Mass vs. Weight
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)
In other words, 1 lbf (pound-force) acting on 1 slug of mass will give the mass an acceleration of 1 ft/s 2.
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
Kg to lb Converter
Related Topics
• Basics
Basic engineering data. SI-system, unit converters, physical constants, drawing scales and more.
• Fluid Mechanics
The study of fluids - liquids and gases. Involving velocity, pressure, density and temperature as functions of space and time.
• Mechanics
The relationships between forces, acceleration, displacement, vectors, motion, momentum, energy of objects and more.
• Statics
Forces acting on bodies at rest under equilibrium conditions - loads, forces and torque, beams and columns.
Related Documents
Acceleration
Change in velocity vs. time used.
Acceleration of Gravity and Newton's Second Law
Acceleration of gravity and Newton's Second Law - SI and Imperial units.
Acceleration Units Converter
Converting between units of acceleration.
Acetone - Density and Specific Weight
Online calculator, figures and tables showing density and specific weight of acetone at temperatures ranging from -95 to 275 °C (-138 to 530 °F) at atmospheric and higher pressure - Imperial and SI Units.
Air - Drying Force
The drying force of air depends on the air moisture holding capacity and the water surface to air evaporation capacity.
Ammonia Gas - Density vs. Temperature and Pressure
Online calculator with figures and tables showing density and specific weight of ammonia for temperatures ranging -50 to 425 °C (-50 to 800 °F) at atmospheric and higher pressure - Imperial and SI Units.
Apothecaries' Weight System
Apothecaries' fluid and weight system with ounces, drachms, grains, scruples and more.
Argon - Density and Specific Weight
Online calculator, figures and tables showing density and specific weight of argon, Ar, at varying temperature and pressure - Imperial and SI Units.
Benzene - Density and Specific Weight vs. Temperature and Pressure
Online calculator, figures and table showing density and specific weight of benzene, C6H6, at temperatures ranging from 5 to 325 °C (42 to 620 °F) at atmospheric and higher pressure - Imperial and SI Units.
Beryllium - Specific Heat vs. Temperatures
Specific heat of beryllium related to temperature.
Bodies Moving on Inclined Planes - Acting Forces
Required forces to move bodies up inclined planes.
Bollard Forces
Friction, load and effort forces acting in ropes turned around bollards.
Butane - Density and Specific Weight vs. Temperature and Pressure
Online calculators, figures and tables showing density and specific weight of liquid and gaseous butane, C4H10, at varying temperarure and pressure, SI and Imperial units.
Center Mass
Calculate position of center mass.
Center of Gravity
A body and the center of gravity.
Density vs. Specific Weight and Specific Gravity
An introduction to density, specific weight and specific gravity.
Ethane - Density and Specific Weight vs. Temperature and Pressure
Online calculator, figures and tables showing density and specific weight of ethane, C2H6, at varying temperature and pressure - Imperial and SI Units.
Ethylene - Density and Specific Weight vs. Temperature and Pressure
Online calculator, figures and tables showing density and specific weight of ethylene, C2H4, at varying temperature and pressure - Imperial and SI Units.
Floors - Live Loads
Floors and minimum uniformly distributed live loads.
Force
Newton's third law - force vs. mass and acceleration.
Forces acting on Body Moving on a Horizontal Plane
The forces acting on bodies moved in horizontal planes.
Gallons vs. Pounds of Water Converter
- and vice versa.
Gases - Densities
Densities and molecular weights of common gases like acetylene, air, methane, nitrogen, oxygen and others.
Gears
Gears effort force vs. load force.
Helium - Density and Specific Weight vs. Temperature and Pressure
Online calculator, figures and tables showing density and specific weight of helium, He, at varying temperature and pressure - Imperial and SI Units.
Hot Air Balloons - Calculate the Lifting Force
Calculate hot air ballon lifting force.
Human Body Composition
Composition of the human body.
Levers
Use levers to magnify forces.
Lifting Wheels
Loads and effort force with lifting wheels.
Liquids - Densities
Densities of common liquids like acetone, beer, oil, water and more.
Mass Moment of Inertia
The Mass Moment of Inertia vs. mass of object, it's shape and relative point of rotation - the Radius of Gyration.
Methane - Density and Specific Weight vs. Temperature and Pressure
Online calculator, figures and tables showing density and specific weight of methane, CH4, at temperatures ranging from -160 to 725 °C (-260 to 1300 °F) at atmospheric and higher pressure - Imperial and SI Units.
Methanol - Density and Specific Weight vs. Temperature and Pressure
Online calculator, figures and tables showing density and specific weight of methanol,CH3OH, at varying temperature and pressure - Imperial and SI Units.
Nitrogen - Density and Specific Weight vs. Temperature and Pressure
Online calculator, figures and tables showing density and specific weight of nitrogen, N2, at temperatures ranging from -175 to 1325 °C (-280 to 2400 °F) at atmospheric and higher pressure - Imperial and SI Units.
Ounces and Pounds vs. Grams
Converting ounces (ozs.) and pounds (lbs.) to grams (g).
Oxygen - Density and Specific Weight vs. Temperature and Pressure
Online calculator, figures and tables showing density and specific weight of oxygen, O2, at varying temperature and pressure - Imperial and SI Units.
Propane - Density and Specific Weight vs. Temperature and Pressure
Online calculator, figures and tables showing density and specific weight of propane, C3H8, at temperatures ranging from -187 to 725 °C (-305 to 1300 °F) at atmospheric and higher pressure - Imperial and SI Units.
Pulleys
Pulleys, blocks and tackles.
SI System
An introduction to the SI metric system.
Solids - Densities
Densities of selected solids.
Support Reactions - Equilibrium
Static equilibrium is achieved when the resultant force and resultant moment equals to zero.
Threaded Rods - Proof Loads - Metric Units
Proof load capacities of metric threaded steel rods.
Toluene - Density and Specific Weight vs. Teemperature and Pressure
Density and specific weight of liquid toluene.
Troy Weight
Weight unit for preciuos metals like gold and silver.
Universal Gravitational Law
Gravitational attraction between two objects vs. mass of the objects and the distance between them.
Water - Density, Specific Weight and Thermal Expansion Coefficients
Definitions, online calculator and figures and tables with water properties like density, specific weight and thermal expansion coefficient of liquid water at temperatures ranging 0 to 360°C (32 to 680°F).