# What is mass (not weight)

I just read this Wikipedia article on what is mass and according to it mass is "the measure of an object's resistance to acceleration". However, that doesn't make sense, for example here on Earth there is some resistance but that's due to air friction but in space there shouldn't be any resistance. So the way I see it, in space, if you apply even a minimal amount of force you are going to make an object move.

Also, doesn't it make more sense for mass to be just the number of elementary particles like protons, neutrons and electrons?

UPDATE: I just read this Wikipedia article on the definition of kilogram. If you look at the first paragraph out of the "Definition" section then you'll see that it is defined as 1 dm3 of water at 4 degrees of Celsius, so that implies that mass is just the number water molecules!?

• In terms of that comment in the article, it is saying that mass requires a greater applied force in order to accelerate it, and thus mass can be thought of as an objects "resistance to acceleration" Picture a large boulder with a lot of mass. you will have a harder time accelerating this than a pebble you can pick up and throw. – bleuofblue Nov 2 '16 at 19:30
• As far as I know you need the same energy/force applied to move an object in space no matter it's size. – Petar Vasilev Nov 2 '16 at 19:32
• @PetarVasilev that is a misconception. Out in space, given the same amount of energy a less massive object will travel faster than a more massive one. $Kinetic\ Energy\ =\ \frac{1}{2}mv^2$ so $v\ =\ \sqrt{\frac{2KE}{m}}$ – pentane Nov 2 '16 at 19:40
• Mass connotes weight but weight is a function of pressure wheras mass of an object is completely independent to what the air is doing. In other words my (and your) mass is the same on earth as in the vacuum of space...whereas what you "weigh" varies with what forces are acting upon you and "what" constitutes you. (we are overwhelmingly made of water...surprisingly massive actually.) – Doctor Zhivago Nov 2 '16 at 19:45
• @pentane If you look at this video youtube.com/watch?v=KDp1tiUsZw8 regarding the moon landing you'll see that the objects fall at the same time no matter their size or weight. – Petar Vasilev Nov 2 '16 at 19:46

So the way I see it, in space, if you apply even a minimal amount of force you are going to make an object move.

No, you need to overcome it's inertia first. If you attempt to push a satellite 100 times as massive as you in space, the force in your arms would cause you to move backwards, the satellite would not respond by very much.

Also, doesn't it make more sense for mass to be just the number of elementary particles like protons, neutrons and electrons?

It's not as straightforward as that, unfortunately. If you are prepared to accept protons and neutrons as basic elementary particles, then yes. But technically, (or pedantically, sorry) the mass of a proton is also composed of massive force-carrying particles and nonvalence quarks, so depending on what level of detail you want to go to, the answer can be more subtle than it first appears.

I just read this Wikipedia article on what is mass and according to it mass is "the measure of an object's resistance to acceleration".

Defining mass is tricky, there is inertial mass, which is what Wikipedia is describing above, and there is gravitational mass, which emerges from a different math equation than inertial mass. Luckily for us they are equivalent in everyday life, although we don't yet understand why this should be the case.

• So there is no definition of mass, that seems crazy for something so fundamental. – Petar Vasilev Nov 2 '16 at 19:47
• Also, regarding your first sentence that doesn't seem to be the case in one of the moon landing videos (youtube.com/watch?v=KDp1tiUsZw8) which proves that two objects with different weight and size are going to move the same distance given that the same force is applied, which in this case was the gravity of the moon. – Petar Vasilev Nov 2 '16 at 19:52
• They might have altered the course of the moon, why not? – Petar Vasilev Nov 2 '16 at 20:00
• We have laser reflectors on the moon, which allow us to measure it's distance since the Apollo missions, we know it has not moved beyond what we expected, and the landing of the Apollo missions has not changed that. – user108787 Nov 2 '16 at 20:04
• can you send me a link where that's discussed in more detail? – Petar Vasilev Nov 2 '16 at 20:05

here on Earth there is some resistance but that's due to air friction but in space there shouldn't be any resistance.

True, here on Earth there is air resistance. But just because air resistance exists, does that mean that no other form of resistance can also exist?

So the way I see it, in space, if you apply even a minimal amount of force you are going to make an object move.

True! Even the slightest force will make stuff move in space. But not equally much!

