Molar mass serves as a bridge between the mass of a material and the number of moles since it is not possible to measure the number of moles directly. Key Terms molar mass: The mass of a given substance (chemical element or chemical compound in g) divided by its amount of substance (mol).
- Medical Definition of mass 1: the property of a body that is a measure of its inertia, that is commonly taken as a measure of the amount of material it contains, that causes it to have weight in a gravitational field, and that along with length and time constitutes one of the fundamental quantities on which all physical measurements are based.
- An object has mass (say 100 kg). This makes it heavy enough to show a weight of '100 kg'.
- Mass fraction can also be expressed, with a denominator of 100, as percentage by mass (in commercial contexts often called percentage by weight, abbreviated wt%; see mass versus weight). It is one way of expressing the composition of a mixture in a dimensionless size; mole fraction (percentage by moles, mol%) and volume fraction ( percentage.
Mass vs. weight - the Gravity Force
Mass and Weight are two often misused and misunderstood terms in mechanics and fluid mechanics.
The fundamental relation between mass and weight is defined by Newton's Second Law. Newton's Second Law can be expressed as
F = m a (1)
where
F = force (N, lbf)
m = mass (kg, slugs)
a = acceleration (m/s2, ft/s2)
Mass
Mass is a measure of the amount of material in an object, being directly related to the number and type of atoms present in the object. Mass does not change with a body's position, movement or alteration of its shape, unless material is added or removed.
- an object with mass 1 kg on earth would have the same mass of 1 kg on the moon
Mass is a fundamental property of an object, a numerical measure of its inertia and a fundamental measure of the amount of matter in the object.
- mass electron 9.1095 10-31 kg
- mass proton 1.67265 10-27 kg
- mass neutron 1.67495 10-27 kg
Weight
Weight is the gravitational force acting on a body mass. The generic expression of Newton's Second Law(1) can be transformed to express weight as a force by replacing the acceleration - a - with the acceleration of gravity - g - as
Fg = m ag (2)
where
Fg = gravitational force - or weight (N, lbf)
m = mass (kg, slugs (lbm))
ag = acceleration of gravity on earth (9.81 m/s2, 32.17405 ft/s2)
Example - The Weight of a Body on Earth vs. Moon
The acceleration of gravity on the moon is approximately 1/6 of the acceleration of gravity on the earth. The weight of a body with mass 1 kg on the earth can be calculated as
Fg_earth = (1 kg) (9.81 m/s2)
= 9.81 N
The weight of the same body on the moon can be calculated as
Fg_moon = (1 kg) ((9.81 m/s2) / 6)
= 1.64 N
The handling of mass and weight depends on the systems of units used. The most common unit systems are
- the International System - SI
- the British Gravitational System - BG
- the English Engineering System - EE
One newton is
- ≈ the weight of one hundred grams - 101.972 gf (gF) or 0.101972 kgf (kgF or kilopond - kp (pondus is latin for weight))
- ≈ halfway between one-fifth and one-fourth of a pound - 0.224809 lb or 3.59694 oz
The International System - SI
In the SI system the mass unit is the kg and since the weight is a force - the weight unit is the Newton (N). Equation (2) for a body with 1 kg mass can be expressed as:
Fg = (1 kg) (9.807 m/s2)
= 9.807 (N)
where
9.807 m/s2 = standard gravity close to earth in the SI system
As a result:
- a 9.807 N force acting on a body with 1 kg mass will give the body an acceleration of 9.807 m/s2
- a body with mass of 1 kg weights 9.807 N
- More about the SI System - A tutorial introduction to the SI-system.
The Imperial British Gravitational System - BG
The British Gravitational System (Imperial System) of units is used by engineers in the English-speaking world with the same relation to the foot - pound - second system as the meter - kilogram - force second system (SI) has to the meter - kilogram - second system. For engineers who deals with forces, instead of masses, it's convenient to use a system that has as its base units length, time, and force, instead of length, time and mass.
The three base units in the Imperial system are foot, second and pound-force.
In the BG system the mass unit is the slug and is defined from the Newton's Second Law (1). The unit of mass, the slug, is derived from the pound-force by defining it as the mass that will accelerate with 1 foot per second per second when a 1 pound-force acts upon it:
1 lbf = (1 slug) (1 ft/s2)
Mass Number Is Determined By
In other words, 1 lbf (pound-force) acting on 1 slug of mass will give the mass an acceleration of 1 ft/s2.
