# Difference between the inertial and gravitational mass

by ZirkMan
Tags: gravitational mass, inertial mass
 P: 136 I'm trying to learn what is the difference between the inertial and gravitational mass. According to: http://www.physlink.com/education/askexperts/ae305.cfm and http://www.physicsforums.com/showthread.php?t=147282 there is practically no difference (as stated by the Equivalence principle) other than the method to find it out. Does that mean for example that when on the Moon the gravity is six times weaker than on the Earth I can with the same force accelerate an object to six times the speed as on the Earth? And then when in a freefall orbit where there is no gravity I can accelerate arbitrary massive object to any speed because it doesn't have any gravitational and thus inertial mass (following the Equivalence principle)? That doesn't make sense, does it? Then how can be the gravitational and inertial mass the same?
 P: 1,506 'And then when in a freefall orbit where there is no gravity ' This statement is not correct
P: 136
 Quote by technician 'And then when in a freefall orbit where there is no gravity ' This statement is not correct
Ok I could say: In deep space far away from any gravitational source. Would that make a difference?

P: 1,506

## Difference between the inertial and gravitational mass

Well yes, you must not equate 'free fall' with the absence of a gravitational force.... free fall is due to a gravitational force.
If you have an object with mass ('amount of stuff') m kg and exert a force F newtons on it then it will accelerate given by a =F/m. This has nothing to do with gravity, it is to do with Inertia..... hence inertial mass.
If you have one mass close to another mass then there is a force of attraction and an acceleration (if they are free to move) and the same equation F = ma gives the answer. This indicates that Gravitational mass and inertial mass are the same thing. I am sure there is more to it than this but I hope this makes some sense !!!.
Also your statement about the Moon is not totally correct: gravity is 6 times weaker than on Earth therefore the downwards acceleration of gravity is 1/6 of that on Earth.
To accelerate a mass m horizontally on the Moon needs exactly the same force (for the same acceleration) as on the Earth
P: 136
 Quote by technician Well yes, you must not equate 'free fall' with the absence of a gravitational force.... free fall is due to a gravitational force.
You are right that the free fall as in an orbit is possible due to gravity but again according to the equivalence principle you should not be able to distinguish (unless you look out of a window) if you are in a free fall or in a deep space away from gravitational sources (but this is off-topic and more general relativity stuff).
 Quote by technician To accelerate a mass m horizontally on the Moon needs exactly the same force (for the same acceleration) as on the Earth
OK, this is what I needed to know. Makes sense now.

So even in an environment with no measurable force of gravity (wherever it is :) objects will resist motion with a force equivalent to their inertial mass.

But then when the inertial mass (measured by horizontal movement in a gravitational field) is absolute in a way that it doesn't depend on strength of surrounding gravitational field how can it be the same as gravitational mass which is relative and its value changes with the surrounding gravitational field?
How can a constant be equal to a relative value?
 P: 1,506 You are getting a bit deep for me.... I would say that the FORCE changes with the gravitational field not the mass..... but I could live to regret saying that
P: 136
 Quote by technician You are getting a bit deep for me.... I would say that the FORCE changes with the gravitational field not the mass..... but I could live to regret saying that
No, I think this is actually right. The only way the statement that the inertial and the gravitational mass are equal can be right in the light of what you have said is that the gravitational mass doesn't change with the strength of the gravitational field. Only the weight changes. And my mistake was that I thought the weight = gravitational mass.

Then the only question that remains is: What is the gravitational mass?
 P: 1,506 Don't laugh !!!!..... it is the same as the inertial mass
P: 136
 Quote by technician Don't laugh !!!!..... it is the same as the inertial mass
No, it's the best answer in the moment!
I have learned something new today though.

Good question is why they are the same? But this is not the question I asked so no problem now.
I'm afraid the answer to that question is more deep than I can venture today. So thanks for help!
 P: 1,506 I have thought of something else! Use a spring balance to hold up 1kg.... it reads 9.81N.... we call this a gravitational force. Drop the 1kg and it accelerates at 9.81 m/s^2 Imagine pulling the 1kg along a horizontal frictionless surface with the spring balance reading 9.81N. If the acceleration was not 9.81m/s^2 it would be a strange world..... I would not be able to cope with it Nice chatting with you.
PF Gold
P: 10,793
 Quote by ZirkMan Does that mean for example that when on the Moon the gravity is six times weaker than on the Earth I can with the same force accelerate an object to six times the speed as on the Earth?
No. The object will take the same amount of energy to reach a given speed.

