Elevator Problem

Puzzles are famous, and all of us have come across them at some point. They are featured in movies, TV shows, and hold a place in popular culture. Some remain unsolved, while others are more ethical dilemmas than true puzzles (like the trolley problem). Similarly, there are unsolved questions in mathematics and physics. When I was a child, I used to have books full of such brainteasers, and solving them with my mother was one of my greatest joys. She would be so happy if she managed to solve one.

As I grew older, I drew away myself from such things, but every now and then, when I come across one, I still think about it or simply try to understand the answer. Today, I want to share with you a brainteaser that is not only a test of intelligence but also a real-world physics problem.

This idea came from a YouTube video by a physics professor. I asked for their permission to adapt it into a written piece, and thankfully, they kindly agreed to my request. I follow their content and genuinely enjoy it. You can watch from here:

Let the Problem Begin

Now, imagine you are living in an eight-story building. Let’s say there are two elevators in the building, and you are a resident on the fourth floor. You step out of your apartment to grab something, and you notice that the first elevator is on the ground floor, while the other is on the eighth floor.

Here’s the question: Which one should you call to save more energy? Which elevator consumes less energy? If you’re someone who cares about the environment, this is a logical question to ask. Is it more reasonable to call the first elevator or the second one? Or perhaps it doesn’t matter which one you call, making that the third option.

Hint and the Atwood Machine

Here’s a small hint: Recall the pulley systems and the Atwood machine you studied in physics. Think about them, and you might be able to find the answer. Take a moment to reflect and come to a conclusion.

A pulley is a simple machine that makes our daily tasks easier. It allows us to accomplish more with less force. Increasing the number of pulleys further divides the force and makes things more interesting. The Atwood machine I mentioned above consists of two objects with different masses connected by a non-elastic, weightless string. Ignoring friction, we can observe uniform acceleration, as the acceleration here is due to gravity. No motion occurs if the two masses are equal and the system is ideal. This system was used to demonstrate Newton’s second law.

How an Elevator Should Work

Returning to the question, and understanding this information makes it much easier to guess the answer. Isn’t an elevator a cabin moving up and down within a shaft? If we want to make it more energy-efficient, wouldn’t we design it similarly to an Atwood machine? In an Atwood machine, bringing the masses closer in value reduces energy consumption.

Elevators use a counterweight attached to the other side of the pulley system. Let’s denote the empty mass of the elevator cabin as mmm, and the counterweight as m′m’m′. The choice of the counterweight is critical here. It cannot be too small because the elevator won’t move properly in that case. The counterweight must at least be equal to the cabin’s weight. Since people use elevators, the average weight of the cabin, including passengers, will generally exceed its empty weight. That means m′>m. This design ensures long-term efficiency.

As a result, lifting an empty cabin upward is easier than lowering it downward.

Answer to the Problem:
Calling the elevator on the ground floor is more logical because lifting an empty cabin is easier. This might seem counterintuitive at first, as we often assume that moving something downward requires less effort.