# Are energy and acceleration related?

1. Dec 8, 2014

### avito009

As we know mass-energy equivalence. But is acceleration also related to energy?

If I am inside a jet which has acceleration of 30 m/s2. So the gravitational acceleration is 9.8 m/s2. So we divide 30 by 9.8. We get 3 approx. This means that the pilot is 3 times more heavier when flying the jet.

So here acceleration is linked to mass. So what is relation of acceleration with that of mass? Is acceleration same as energy?

2. Dec 8, 2014

### Orodruin

Staff Emeritus
The mass of the pilot is the same regardless of the acceleration. The force required to give the pilot this acceleration is not.

3. Dec 8, 2014

Staff Emeritus
No, it doesn't. Why don't you write down an equation for the mass of the pilot in symbols? You can't just say "OK, we'll add this, and multiply that..." - try writing down the expression for what you are calculating.

4. Dec 8, 2014

### sophiecentaur

You seem to be mixing up Relativistic and Classical Ideas and terms here. What level of answer do you want?

5. Dec 9, 2014

### avito009

I want a beginners level explanation. (Laymans terms).

6. Dec 9, 2014

### Staff: Mentor

I'm not sure what else there is to say -- is there anything specific in the above explanations you had trouble with?

7. Dec 9, 2014

### sophiecentaur

You seem to be confusing Mass with Weight, for a start (as everyone does, at first). Only under extreme conditions will apparent Mass be effected but Weight (the force that you experience when you are standing on the ground) will be affected (at least, your apparent weight). If you are on a platform that is accelerating upwards, you will 'feel' heavier and bathroom scales will tell you that your weight is significantly increased, possibly. Your mass is not affected in an aeroplane, though.
This ties in with F =ma when you realise F is the weight force for a given mass m and a is the acceleration (which is totally the equivalent to and indistinguishable from the gravitational acceleration g)
The "Mass - energy equivalence" has nothing to do with this. It involves Relativity, which is best approached once the Classical stuff is sorted out.

8. Dec 9, 2014

### ovais

What will happen if you in your jet is moving towards earth with an acceleration of 30m/s^2. Will you consider you mass negative?
Since you want to define mass as net force acting on you divide by magnitude of acceleration due to gravity(as apparent from your conclusion) if you and your jet is moving down towards earth with acceleration(if acceleration just a bit greater than acceleration due to gravity(9.8m/s^2)you will rather experience an upward force giving you a feel that you lose your mass greater than you possessed before. And reduce to negative mass.

9. Dec 12, 2014

### avito009

Weight of an object is usually taken to be the force on the object due to gravity. So if you go to the moon and your weight on Earth is 90 kg's. On the moon your weight would be 14.94 kg's. Since gravitational acceleration on the moon is lesser than the Earth, Earth =9.8m/s2, Moon= 1.6249 m/s2 . This means lesser the acceleration, lesser weight you would feel increasing. If the aeroplane is moving forward you would be pushed backwards and so since its accelerating 3 times the 'g' you would feel your weight 3 times more than rest mass.

10. Dec 12, 2014

### ovais

Correct
Correct

Wrong!! Weight is force due to gravity on which you yourself is agree and you must not dilute this fact by simply saying lesser the acceleration lesser the weight instead the correct statement would be lesser the acceleration due to gravity lesser will be the weight.

But if you care more for force(normal reaction force in this case) than you should say lesaer the acceleration lesser will be the force(net force) not weight.

If you do not get it feel free to ask more :-)

11. Dec 12, 2014

### Orodruin

Staff Emeritus
There is a confusion here and I believe it is based on your unit of force. Weight is a force and therefore measured in the SI unit Newton (1 N = 1 kg m/s^2), while kg is a unit of mass. You cannot measure mass in units of force or vice versa. You will sometimes see forces in units of kg-wt, which is simply the weight of 1 kg in standard Earth gravity, i.e., 1 kg-wt ≈ 9.8 N. Now the weight of an object on the Moon would be smaller by a factor of around 6 and thus a 1 kg mass would have a weight of 1/6 kg-wt on the Moon. However, this is due to the lower gravity on the Moon and its mass would still be 1 kg.

It should be added that the easiest way of avoiding this confusion is to simply not use the kg-wt unit and stick to the SI system of units.

12. Dec 18, 2014

### bmrick

Ugh, I think this is all being made more complicated than necessary. When you're accelerating, there is a force keeping you pushed into your seat. This force can be considered to be weight, since it has all the same attributes as weight. But weight and mass are not synonymous. Weight is a measure of that force pushing you up, mass is a measure of how much" stuff you're made off" if you want a simple definition. If you want a precise definition, it's the force of the seat pushing against you divided by the acceleration you are experiencing, and classic experiments show this value to be constant at all but relativistic speeds I.e. speeds greater than 50 percent light speed.

13. Dec 18, 2014

### bmrick

Wow I intended that to sound less complicated. I eat my words.

14. Dec 18, 2014

### 256bits

That is not the way to say it when talking scientifically.
Sure, your bathroom scale may be marked off into units of kg's, but that is only for the general population ease of use.
The bathroom scale measures force, which are newtons, in SI units.
The manufacturer has translated the force into kg's, which people are more familiar with.

Take your earth scale to the moon, and weigh yourself. It will register less force.
to make a moon scale, the manufacturer will have to re-calibrate, ( ie mark off the kg units differently) to give you the mass.
The force(newtons) has changed, but the mass(kilograms) has not.

15. Dec 18, 2014

### Orodruin

Staff Emeritus
Weight is the force pulling you down. The force from the ground on your feet is what is pushing you up.

This is not a definition and "stuff" is not a very physical statement, it is more of an interpretation. There are different masses in classical mechanics that turn out to have the same value:
• Inertial mass: Defined as the resistance of an object to acceleration. If you push an object of inertial mass m with force F, it will have acceleration a = F/m.
• Gravitational mass: Defined as the strength with which gravity acts on an object. If an object of gravitational mass m is placed in a gravitational field of strength g, the resulting gravitational force on the object is F = mg.
Now, experimentally these turn out to be equivalent, resulting in ma = mg, or a = g.

First of all, your choice of 50% is completely arbitrary. If you want to bring relativity into the game, its effects are there also at lower velocities, they are just negligible. When you have to start taking relativistic effects into account depends on how much precision you require. Second, neither of the definitions of mass from classical mechanics is really a good one in special relativity. A priori, there is no gravitation involved and the inertia of an object depends on its velocity and the direction of motion relative to the force. When we talk about mass in special relativity, the most accepted definition is simply the energy content of an object in its rest frame. For small velocities, this turns out to be equivalent to its inertia up to corrections suppressed by v^2/c^2. See also our https://www.physicsforums.com/threads/what-is-relativistic-mass-and-why-is-it-not-used-much.783220/#post-4919337 [Broken].

Last edited by a moderator: May 7, 2017
16. Dec 18, 2014

### jsrds

I think so because weight is the force pulling object down. The force from the ground on object is what is pushing object up.

17. Dec 18, 2014

### Staff: Mentor

The original poster's question has been answered, and the thread is starting to ramble. Time to close it.