Why is Mass Special? Understanding Force, Momentum, Energy, Work & Power

[CaptainADHD]

I'm trying to better understand these concepts:

Force
Momentum
Energy
Work
Power

One major thing I noticed was that every single one of those quantities is directly proportional to mass. Length and time have various positive and negative exponents, but mass never, ever gets touched.

Why don't we play with the dimensions of mass the way we play with the dimensions of everything else?

 

[Chi Meson]

First of all, it is a little misleading to say that force is proportional to mass. The force of gravity (weight) is proportional to mass, that is true, but that is due to the fact the acceleration due to gravity (in free fall) is the same for everything.

Other forces can be applied to a mass that can be of any quantity at all. Newton's 2nd law specifically says that the acceleration is directly proportional to net force and inversely proportional to mass.

Mass is not a vector quantity, so there is no inherent direction to a mass, and therefore no "opposite" direction. Furthermore, mass is defined as the total quantity of matter in an object. Once the amount of matter goes to zero, it doesn't get less. Even "anti-matter" has positive mass.

 

[CaptainADHD]

First of all, it is a little misleading to say that force is proportional to mass. The force of gravity (weight) is proportional to mass, that is true, but that is due to the fact the acceleration due to gravity (in free fall) is the same for everything.

Before I go off the deep end here, let me say that I only have exposure to classical mechanics, so if I say something ridiculous, just respond that it gets explained at some higher level and I'll shut up:

...But force is proportional to mass and to the acceleration. 10 times larger mass with unchanged acceleration produces/yields/implies 10 times more force. Is mass not just some measure of the magnitude of inertia?

Or is this a better definition: force is the cause of acceleration, and what that acceleration is going to look like depends on the mass that force is acting upon... ? (chicken makes eggs, eggs don't make chickens)

Maybe I'm looking at this wrong...

 

[Hootenanny]

Length and time have various positive and negative exponents, but mass never, ever gets touched.

There are many examples of physical quantities that are always non-negative, for example:

1. Speed
2. Kinetic Energy
3. Frequency
4. Wavelength
5. Distance
6. Absolute Temperature
7. ...

mass isn't special in this respect. However, you are quite right that mass is an interesting concept. For example, we still have no explanation for why the inertial mass (the mass is Newton's second law) should be equal to the gravitational mass of an object.

Why don't we play with the dimensions of mass the way we play with the dimensions of everything else?

What do you mean, "play with the dimensions"?

 

[Chi Meson]

Or is this a better definition: force is the cause of acceleration, and what that acceleration is going to look like depends on the mass that force is acting upon... ? (chicken makes eggs, eggs don't make chickens)
/QUOTE]

Exactly. This is the much better way of looking at it. In fact this is the only way to look at it. You have just paraphrased Newton's 2nd law. Net forces produce accelerations. The mass of the object is indeed also the amount of inertia in the object and therefore a greater mass resists acceleration more.

 

[CaptainADHD]

Or is this a better definition: force is the cause of acceleration, and what that acceleration is going to look like depends on the mass that force is acting upon... ? (chicken makes eggs, eggs don't make chickens)
/QUOTE]

Exactly. This is the much better way of looking at it. In fact this is the only way to look at it. You have just paraphrased Newton's 2nd law. Net forces produce accelerations. The mass of the object is indeed also the amount of inertia in the object and therefore a greater mass resists acceleration more.

I think this sometimes confuses new people like me, since a great deal of questions ask us to solve an equation backwards for force.

Thank you for the clarification ^^. This helps a great deal.

 

[CaptainADHD]

A 3.00-kg object undergoes an acceleration given by
a = (2.00ˆi + 5.00ˆj)m
s2. Find the
resultant force acting on it and the magnitude of the resultant force.

That's what I mean ><. The very first question given in a chapter introducing students to force implies that acceleration results in force. That's just disgusting. I won't name any names, but it rhymes with Bhomson Crookes/Bole. No wonder physics is so hard.

 

[Nissen, Søren Rune]

A 3.00-kg object undergoes an acceleration given by
a = (2.00ˆi + 5.00ˆj)m
s2. Find the
resultant force acting on it and the magnitude of the resultant force.

That's what I mean ><. The very first question given in a chapter introducing students to force implies that acceleration results in force. That's just disgusting. I won't name any names, but it rhymes with Bhomson Crookes/Bole. No wonder physics is so hard.

The second law is clasically written F=m*a, despite the fact that it really should be F/m=a but that's physics for you.