The weight (force) of the mass can be calculated from equation (2) in BG units as
Fg (lbf) = m (slugs) ag (ft/s2)
With standard gravity - ag = 32.17405 ft/s2 - the weight (force) of 1 slug mass can be calculated as
Fg = (1 slug) (32.17405 ft/s2)
= 32.17405 lbf
The English Engineering System - EE
In the English Engineering system of units the primary dimensions are are force, mass, length, time and temperature. The units for force and mass are defined independently
- the basic unit of mass is pound-mass (lbm)
- the unit of force is the pound (lb) alternatively pound-force (lbf).
In the EE system 1 lbf of force will give a mass of 1 lbm a standard acceleration of 32.17405 ft/s2.
Since the EE system operates with these units of force and mass, the Newton's Second Law can be modified to
F = m a / gc (3)
where
gc = a proportionality constant
or transformed to weight (force)
Fg = m ag / gc (4)
The proportionality constant gc makes it possible to define suitable units for force and mass. We can transform (4) to
1 lbf = (1 lbm) (32.174 ft/s2) / gc
or
gc = (1 lbm) (32.174 ft/s2) / (1 lbf)
Since 1 lbf gives a mass of 1 lbm an acceleration of 32.17405 ft/s2 and a mass of 1 slug an acceleration of 1 ft/s2, then
1 slug = 32.17405 lbm
Example - Weight versus Mass
The mass of a car is 1644 kg. The weight can be calculated:
Fg = (1644 kg) (9.807 m/s2)
= 16122.7 N
= 16.1 kN
- there is a force (weight) of 16.1 kN between the car and the earth.
- 1 kg gravitation force = 9.81 N = 2.20462 lbf
Weight Converter
weight
(kgf)
(N)
(lbf)
Kg to lb Converter
Related Topics
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- Statics - Loads - force and torque, beams and columns
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Q: Aren't 'weight' and 'mass' the same?
A: Not really.
An object has mass (say 100 kg). This makes it heavy enough to show a weight of '100 kg'. |
But the scales are only showing a guess of the mass above them!
Gravity causes Weight
An object's weight is how hard gravity is pulling on it.
We think the weight is the same everywhere ... because we all live on the surface of the planet Earth!
But in orbit it would not push on the scales at all.
The scales would show 0 ...
... but the mass is still 100 kg !
An object's mass doesn't change (unless you remove some!), but its weight can change.
On the Moon the scales would wrongly show 16.6
for a mass of 100 kg
Because the pull of gravity on the Moon
is much less than on Earth
So Why Do People Say Weight instead of Mass?
People often use 'weight' to mean 'mass', and vice versa, because Gravity is almost the same everywhere on Earth and we don't notice a difference.
Mass Number Is The Number Of Protons
But remember .. they do not mean the same thing,
and they can have different measurements.
Weight is a Force
So ... if weight and mass are different, why are they both in kilograms?
Well, weight should not really be in kilograms!
Mass Number Isotope
I have used 'kilogram' so far because that is what you see on a pair of scales, but it is technically wrong to talk about weight in kilograms ...
... weight is a force ...
... which is measured in Newtons
Newtons
The correct unit for force is the Newton (=1 kg·m/s2) which is abbreviated N.
| On the Earth's surface gravity makes a 1 kilogram mass exert about 9.8 Newtons of force |
So a 100 kg mass really weighs about 980 Newtons on Earth.
Why Do Scales Show Kilograms?
Scales show Kilograms because that is what people understand best ...
... but it is really just an estimate of the mass above them.
Scales should really show Newtons, but that might confuse people!
Question: how many Newtons should the scales show when you stand on them (hint: multiply kg by 9.8)?
- So the scales show an estimate of your mass based on the force your body exerts on it.
- And to find out how much force your body is exerting on the scales, multiply by 9.8 (to convert kg into Newtons).
Apparent Weight
But scales can be fooled ... because they measure a 'downwards force' and don't know if it is gravity or some other force!
Just jump up and down (gently!) on your scales at home to see your apparent weight change, while your mass stays the same.
So your mass is the same, and your weight is the same (because the force of gravity hasn't changed), but your 'apparent' weight changes. Read more at Apparent Weight
Conclusion
- Mass is a measure of how much matter something contains
- Weight is a measure of how strongly gravity pulls
- Apparent Weight is a measure of downwards force
- Force is measured in Newtons, not kilograms
- When scales show 'kg' it is just an estimate of the mass above them