# Resistance to acceleration dependent upon mass or weight?

1. Dec 24, 2013

### inertiaforce

I am not a physics professional. I have just found an interest in physics on my own. My question is as follows:

Imagine a 50 pound weight here on earth. It's mass has a weight of 50 pounds in 1g gravity. This mass, weighing 50 pounds, has a certain amount of resistance to acceleration (inertia).

Now let's take this mass, which weighs 50 pounds, into an elevator, and have the elevator go into free fall. The mass would then be weightless and no longer have a weight of 50 pounds. Instead, it would have a weight of 0 pounds. Now that the mass weighs 0 pounds (weightless), does it become easier to accelerate?

Also, let's take this same mass and now put it into an upward accelerating elevator with an acceleration of 2g. This mass now weighs 100 pounds in this 2g gravity. Now that the mass weighs 100 pounds, does it become harder to accelerate?

2. Dec 24, 2013

### TumblingDice

Mass is invariant - always the same.

'Weight' is a variable attribute resulting from gravitational force and/or acceleration.

Mass is related *directly* to the amount of force required to accelerate it. The 'weightless' object in a free fall elevator will still retain its mass. If it has the same mass as you, and you push it as both of you are in free fall, you will accelerate backward at the same rate it accelerates away from you.

Weight is *relative* to the gravitational or accelerating force acting upon it. So weight is less on the Moon than on the Earth, and also in an elevator accelerating at a slower rate than a faster one.

3. Dec 24, 2013

### ShayanJ

I guess your confusion is because of the unit you're using.Pound seems to be a unit of both mass and force!
In accelerated frames,its the weight that changes.Also in places with different gravitational acceleration,its the weight which is different.And weight is a kind of force.
But inertia,or the resistance to acceleration,is because of mass which nor changes in an accelerated frame neither is different in places with different gravitational acceleration!

4. Dec 24, 2013

### TumblingDice

It requires more energy to have the same influence on the velocity of the mass. So, "Yes", is is harder to change/accelerate the mass at 2g.

When I was a lad in Michigan, one of the activities in muscle cars on Woodward avenue went like this: A \$20 bill (often higher) was placed on the dashboard in front of the passenger. When the traffic light turns green, the passenger wins the money if they can grab it before the driver hits 60 MPH. Naive passengers didn't realize how hard it was to grab the bill with the acceleration we could produce.

5. Dec 24, 2013

### inertiaforce

I am aware of the difference between mass and weight. Let me try to clarify my question.

Would the mass, when it weighs 0 pounds in a free fall elevator, have the same resistance to acceleration as it did when it weighed 50 pounds in 1g, or would it have less resistance to acceleration?

Also, would the mass, when it weighs 100 pounds in an upward accelerating elevator with a total gravity of 2g, have the same resistance to acceleration as it did when it weighed 50 pounds in 1g, or would have it more resistance to acceleration?

Because theoretically speaking, the mass should have less resistance to acceleration when it loses its weight, and more resistance to acceleration when it doubles its weight. But I have also heard that inertia, an object's resistance to acceleration, is dependent upon its mass, not its weight. So I'm a little confused.

Last edited: Dec 24, 2013
6. Dec 24, 2013

### Staff: Mentor

The same, in both cases.
The easiest way to think about it is to imagine that the floor of the elevator is frictionless (think smooth ice, or the surface of an air-hockey table). Now if I apply a sideways force to something sitting on that frictionless surface, it will accelerate sideways according to $F=ma$ no matter what the force in the downwards direction is.

7. Dec 24, 2013

### TumblingDice

Hmmm.... That really seems counter-intuitive. The same amount of force would add the same amount of kinetic energy, but it would represent a smaller percentage of total energy. If we took it to a further extreme, wouldn't a suspended object at 10g's resist sideways acceleration more than it would at 1g? How does it work?

8. Dec 25, 2013

### inertiaforce

So tumblingdice, you don't agree with Nugatory?

9. Dec 25, 2013

### TumblingDice

I don't feel qualified to disagree. This scenario can be viewed from different theories and terminology is important. It just sounds like Nug is saying that on a frictionless surface, I could push an elephant as easily as a mouse. It could be that the classical F=ma relationship should be treating 'm' as variant mass, but I have a bad feeling about suggesting that.

10. Dec 25, 2013

### Bandersnatch

No, he's saying that on a frictionless surface you could push an elephant as "easily" as if it was floating in free-fall. You'd still need a lot of force to impart the pachyderm with any significant acceleration because F=ma, and m is equally large in both cases.

