by If you drop a light object and a heavy object from a tower, which one reaches the ground first? As you may recall from high school physics, this is a trick question. Neglecting air resistance, they both fall the same way and reach the ground at the same time – gravity means their speeds increase at 9.8 meters per second squared, regardless of their mass.
This is the basis behind Galileo Galilei’s Leaning Tower of Pisa experiment, a classic thought experiment in the field of dynamics.
Dynamics is the specialization in physics that studies motion and force. A “dynamicist,” a person who studies dynamics, can do everything from improve a basketball player’s free throws to help design spacecraft for interstellar travel.
As a dynamicist, I have spent much of my life helping students make sense of modern dynamics. One good way to do this is the Leaning Tower of Pisa experiment. He can explain how classical mechanics – the field used by engineers and educators every day – was brought into the modern world.
Galileo’s Leaning Tower of Pisa Experiment
As a result of the Leaning Tower of Pisa experiment it was curiously observed that objects fall with the same accelerations regardless of their mass. But what happens when you place objects of different masses on a flat table and push each with the same force?
Even without accounting for friction, the accelerations of the objects are now different. The lighter objects sharpen more than the heavy ones. When they are falling, their accelerations are the same, but when they are sliding, they are different.
Let’s now put the two objects into orbit. Imagine that one is the Sun and the other is the Earth. In classical mechanics, the Sun exerts a force on the Earth equal in magnitude to the force exerted by the Earth back on the Sun.
But the Sun is huge compared to the Earth. Shouldn’t the size of the larger object’s force be greater? While we’re at it, how could the magnitude of the Sun’s force on the Earth be equal to the magnitude of the Earth’s force on the Sun?
Heavy and light objects have equal accelerations when falling but different accelerations when sliding, and objects in space exert equal gravitational forces on each other despite having different masses. This all seems inconsistent, and a bit confusing, right?
Modern mechanics
The above problems arose from an ambiguity in the concept of force in classical mechanics. In classical mechanics, a force is an interaction between two objects, which are related to each other. The magnitudes of the gravitational forces exerted by the Sun and the Earth depend on the mass of the two bodies. The force has never been only the Sun or the Earth regardless of the other side.
But modern mechanics – the physics of light, atoms, quantum mechanics and curved space-time – changed this concept of force. The modern force of the sun and the modern force of the Earth are two separate forces, and they depend only on their own mass, excluding relativistic effects.
In modern mechanics, force is now an action of objects, not an interaction between them. It is seen as a field of force radiating out from its source, which grows smaller the further it is from its source. Modern mechanics is field theory – it deals with objects and the accelerations created by their force fields.
So what happened to the interaction force? Was it discarded? The answer is yes, but it’s no longer the most basic definition of force, either. In modern mechanics, the interaction force, represented by the letter F, is defined in terms of the action force field, represented by the letter P. The interaction force is now the action force P times the mass m on which P acts , so F. = mP.
Newton’s second law of motion, a fundamental part of classical mechanics, sets the interaction force F about an object equal to the mass m the object acts on multiplied by its acceleration, so F = ma. The modern version sets the force P acting on an object equal to the acceleration of the other object, so P = a. When P = a is multiplied by m we get back F = ma.
Note that it wasn’t about math in classical mechanics being wrong – but more about the fundamental force being an action force and not an interaction force.
The modern thinking
Modern thinking reinterprets Galileo’s Leaning Tower of Pisa experiment, the sliding blocks, the Earth’s orbit around the Sun – and interactions in general.
In Galileo’s Leaning Tower of Pisa experiment, the light and heavy objects were falling due to the action force of the Earth, which does not depend on the mass of the falling objects, so their accelerations are naturally the same.
The same interacting forces were acting on the light and heavy objects sliding on the smooth table. But the fundamental forces – the forces of action – are different, and so their accelerations are naturally also different.
As the Earth orbits the Sun, the forces of action of the Sun and the Earth are no longer equal. The force of action of the Sun, with its enormous mass, is proportionally greater than that of the Earth – as intuition suggests.
Science takes many years to evolve as it gets closer to uncovering the nature of reality. This is seen in the evolution that led to modern mechanics – where scientists now accept the theory of force fields predicting the dynamics of objects, despite it being almost counter to common sense.
This article is republished from The Conversation, a non-profit, independent news organization that brings you facts and analysis to help you make sense of our complex world.
It was written by: Larry M. Silverberg, North Carolina State University.
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Larry M. Silverberg does not work for, consult with, own shares in, or receive funding from any company or organization that would benefit from this article this article, and did not disclose any relevant connections beyond their academic appointment.