Read the statement that mass is "the measure of an object's resistance to acceleration" again. This statement doesn't prevent motion in space - it is only about how fast such motion speeds up (or down).

In other words, mass is not a measure of an object's resistance against motion; it is a measure of it's resistance against speeding up that motion! (Or speeding down.) In other words, acceleration.

• Example: If you in outerspace push on one book and then on two books (double mass), then the two books only gain half the speed as the single book - because their double mass resists the speeding up (the acceleration), which your force causes, double as much.

If you did the same thing on Earth, the same resistance will be seen because of mass PLUS the air resistance (and gravity and any other force that works on the books at that time).

• How would then explain the results from the moon landing where the feather and the hammer fall at the same time? – Petar Vasilev Nov 3 '16 at 7:23
• @PeterVasilev Good question. The explanation is that the forces that pull them down are different. Their weights are different. – Steeven Nov 3 '16 at 7:59
• The gravity force is not different, in fact it's alway the same. – Petar Vasilev Nov 3 '16 at 9:17
• @PeterVasilev No, the acceleration caused by gravity is always the same. Not the force of gravity. The force of gravity is called weight - and two objects can surely weigh differently. – Steeven Nov 3 '16 at 9:23
• @PeterVasilev The peculiar thing here is, that the weight differs from object to object exactly enough to make the acceleration always be constant. That's why you see two objects speed up equally on the Moon. When an object has double the mass (so that it resists acceleration double as much), the gravitational force (its weight) is also double as large, so that it still falls with the same acceleration as a lighter object. – Steeven Nov 3 '16 at 9:25

So the way I see it, in space, if you apply even a minimal amount of force you are going to make an object move.

Yep; that’s right!

All it takes is a tiny nudge to get a car moving in space. After all, $F_{nudge} = m a$; therefore $a = \frac{F_{nudge}}{m}$. That means even a tiny nudge on a massive object will move it (but not a lot).

Well, why can't you do this on Earth?

How much force would you need to budge a car on Earth? Let's neglect air resistance, and focus on just friction.

You may know that $F_{friction} = \mu F_{weight}$, where $F_{friction} \le F_{nudge}$.

This is a statistical law that tells us how the friction force corresponds to the weight (and therefore mass, see following) of an object.

$F_{friction} = \mu F_{weight} = \mu g m$

To get the car moving, we need a nudge greater than friction.

$F_{nudge} > F_{friction}$

$F_{nudge} > \mu m g$

OK, now let's get some concrete numbers.

• Our car weighs ($m$) $1000 [kg]^*$.
• The friction coefficient ($\mu$) between rubber and asphalt is $0.1^*$.
• The gravitational acceleration on Earth ($g$) is $10 [\frac{m}{s^2}]^*$.

Plug the numbers in: $F_{nudge} > 0.1 \times 1000 \times 10$, or

$F_{nudge} > 1000 [N]$

$^*$ Note that I underestimated the car weight drastically, and overestimated the other parameters slightly; so, in reality it would be much greater.

Now, what's $1000 [N]$? That's about holding up a box of $1000$ apples. That's not so easy, right?

Also, doesn't it make more sense for mass to be just the number of elementary particles like protons, neutrons and electrons?

No.

1. For one thing, protons, neutrons, and electrons have different masses (protons and neutrons are almost equal).

• proton: $1.6727 \times 10^{27} [kg]$
• neutron: $1.6750 \times 10^{27} [kg]$
• electron: $9.110 \times 10^{31} [kg]$

1.1. In addition, how would you like to like to say $1.6727e10^{27}$ [protons masses] instead of $1 [kg]$?

2. Also, the kilogram has been around since 1795 (and other units of mass have been used long before then), but the first elementary particle to be discovered (the electron) was in 1897.

So the way I see it, in space, if you apply even a minimal amount of force you are going to make an object move.

To be sure, even a minimal amount of net force on an object will produce an acceleration; the motion of the object will change.

Put simply, mass (inertial mass) is the measure of an object's inertia. That is to say, the more mass (inertia) an object has, the more net force is required to produce the same acceleration as an object with less mass (inertia).

More precisely, if one object is twice as massive as another object and both objects have the same acceleration, you know that there is twice as much net force on the more massive object.