11. Dec 25, 2013

### inertiaforce

Tumblingdice, I understand your confusion. I have been thinking about this myself. It appears that is exactly the case based on what Nugatory is saying. "You can push an elephant as easily as a mouse" lol. One of those "oh SH*T" moments. I am still trying to verify if this is actually correct though. I'm not sure if Nugatory realizes that what he is saying is that "you can push an elephant as easily as a mouse lol."

12. Dec 25, 2013

### TumblingDice

So a mass that weighs 20lb on the Earth's surface can be accelerated sideways as easily as the same mass that's accelerating in an elevator and indicating '40lbs'...? How is that different than a 20lb vs. 40lb weight on the Earth's surface? I'm sure I'm missing something. Please stick my nose in it. :)

13. Dec 25, 2013

### voko

Using correct terminology would help.

Mass is not resistance to acceleration, it is resistance to force.

Mass is an intrinsic property of bodies. Unless a body is modified, its mass stays constant.

Weight is a confusing concept because it is a measure of "gravitational force". This is not an intrinsic property of any body and the meaning of it depends on the definition and even the manner of measurement.

It may have no meaning at all, for example, in general relativity, there is no "gravitational force" so there is no weight.

In more traditional physics, weight is sometimes defined as the magnitude of the force of reaction that keeps a body stationary with regard to its support. This can be measured directly with a scale. If the support, i.e., the scale (and the body on it) is made to accelerate, the scale registers a different weight. Obviously, this is not a very useful definition because of this. Yet this is precisely the definition that is used when one speaks of "weightlessness".

Another more traditional definition simply assigns to any body a weight that is equal to its mass times the local acceleration of gravity. This is not measurable directly, so this is a rather abstract concept.

14. Dec 25, 2013

### inertiaforce

Tumblingdice, I have come to a strange thought experiment. Imagine a tennis ball in your hand. The tennis ball weighs, say 1/10th of a pound in earth's 1g gravity. Now, imagine you go into an elevator that accelerates upward at 1000g. The tennis ball now weighs 100 pounds.

It appears that the tennis ball, although now weighing 100 pounds, can still be thrown with the same resistance to acceleration that it had in earth's 1g gravity. "move an elephant as though its a mouse" lol.

Here on earth, the only reason a 100 pound weight resists acceleration more than a 50 pound weight is because the 100 pound weight has more MASS. The resistance to acceleration, and the weight, of the 100 pound object are because of its MASS. This means that resistance to acceleration appears to be MASS based, and not weight based. If you increased the weight of the object by increasing the gravitational field strength, the resistance to acceleration would not increase because resistance to acceleration (inertia) is MASS based, not weight based. Am I right Physicsforums? Is this what you are saying Nugatory?

Last edited: Dec 25, 2013
15. Dec 25, 2013

### TumblingDice

well, I stepped out onto the patio for a cigarette hoping someone would have posted words of illumination. Then I read Wikipedia mass / weight /acceleration. The answer seemed to be what Nug and Bandrsnatch are saying, but not clear enough for me to tell. First, regarding Wiki, they say mass is constant (of course) and will always deliver the same inertial 'bump' for example a person on a swingset, with or without gravity. Going on to say that mass will always react identically in kinetic/recoil, mass, velocity types of scenarios. But then I'm thinking well, of course, everything in the reference frame is on equal terms whether stationary or accelerating. But what if we just used a compressed spring to exert an identical force?

In another direction, while I was on the patio, I tried to think back to velocity and vectors and acceleration and treat the elevator scenario as a moving object. When the elevator isn't moving, a force of let's say 'three' units applied sideways for one second accelerates the object to 3 feet per second. Now let's get the elevator moving upward and at the point it's moving 4 ft/sec vertically, we push our object again with 'three' units for one second.

Now I know I'm about to mix static measurements with dynamics, but if the object accelerated sideways at three feet per second as before, wouldn't that make the true acceleration greater because we're looking at something traveling in two directions - like a 3x4x5 right triangle the actual would be the hypotenuse. (?) So IOW, the same force would actually accelerate the object less sideways, because the vector addition would need to be three feet per second along the hypotenuse...?

Mentors - please don't penalize me for just being naive or not thinking as well as I should.

16. Dec 25, 2013

### TumblingDice

Took another break and had some egg nog this time - 20 min 'til Xmas here in Califonia. Everything makes more sense now.

