If you drop a light object and a heavy object from a tower, which one will reach the ground first? As you may remember from high school physics, this is a trick question. Neglecting air resistance, they both fall in the same way and reach the ground at the same time; gravity means that their speed increases by 9.8 square meters per second, regardless of their mass.
This is the idea behind Galileo Galilei’s Leaning Tower of Pisa experiment, a classic thought experiment in the field of dynamics.
Dynamics is the specialty of physics that studies motion and force. A “dynamicist” who studies dynamics can do anything from improving a basketball player’s free throw ability to designing spacecraft for interstellar travel.
As a dynamicist, I have spent much of my career helping students understand modern dynamics. The Leaning Tower of Pisa experiment is a good way to do this. It can explain how classical mechanics, the field that engineers and educators use every day, was brought into the modern world.
Galileo’s Leaning Tower of Pisa experiment
The Leaning Tower of Pisa experiment led to the interesting realization that objects fall with the same acceleration regardless of their mass. So what happens when you place objects of different masses on a flat table and push each one with the same force?
Even if we don’t take friction into account, the accelerations of the objects are now different. Lighter objects accelerate more than heavier ones. Their accelerations are the same when falling, but different when sliding.
Now let’s put the two objects into orbit. Imagine that one of them is the Sun and the other is the Earth. In classical mechanics, the Sun exerts a force on the Earth equal to the force that the Earth exerts on the Sun.
However, the Sun is very large compared to the Earth. Shouldn’t the magnitude of the force of a larger object be greater? And having said that, how come the magnitude of the force of the Sun on the Earth is equal to the magnitude of the force of the Earth on the Sun?
Heavy and light objects have equal accelerations when falling, but different accelerations when sliding, and objects in space apply equal gravitational forces to each other despite having different masses. This all seems inconsistent and a little confusing, right?
modern mechanics
The above problems were caused by the uncertainty in the concept of force in classical mechanics. In classical mechanics, a force is an interaction between two objects and involving both objects. The magnitudes of the gravitational forces exerted by the Sun and the Earth depend on the mass of both objects. Power has never emanated solely from the Sun or solely from the Earth; regardless of the other.
But modern mechanics (physics of light, atoms, quantum mechanics and curved space-time) has changed this concept of force. The modern force of the Sun and the modern force of the Earth are two separate forces and, excluding relativistic effects, depend only on their respective masses.
In modern mechanics, force is now the action of an object, not the interaction between objects. It is viewed as a force field radiating outward from its source, decreasing in magnitude as it moves away from its source. Modern mechanics is a field theory; It deals with objects and the accelerations created by their force fields.
So what happened to the interaction force? Was it thrown away? The answer is no, but it is no longer the most basic definition of force. In modern mechanics, the interaction force, represented by the letter F, is defined in terms of the impact force field, represented by the letter P. The interaction force is now the impact force P times the mass m on which P acts, which is F. =MP.
Newton’s second law of motion, a fundamental part of classical mechanics, makes the interaction force F of an object equal to the product of the object’s mass m on which it acts and its acceleration, that is, F = ma. The modern version sets the impact force P so that one object is equal to the acceleration of the other object, i.e. P = a. When we multiply P = a by m, we get F = ma.
Note that this is not about the mathematics in classical mechanics being wrong, but rather about the fundamental force being a force of action, not an interaction force.
contemporary thought
Modern thought reinterprets Galileo’s Leaning Tower of Pisa experiment, sliding blocks, the Earth’s orbit around the Sun, and interactions in general.
In Galileo’s Leaning Tower of Pisa experiment, light and heavy objects were falling due to the impact force of the Earth, which did not depend on the masses of the falling objects, so their accelerations were naturally the same.
The same interaction forces acted on light and heavy objects sliding on the smooth table. However, the fundamental forces (action forces) are different, so their accelerations are naturally different.
In the Earth’s orbit around the Sun, the forces of influence of the Sun and the Earth are no longer equal. The impact force of the Sun, with its large mass, is proportionally greater than the force of the Earth, as intuition suggests.
Science takes many years to develop as it comes closer to revealing the nature of reality. We can see this in the evolution that led to modern mechanics; here scientists now embrace a theory of force fields that, although almost contrary to common sense, predicts the dynamics of objects.
This article is republished from The Conversation, an independent, nonprofit news organization providing facts and authoritative analysis to help you understand our complex world. The Conversation is trusted news from experts. Try our free newsletters.
Written by: Larry M. Silverberg, North Carolina State University.
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Larry M. Silverberg does not work for, consult for, own shares in, or receive funding from any company or organization that would benefit from this article, and has disclosed no relevant affiliations beyond his academic duties.