# Difference between weight and mass?

1. Dec 30, 2012

### Xetman

Okay so I was going through my calculus textbook and I am stumbled on the WORK section.
Here it says work=force*distance, and force=mass*acceleration.
In a problem they use gravity for acceleration which I guess you can do.
So they have:

F=mass*gravity

So to calculate the WORK they use that Force and multiply it by the distance.
The mass they have was in kilograms.

Then, in a similar problem they have weight which is in pounds. They say F=the pounds, because weight is a force and not the mass of the object. Then they just multiply the pounds by the distance to get the WORK. So they don't multiply the pounds by gravity.

So my question is: how do you tell the difference between mass and weight by looking at the units? Up until now, I always thought weight=mass. That's the reason why I thought we can change the units of pounds into kilograms. If kilograms=mass and pounds=weight (where weight is a force and mass is matter in an object), why can we change the units by multiplying/dividing either kilograms/pounds by some constant (I don't know the constant but I know that it can easily be found by using Google :D)? Also, why is weight a force and mass just mass?

Note: I have not taken physics yet; I am taking chemistry in school. So I knew that F=mass*acceleration from middle school, but I am not thoroughly well known that work=force*distance so that stuff is pretty new to me. So please try to explain this stuff as simple as possible XD.

Thanks and have a great day!

Last edited: Dec 30, 2012
2. Dec 30, 2012

### Drakkith

Staff Emeritus
Mass is almost always in kilograms, while weight is in either pounds or newtons. (Since weight is the result of the force of gravity on an object) On Earth it is easy to convert pounds to kilograms, but the formula changes if you move someplace with different gravity, such as the Moon or Mars.

For example, your weight, W, is the result of the product of your mass times the gravitational acceleration. W=m*g. A block of 1 kg has a weight of 9.8 newtons, or about 2.2 lbs. W=1*9.8. (1 newton = about 0.225 lbs)

On the Moon the gravitational acceleration is about 1/6 that of earth, so W=1*1.622 (g on the Moon is 1.622 m/s2) A 1 kg block would weigh 1.622 newtons.

Mass is mass and weight is a force because that is how they are defined in physics.

See here: http://en.wikipedia.org/wiki/Weight

3. Dec 30, 2012

### Staff: Mentor

4. Dec 31, 2012

### TheAbsoluTurk

The newton (N) is the metric unit for force while the pound (lb) is the imperial unit for force.

The kilogram (kg) is the metric unit for mass while the slug is the imperial unit for mass.

5. Dec 31, 2012

### Drakkith

Staff Emeritus
Ah, the good ol' Slug...as weird and slimy as ever.

6. Jan 1, 2013

### D H

Staff Emeritus
Correction:
The newton (N) is the metric unit for force while the pound force (lbf) is the imperial unit for force.

The kilogram (kg) is the metric unit for mass while the pound (lb) is the imperial unit for mass.

Some engineers, in a vain attempt to avoid going metric, use the slug instead of pounds. The slug is a fairly recent invention, less than 100 years old.

7. Jan 1, 2013

### ModusPwnd

If you are going to deny the use of the slug because its only 100 years old you should at least call lb a pound-mass. Seems silly to deny a unit just because of its age though. Particularly when it means you have to make the word 'pound' ambiguous.

When I was in school and teaching/tutoring pound was always a force and never a mass. Slug is the mass. Making this distinction is key to helping beginning students understand the difference between mass and force and their metric counterparts.

8. Jan 1, 2013

### K^2

And that gives g = 1 of WHAT per second in imperial units?

9. Jan 1, 2013

### D H

Staff Emeritus
Huh?

Presumably you are using the mistaken notion that Newton's second law is $\vec F=m\vec a$. Newton expressed his second law as (translated from Latin) "The alteration of motion is ever proportional to the motive force impress'd." In modern parlance, $\vec F \propto m \vec a$. Expressing that proportionality as an equality, $\vec F = \frac 1 k m \vec a$, where $k$ is some constant of proportionality. That constant has a numerical value of 1 in the metric system. It has a numerical value of 32.174 when one uses a system when force, mass, distance, and time are expressed in units of pounds force, avoirdupois pounds, feet, and seconds.