It's the 'perpendicular' aspect I think I wasn't focusing on. Acceleration in any other direction will also work according to force calculations, because they must consider the gravitational (or acceleration) force as well. So it would be more difficult to accelerate upwards in the moving elevator, but likewise it would be easier to accelerate downwards. (Using difficult and easy in terms of required force for a given acceleration.) And it's exactly the same force required *when* it's perpendicular.

Am I back in Kansas now?

17. Dec 25, 2013

### inertiaforce

You know from life experience that a 100 pound object is harder to accelerate than a 50 pound object. Why is it harder to accelerate? Because it has more weight. Why does it have more weight? Because it has more mass. Therefore, it appears that mass is what's causing the resistance to acceleration, not the weight. Every object that has more weight also has more mass. We don't know of objects having more weight with less mass in a given gravitational field.

Here's another thought experiment. Take an object that weighs 100 pounds in earth's 1g gravity. Now take another object that weighs 100 pounds in 2g gravity. Both these objects have the same weight of 100 pounds, but they have different mass. That's why it took 2g gravity to give the second object a 100 pound weight, but only 1g gravity to give the first object a 100 pound weight. The reason for this is the difference in mass between the two objects. Although they weigh the same in their respective gravity fields, they won't resist acceleration the same because the 2g object has half the mass as the 1g object. The 2g object would therefore be easier to accelerate than the 1g object because the 2g object has half the mass of the 1g object. This means we have two objects that both weigh the same 100 pounds, but accelerate at vastly different rates from one another. Does this sound right?

18. Dec 25, 2013

### voko

Which it would. Correct so far.

Not the "true" acceleration, but total acceleration. There is nothing wrong with the object's having the total acceleration greater than the sideways acceleration.

The total acceleration is not entirely due to the sideways force, so its magnitude need not be the same as if only the sideways force acted on it.

Perhaps a simpler example. Forget gravity. You have a frictionless flat horizontal surface. You apply 3 units of force in the direction of North. The acceleration is 3 units. You apply 4 units of force in the direction of East. The acceleration is 4 units. Now, if you apply both forces simultaneously, the total force will be 5 units in the direction of North-East by East, and the total acceleration will be also 5 units in the same direction.

It would not be any more difficult to accelerate the object Eastward just because it is accelerating Northward.

19. Dec 25, 2013

### voko

That is correct.

Except I dislike the sound of "weigh the same 100 pounds". There weights are measured in vastly different conditions, and that should always be made explicit.

20. Dec 25, 2013

### TumblingDice

Ah, but therein lies the rub, I think. The 100lb is harder to *lift* (i.e., accelerate upwards), but easier to accelerate downwards. And I think it's our experience lifting and overcoming friction that creates the misplaced intuition about difficulty in accelerating.

If gravity was twice as strong, it would require the same force to accelerate the same mass sideways, perpendicular to gravity (or elevator acceleration), just as you said.

Edit: Merry Christmas!

21. Dec 25, 2013

### inertiaforce

I agree. I thought I had mentioned that they were in vastly different conditions. 1g as opposed to 2g.

This means that a tennis ball always accelerates like a tennis ball regardless of the strength of the gravity field it is in. This means that a tennis ball always accelerates like a tennis ball regardless of its weight. This is absolutely amazing. We as humans don't have every day experience with changing gravity fields. If we did, this would be common sense knowledge.

22. Dec 25, 2013

### inertiaforce

Good point. I had not considered this.

23. Dec 25, 2013

### inertiaforce

Wouldn't that mean it weighs more though? If something is harder to lift and accelerate upward, that means its weighs more doesn't it?

24. Dec 25, 2013

### TumblingDice

Yes, but weight is the effect of gravity on mass. So force applied to lift/accelerate upwards must work opposed to gravity, hence more force required than for same acceleration sideways (working only on mass).

Hope I'm on the right track. Feels a lot better than earlier.

25. Dec 25, 2013

### voko

Except in the vertical direction. In the vertical direction, the force applied to the ball is added to or subtracted from the weight, and it is this effective force that then acts on the mass and produces acceleration. This does in fact mean that it is more difficult to accelerate (or decelerate) a body vertically in a stronger field of gravity, so you could say that bodies with more weight are harder to accelerate vertically.

Then, we live in a world ruled by friction. Friction is proportional to the weight, so unless you find a way how to reduce friction (say, by adding wheels to the body), it will also be harder to accelerate horizontally.

Yet, fundamentally, it is the mass that characterizes the inertia of the body, not its weight. The effects I just mentioned where weight seemingly has to do with inertia are due to an interaction with something else.