Mass and Weight
Weight and mass - the difference
Mass and weight are two common often misused and misunderstood terms in mechanics and fluid mechanics.
The fundamental relation between the mass and the weight is defined by Newton's Second Law and can be
expressed as
F=ma
(1)
where
F = force (N)
m = mass (kg)
a = acceleration (m/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.
The 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.
Weight
Weight is the gravitational force acting on a body mass. Transforming Newton's Second Law related to the weight
as a force due to gravity can be expressed as
W=mg
(2)
where
W = weight (N)
m = mass (kg)
g = acceleration of gravity (m/s2)
The handling of mass and weight depends on the systems of units that is used. The most common systems of units
are the
International System - SI
British Gravitational System - BG
English Engineering System - EE
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:
w = (1 kg) (9.807 m/s2)
= 9.807 (N) (2b)
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 weighs 9.807 N
More about the SI System - A tutorial introduction to the SI-system.
The 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 the foot, the second, and the 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 at 1 foot per second per
second when a 1 pound-force acts upon it:
1 lb = (1 slug)(1 ft/s2)
In other words, 1 lb (pound) force acting on 1 slug mass will give the mass an acceleration of 1 ft/s2.
The weight of the mass from equation (2) in BG units can be expressed as:
w (lb) = m (slugs) g (ft/s2)
With a standard gravity - g = 32.17405 ft/s2 - the mass of 1 slug weights 32.17405 lbf (pound-force).
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 lb 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
w = m g / 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
A car's mass is 1,644 kg. The weight can be calculated:
w = (1,644 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
What is the difference between mass and weight?
Answer:
Mass is the size of an object and weight is the amount of force gravity has on an object.
Mass is an intrinsic property of a body, as it remains the same everywhere in the universe.
Weight is variable due to change in the magnitude of the gravitational force applied by the earth.
Mass is scalar and has no direction dependency
Weight is vector and is directed towards the center of the earth
--Mass is constant all the time. It is measured in kilograms (kg). Weight is mass X gravity, so on Earth 1 gram equals
10 Newtons (the measure of Weight). Weight depends on gravity. When you are 'weighing' yourself, you are really
massing yourself - who gives their weight in Newtons? So both mass and weight will typically use kilograms.
Read more: http://wiki.answers.com/Q/What_is_the_difference_between_mass_and_weight#ixzz29ZRePLqy
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