If a force of $10\,\mathrm{N}$ is applied to different objects of different mass in empty space, in the absence of gravity, why do lighter objects accelerate faster than heavier objects? Why does mass cause inertia?
[Physics] Why does mass limit acceleration
accelerationforcesinertiamassnewtonian-mechanics
Best Answer
I do not think it is mass that "CAUSES" inertia. Rather mass is DEFINED to be the property of an object which gives it inertia
For example, imagine that you were a theoretical observer who did not know of the concept of mass. There were just 3 objects in front of you. You applied $10 \mathrm{N}$ to each object and observed that the different objects accelerated at a different rates. One accelerated at $1 \mathrm{m}/\mathrm{s}^2$. Others at $2\mathrm{m}/\mathrm{s}^2$ and $4\mathrm{m}/\mathrm{s}^2$ respectively. So, you can conclude that the different objects have some property that determines how much they accelerate under a given force. You would also notice that there was a linear relationship between the force on a body and its acceleration.
Now, you can calculate what would be the value of this property. And you can see that the body that accelerated at $1 \mathrm{m}/\mathrm{s}^2$ would have a higher value of this property than the one that accelerated at $4 \mathrm{m}/\mathrm{s}^2$.
The theoretical observer can see that this property is directly related to what people call "heavier" and "lighter" objects. So, it is safe to conclude that lighter objects accelerate faster than heavier objects.
To summarise, the reason lighter objects accelerate faster than heavier objects is because that is how we have defined the terms "lighter" and "heavier".
Mass "causes" inertia, because that is how we have defined "mass".
If you want to further ask, why objects with different values of this "mass" property accelerate differently, then you are asking a more fundamental 'why' question. And like most fundamental why questions in physics, it boils down to , because those are the laws of physics in our universe. And if you want to ask why are the laws of physics like that, the answer is " because of the initial conditions at the Big Bang. And researchers are working to figure this out "
EDIT : As some comments have pointed out, there is also the quantum mechanics aspect of this.
All particles get their inertia or the "tendency to resist motion under a force", through the way the fundamental particles interact with the Higgs field.
To understand why massive objects have inertia, we need to understand where the mass of objects comes from. We know that all massive objects are made up of atoms. So, atoms give objects their mass. But where do the atoms get their mass from?
Atoms are made up of protons and neutrons (and electrons but they have negligible mass). So, protons and neutrons give atoms their mass. But where do protons and neutrons get there mass from ?
According to the standard model, protons and neutrons are made of quarks. So, quarks should be giving atoms their mass, right ? WRONG.
Quarks have substantially smaller and lighter mass than the protons and neutrons that they comprise. It is estimated that the masses of the quarks, derived through their interaction with the Higgs field, account for only about 1% of the mass of a proton, for example.
So, 99% of the mass of a proton is not to be found in its constituent quarks. Rather, it resides in the massless gluons that bind together the quarks inside the proton. These gluons are the carriers of the strong nuclear force, that pass between the quarks and bind them together inside the proton. These gluons are "massless" but their interaction with the Higgs field is what we experience as mass.
So, at a quantum level , the Higgs field ‘drags’ on the gluons , as though the particle were moving through molasses, (Another analogy used is moving through a crowded dance floor) . In other words, the energy of this interaction is manifested as a resistance to acceleration. These interactions slow the particles down, giving rise to inertia which we interpret as mass.