When the metric system was first devised, defining the units of force, mass, and acceleration such that this proportionality constant had a numeric value of 1 was viewed as a trick to make the math easier. Even within the metric system, you'll still find some pockets that use the kilogram-force instead of the newton as the unit of force. It wasn't until later that this trick of using the newton as the unit of force was viewed as being something much more than just a trick.

It's not as if the metric system is the be-all and end-all of consistent units. It's just the start of a truly consistent set of units. The speed of light and Newton's universal gravitational constant would both be 1 in a consistent set of units. This isn't the case in the metric system.

10. Jan 1, 2013

### ModusPwnd

Thats why you should use slugs... To avoid having to convert units with a proportionality constant. Its best to use consistent units within an equation.

11. Jan 1, 2013

### K^2

That is, admittedly, internally consistent. But why?

12. Jan 1, 2013

### D H

Staff Emeritus
It's best to use the metric system if at all possible. The slug was a rather late invention (late 1920s) conjured solely to avoid "going metric".

The only reasons to use customary units are because you have to do so for some reason, and then you typically don't have any choice over whether to use pounds versus slugs for mass. The rationale might be because parts are machined using customary units, the contract mandates the use of customary units, you employer has decided to stick with customary units because the metric system is one world communism, etc.

It's not fun working with mixed units. Just try working on an international endeavor where the units are all mixed up. Component A will be fully metric, component B will be mostly metric but with force in kilogram-force, component C will have force in pounds-force, mass in pounds (mass), center of mass in inches, and moment of inertia in slug-feet2.

13. Jan 3, 2013

### Mr. Einstein

I see a lot of confusion on what mass is versus what weight is. So I had to ask myself, what is mass?

That prompted me to remember what I was taught in chemistry. A balance scale was used. A known quantity on matter is compared to an unknown quantity. And the ratio of these two quantities {or weights) is what is referred to as mass.

But mass is a dimensionless quantity. So in order to legally make the weight dimensionless, one has to define it. The equation "mass=weight/weight" or "mass=newtons/newtons" or "mass=pounds/pounds". In this manner you can see all the actual vector dimensions cancel out.

But I found an example where I don't think it is entirely legal to cancel out the dimensions of weight. The equation F=MA, when used on an inertial accelerating body parallel to the Earth's surface, can be expressed as Force=(Inertial weight/Gravitational weight)(Acceleration). The inertial weight varies with the applied force. While the gravitational weight will decrease due to the ever increasing centrifugal force.

So I see the two different weight vectors as behaving independently of each other. The weight vectors used this way do also suggest they are NOT equivalent to each other.

But these are just my thoughts on mass versus weight.

14. Jan 3, 2013

### ModusPwnd

Mass is not a dimensionless ratio of two quantities. Its a quantity that does have a dimension, the kg.

The reason you have two masses in a chemistry balance is to calibrate the scale.

15. Jan 3, 2013

### Mr. Einstein

ModusPwnd

I would definitely have to disagree with you. The kg is a dimensionless unit. And my description of the use of a scale was accurate.

16. Jan 3, 2013

### ModusPwnd

17. Jan 3, 2013

### Mr. Einstein

ModusPwnd

Don't you ever question what you are taught? You seen from the equation that mass is just a ratio between two weights. The weights which do have dimensions cancel out leaving just a number which is a ratio. Just like pi is a ratio between two lengths. By your reasoning are you willing to call pi a dimension?

18. Jan 3, 2013

### Staff: Mentor

19. Jan 3, 2013

### Staff: Mentor

Folks we are getting sidetracked here. The discussion is about mass vs weight not about whether mass as measured in whatever units of mass is dimensionless or not.

20. Jan 3, 2013

### Staff: Mentor

This part is where you go wrong. When you write m = 5.0 kg what you are saying is that the dimensionless ratio between the mass of the object and the mass of the international prototype kilogram is 5.0. I.e. m/kg = 5.0 (dimensionless). Because the kg is dimensionful (dimensions of mass) and because 5.0 is dimensionless, in order to make that equality work m must also be a dimensionful quantity (with dimensions of mass).