 And then when in a freefall orbit where there is no gravity I can accelerate arbitrary massive object to any speed because it doesn't have any gravitational and thus inertial mass (following the Equivalence principle)? That doesn't make sense, does it? Then how can be the gravitational and inertial mass the same?
Gravitational mass refers to the amount of force an object feels from a gravitational field and the strength of the field it puts out. If there were an object with half as much inertial mass as gravitational mass, then when a force is applied through gravity, the object will experience half the acceleration as it would if the force is applied through other means. (Such as a rocket accelerating itself)
To this day there has never been an observed difference between the two types of masses, meaning they are equivalent as far as they know.
Mentor
P: 14,246
 Quote by ZirkMan Then the only question that remains is: What is the gravitational mass?
In the sense, we don't know. Newton's law of gravity assumed gravitational mass (the masses in F=GMm/r2) is inertial mass (the mass in F=ma). General relativity makes this assumption explicit, but it is still an assumption.

Now compare gravitation to the other fundamental interactions. Physicists now have a very good picture of what charge is, how charged particles interact, and the mechanisms behind these interactions. The same cannot be said of gravitation. Finding that deeper explanation is close to the holy grail of theoretical physics. The holy grail would be showing how gravitation, the weak force, electromagnetism, and the strong force are fundamentally related. This has already been done for the weak force, electromagnetism, and the strong force. Gravitation is the odd man out.

 Quote by technician I have thought of something else! Use a spring balance to hold up 1kg.... it reads 9.81N.... we call this a gravitational force. Drop the 1kg and it accelerates at 9.81 m/s^2 Imagine pulling the 1kg along a horizontal frictionless surface with the spring balance reading 9.81N. If the acceleration was not 9.81m/s^2 it would be a strange world..... I would not be able to cope with it Nice chatting with you.
In order to help you cope with this strange world, I suggest that you only do this experiment at 45.5o latitude at sea level, where g=9.80665 m/s2. Don't try it at the north pole (g=9.832 m/s2) or at sea level the equator (g=9.780 m/s2). Don't try it in Mexico City (g=9.779 m/s2), and especially don't try it atop Mt. Chimborazo. I will not be held responsible for your loss of ability to cope.
 P: 239 If you jump off a cliff on the moon the force pulling down toward the center of the moon is 1/6 as strong as it would be on earth so obviously you wouldn't hit as hard if you jumped off the same cliff on the moon and then on the earth. But if you accelerated your car on a level track on the moon with maximum force of the engine assuming the tires don't slip you will have the same acceleration as you would if you repeated the experiment on earth. forces are vector quantities meaning vertical forces don't affect horizontal acceleration and horizontal forces don't affect vertical acceleration. But regardless of the directions of the forces and the accelerations they are always proportional to the mass of the object on which they act. So gravitational mass is nothing more than obtaining the mass of an object by using gravity as the force on it and the acceleration due to gravity, whereas inertial mass just uses other forces and their corresponding accelerations to determine the same mass. So regardless of what force causes the acceleration on the mass, the same force will cause the same acceleration when acting on the same mass.
 Sci Advisor P: 7,917 Newton's 2nd law for a particle is F=Ma. The right-hand side refers to how the particle moves when it feels a force. The inertial mass M is simply a constant of proportionality, like a choice of units. But the equation is meaningless unless we specify the left-hand side "force". If the mass has electric charge Q, and is in the vicinity of another charge P, then F=QP/r2. Now there is nothing that says that electric charge Q has to be proportional to inertial mass M. Gravity is like electricity, just a different sort of charge. Since it's just a different sort of charge, let's now take Q,P to be gravitational charge. The bizarre thing about gravitation, compared to electricity, is that Q of a particle is always proportional to its inertial mass M. Instead of saying gravitational charge Q, we say gravitational mass Q. But that's the idea - gravitational mass Q is a sort of charge, and generally charge has nothing to do with inertial mass M, except in the case that Q is a gravitational charge.

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