this thing is not always at hand when needed, there are still people who use it constantly. The spirit level has a narrow glass tube with coloured liquid and an air bubble inside. Each time a spirit level is placed on a perfectly horizontal surface, the bubble is in the middle of the tube. If the surface is not horizontal, the bubble moves toward the higher part of the tube. The analogy here is that a bubble is just a “hole” in a liquid. When the surface is not even, gravity pushes the fluid toward the lower edge. In turn, this moves the bubble to the opposite edge where there is no liquid.

 

Untie the balloon and let it hit the roof. Now it will become a kind of level. A ball is a “bubble” consisting of helium and a gas with a lower density in denser air. All this combination of gases is stored in a car. Gravity pushes heavier air downward, forcing a ball to press on the roof.

 

When the vehicle accelerates, air and your body are thrown backwards. It forces a more lightweight balloon moving forward. If you sharply press the brakes, the air will press on the windscreen, but the ball will be thrown back. You can face the same situation when cornering. In this case, the centrifugal force pushes the air in the direction opposite to the rotation axis, and the ball is pushed in its direction. Surely, the same thing happens when the balloon is tied to something, but now it has less freedom to move. Thus, the short solution to this challenge is the following: a helium balloon shifts toward the acceleration direction.

 

You do not believe? Then go to the supermarket right now, buy a helium balloon, and tie it with a rope to the gear shift lever or to the parking brake lever. Then go home and conduct a test. You will be shocked, but the ball really shifts in a different direction you could not even think about. When you accelerate, the ball rushes forward.  Press the brakes coarsely and you will see that the balloon moves back. When twisting at high speed, your body is shifting strictly in one direction, but the balloon moves sharply in the other. You can watch many videos on YouTube about this strange fact.

 

Why does our intuition suggest us the correct solution about the spirit level, but the wrong one about a helium ball? Considering the spirit level, the inside heavy liquid is painted with fluorescent paint, while the bubble in it is almost colourless. We associate the colour with density, and transparency with emptiness. Accordingly, this instinct appears to be completely wrong in the case of a helium ball. The ball is painted in a pretty colour and looks like shouting: “Look at me!” We all forget that there is always a partial vacuum in the surrounding air. A helium ball shifts in the opposite direction to the bulk movement because it lacks weight. The real mass (air) remains invisible.

 

Interviewers giving this task do not expect to face a good knowledge of physics from your side. There is an alternative task version which is based on the principle of relativity. Let’s take a closer look at it.

 

This principle is related to the famous mental experiment of Albert Einstein in terms of the elevator. Imagine that you are in an elevator and going to the office. At that moment, someone decides it would be fun to teleport the elevator with you into intergalactic space. The elevator is an enclosed space, so there is enough air to stay alive for a while. The elevator does not have windows, so you cannot see where you are. This person tied the elevator to the cable and pulls it with constant acceleration, completely equal to the Earth’s gravity. Here is the question: can you define whether you are influenced by the actual Earth acceleration or by gravity?

Einstein suggested that no. If you would pull the keys out of your pocket and toss them, they would fall on the floor as is usually the case. Moreover, in case you would tie a helium ball to a rope, it would rush up as usual. Put it simply, you will not find any strange things in the elevator.

 

Einstein’s principle of equivalence states that there is no simple physical experiment that can show the difference between gravity and acceleration. This hypothesis is central in Einstein’s theory of gravity, known as the general theory of relativity. Physicists have been trying to find failures in the principle of equivalence for almost a century. Finally, they failed. Consequently, we can state without any doubts that Einstein’s idea is correct, at least for any experiments that you can conduct with a ball for only $2.

 

So, here is a physical experiment. Tie the rope to the lead weight on one side, and to your right-hand index finger on the other. Tie a helium balloon to the same finger. Pay attention to the angle between those two ropes.

 

You will face completely the same results in a parked car and in a crashing jet plane. The rope with the tied load will be directed straight down, the ball’s rope will be directed straight up. Consequently, the two ropes tied to your finger will form a straight line. You will face such a situation each time you are exposed to gravity. 

 

Now, let’s take a look at what will happen when you start moving. With increasing speed, your body will be pushed into the seat. When the car is subjected only to gravity, two ropes form a straight line. However, when they are affected by centrifugal forces or another type of acceleration, an angle with your finger as its peak is formed. That’s all you need to prove that the general theory of relativity is wrong. In case this happens, you should forget about your desire to get a job at Google because your ambitions will increase sharply to receive the Nobel Prize.

 

However, the principle of equivalence has been rigorously and regularly tested and its correctness has always been demonstrated. For this reason, the mentioned-above option will not happen, and you can use the principle of equivalence as the solution for this challenge. Physics will manifest itself in exactly the same way in both an accelerating car and a gravity subject vehicle. In both cases, the ball, your finger and the lead load will form a straight line. All in all, we can conclude that the helium ball really moves in the opposite direction to the expected movement of an object with mass. In other words, it will shift forward, not backwards, to the left, not to the right, and up, not down.


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